파이썬통계11_통계와데이터.ipynb

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      "name": "파이썬통계11-통계와데이터.ipynb",
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lNpvI1kpbJG4",
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      "source": [
        "# 통계\n",
        "```\n",
        "* 분석하고자 하는 집단과 관련해 조사나 실험의 결과로 얻는 자료 또는 이의 요약된 형태를 의미\n",
        "* 통계학 : 좀더 효과적인 의사결정을 할 수 있도록 수치자료를 수집,정리,표현,분석하는 학문\n",
        "* 통계는 항상 반례 가능성을 가지고 있음\n",
        "* 관련 통계 분야 : 사회과학통계, 자연과학통계, 수학학통계\n",
        "```"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TAU-KHypbl0P",
        "colab_type": "text"
      },
      "source": [
        "# 통계학의 유형\n",
        "\t1. 기술통계학 - 자료중심 통계\n",
        "\t                수집한 데이터를 요약, 묘사, 설명하는 통계기법 \n",
        "                   그래프,표,수치를 이용해서 집단의 특성 파악\n",
        "                   대표값, 분산\n",
        "\n",
        "\t2. 추론통계학 - 예측 중심 통계 (중요도높음)\n",
        "\t                수집된 데이터를 바탕으로 예측하는 통계기법\n",
        "                   관측된 자료를 이용해서 모집단 특성 추측\n",
        "\t\t1).모수통계 \n",
        "\t\t\t가.빈도분석\n",
        "\t\t\t나.상관분석\n",
        "\t\t\t다.세 집단이상 평균분석\n",
        "\t\t\t라.회귀분석(!!!)\n",
        "\t\t2).비모수통계\n",
        "\t\t\t가.적합도검증\n",
        "\t\t\t나.변수간 상관분석"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mUDj4yoG3L6A",
        "colab_type": "text"
      },
      "source": [
        "데이터를 이해하는 마음가짐\n",
        "* 데이터가 숲이라고 가정한다면\n",
        "\t+ 처음부터 숲의 나무를 보고 자세히 관찰한다기 보다는\n",
        "\t+ 개략적으로 숲의 모양을 보고 특징을 파악하고 나무를 관찰할 것!\n",
        "\t+ 데이터도 이런식의 접근방식을 사용해야 함\n",
        "\n",
        "* 데이터의 특징이란\n",
        "\t+ 말로 표현하기 보다는\n",
        "\t+ 숫자로 표현하여야 하고\n",
        "\t+ 주로 평균,편차 등등을 활용하는데\n",
        "\t+ 이렇게 숫자로 데이터의 특징을 표현하는 과정을 \"요약summary\" 이라함\n",
        "\n",
        "* 데이터 분석 순서\n",
        "\t+ 데이터를 처음 만나면\n",
        "\t+ 요약을 먼저하고 데이터의 특징을 파악해서\n",
        "\t+ 어떤 차이가 있는지 파악해서\n",
        " \t+ 데이터 분석방향을 설정할 것!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VypI-hx83F6C",
        "colab_type": "text"
      },
      "source": [
        "# 표본 추출방법\n",
        "표본조사 : 더조은 수강생 5000명 대상\n",
        "\t 사용중인 핸드폰 선호도 조사를 위해 25명 선정\n",
        "         모집단 : 수강생 5000명\n",
        "         표본 : 수강생 30명\n",
        "\n",
        "단순 랜덤 : Simple Random Sampling\n",
        "\t모집단 개체에 번호표 부여 후 30명 추출\n",
        "        추출틀 이용\n",
        "\n",
        "계통 추출 : 기본적으로 SRS와 유사\n",
        "          단, '개체수/표본수'로 계산되는 k값을 알아냄\n",
        "\t  1 ~ n의 숫자중 하나를 선택하고\n",
        "   \t  그 숫자에 k를 더해서 개체들을 선택\n",
        "\t  예) k : 3000 / 30 => 100\n",
        "          임의의 숫자 뽑음(1~3000): 25\n",
        "          25, 125, 225, 325,..., 2925\n",
        "\n",
        "층화 추출 : 모집단을 몇개의 계층(고유특성)으로 나누어 표본 추출\n",
        "          ex) 모집단 : 3000명 => 남/여 수 파악\n",
        "          각 계층별로 번호 부여 : 남=2100, 여=900\n",
        "          계층별 비율 계산 : 남여비율 = 7:3\n",
        "          따라서, 남자은 21명, 여자는 9명을 SRS으로 추출\n",
        "\n",
        "군집 추출 : 모집단을 몇개의 군집(가변특성)으로 나누어 표본 추출\n",
        "          ex)모집단을 학력수준/거주지역으로 나눔\n",
        "          각 군집별로 번호부여 (고졸,대졸,대학원졸/서울/경기/부산)_\n",
        "          임의의 그룹을 선택하고 번호표 부여후 비율별로 SRS 추출"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fLubcL_LcSox",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "nums = np.arange(1,10+1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oC_-Y4p7ldFp",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "fce1ba0c-43c1-4f59-8aae-cd2625205901"
      },
      "source": [
        "# 1~10사이 정수 중 3개를 복원추출\n",
        "np.random.choice(nums, 5, replace=True)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 1, 10,  7,  2,  2])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9u00_MAcl7f5",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "a6f84dd8-3a80-4162-9fd7-0c45964ac315"
      },
      "source": [
        "# 1~10사이 정수 중 5개를 비복원추출\n",
        "np.random.choice(nums, 5, replace=False)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 5,  3,  9, 10,  7])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zoLNbOtAmpFp",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "c9d5bd59-a764-4418-9fea-fec5c7ebe0bf"
      },
      "source": [
        "# 1~5사이 정수 중 1개를 복원추출로 표본을 선택하세요\n",
        "# 단, 각 표본의 확률은 [0.0 0.5 0.0 0.5 0.0]으로 설정함\n",
        "nums = [1,2,3,4,5]\n",
        "np.random.choice(nums, 1, replace=True,\tp=[0.0, 0.5, 0.0, 0.5, 0.0])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([4])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u1oTmnV4w1Lk",
        "colab_type": "text"
      },
      "source": [
        "# 자료의 종류\n",
        "\n",
        "* 질적자료 : 문자로 표현된 자료\n",
        "\t\t+ 명목자료 : 일반적인 범주형 데이터\n",
        "\t\t\tex) 남,여\n",
        "\t\t+ 순서자료 : 순서의 의미가 포함된 데이터\n",
        "\t\t\tex) 초등학교,중학교,고등학교,대학교\n",
        "\t\t+ 구간자료 : 양적자료를 구간별로 나누어 명목/순서의 의미를 포함시킨 데이터\n",
        "\t\t\tex) 수,우,미,양,가\n",
        "\t\t+ 비율자료 : 양적자료를 구간별로 나누어 서열/비율(산술)의 의미를 포함시킨 데이터\n",
        "\t\t\tex) 몸무게, 시간, 키 \n",
        "\n",
        "* 양적자료 : 숫자로 표현된 자료\n",
        "\t\t+ 이산형 : 셈이 가능한 양적자료, 정수형데이터\n",
        "\t\t+ 연속형 : 셈이 불가능한 양적자료, 실수형 데이터"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MZIAbsdJ2LzY",
        "colab_type": "text"
      },
      "source": [
        "# 통계분석시 중요 개념\n",
        "* 개체item     : 연구자 또는 관찰자가 관심을 가지는 대상\n",
        "\t\tex) 더조은 수강생\n",
        "\n",
        "* 요인factor   : 개체가 가지는 특성 중 연구자 또는 관찰자가\n",
        "\t\t특별히 관심을 갖는 특성  ex) 수강생 신체조건, 경력사항\n",
        "\n",
        "* 변수variable : 요인을 구성하고 있는 요소\n",
        "\t\tex) 키, 몸무게, 성별, 혈액형\n",
        "\t\tex) 학위, 직장명, 근무연수, 직무"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M6kVVfHZvfNf",
        "colab_type": "text"
      },
      "source": [
        "# 모집단과 표본\n",
        ">>\n",
        "  * **모집단** : 통계 목적에 부합하는 모든 자료들의 집단  \n",
        "      + $U$ 로 표현, 모집단의 크기는 $N$으로 표현\n",
        ">>\n",
        "  * **표본** : 모집단의 일부인 자료들의 집단\t  \n",
        "      + $S$ 로 표현, 표본의 크기는 $n$으로 표현"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EkytxESk4lxY",
        "colab_type": "text"
      },
      "source": [
        "# 중심화경향 - 수집한 자료 전체를 대표하는 값이 무엇인지 나타내는 통계 (대표값)\n",
        "      * 평균    \n",
        "      * 중앙값\n",
        "      * 최빈값      \n",
        "# 분산경향 - 데이터가 어떻게 분포되어 있는지 설명하는 통계치\n",
        "      * 범위\n",
        "      * 사분위수\n",
        "      * 분산\n",
        "      * 표준편차\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SaGJn4Lh7qzg",
        "colab_type": "text"
      },
      "source": [
        "# 대표값\n",
        "평균 : 중심 척도의 대표적인 통계값\n",
        "* 평균은 유일하다\n",
        "* 평균은 계산하기 쉽다\n",
        "* 모든 측정값을 반영한다\n",
        "* 단, 평균은 특이값(이상치)에 영향을 받는다\n",
        "\n",
        "모평균 : $ \\mu $, 모집단의 모든 값을 더한 후 모집단의 갯수로 나눈 수치\n",
        ">>\n",
        "$$ {\\mu} = \\dfrac{1}{N} \\sum_{i=1}^N x_i $$\n",
        "\n",
        "표본평균 : $ \\bar x$, 표본의 모든 값을 더한 후 표본의 갯수로 나눈 수치\n",
        ">>\n",
        "$$ {\\bar x} = \\dfrac{1}{n}\\sum_{i=1}^{n}x_i $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GDbfuWGT7qjj",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "outputId": "7a129193-9e49-4edc-8fb0-232fb18ab305"
      },
      "source": [
        "# 특이값(이상치)에 영향을 받는다\n",
        "nums1 = [1,2,3,4,5,6,7,8,9,10]\n",
        "nums2 = [1,2,3,4,5,6,7,8,9,100]\n",
        "\n",
        "print(sum(nums1) / len(nums1))\n",
        "print(np.mean(nums2))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "5.5\n",
            "14.5\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Bl-bzkfD-UP-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "0288fe02-96d6-40cf-d820-8c70500ad8ff"
      },
      "source": [
        "# 조선조 왕들의 평균수명을 조사\n",
        "kings = [73,62,45,53,38,16,51,28,37,30,56,30,33,56,\n",
        "         66,54,40,33,59,36,82,48,44,22,32,67,52]\n",
        "print(np.mean(kings).round(1))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "46.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GEPuytHwAf-x",
        "colab_type": "text"
      },
      "source": [
        "# 중앙값median\n",
        "* 자료를 오름차순으로 나열한 후 가장 가운데 놓인 수  \n",
        "* 특이값의 영향을 받는 평균을 보완한 수치  \n",
        "* 자료 갯수가 짝수인 경우와 홀수인 경우 계산하는 방법이 다름  \n",
        "\n",
        "$$ M_e $$\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jdtPiOrGDE9e",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "71d2c79f-731d-4fd7-eca6-e3b432af3e1d"
      },
      "source": [
        "# 조선조 왕들 수명의 중앙값을 조사\n",
        "# numpy의 median함수를 사용함\n",
        "kings = [73,62,45,53,38,16,51,28,37,30,56,30,33,56,66,54,40,33,59,36,82,48,44,22,32,67,52]\n",
        "\n",
        "kings = sorted(kings)         # 정렬하기\n",
        "pos = int((len(kings)+1) / 2) # 위치 계산\n",
        "print(kings[pos-1], np.median(kings))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "45 45.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8Q-65iKEsMkf",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 359
        },
        "outputId": "41149fac-67cc-4223-93fa-afa0e224d5b3"
      },
      "source": [
        "# 중앙값 계산\n",
        "scores = pd.DataFrame({'score':[42,69,56,41,57,48,65,49,65,58]})\n",
        "scores.index = np.arange(1,10+1)\n",
        "scores"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>score</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>42</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>69</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>56</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>41</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>57</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>48</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>65</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>49</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>65</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>58</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "    score\n",
              "1      42\n",
              "2      69\n",
              "3      56\n",
              "4      41\n",
              "5      57\n",
              "6      48\n",
              "7      65\n",
              "8      49\n",
              "9      65\n",
              "10     58"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Tva-AWPJs4Ru",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "21ba81f8-6e66-4bfc-d240-60a5a4db88e1"
      },
      "source": [
        "sorted_sc = np.sort(scores['score'])\n",
        "\n",
        "n = len(sorted_sc)\n",
        "\n",
        "med = 0\n",
        "if n % 2 != 0: # 홀수\n",
        "   med = sorted_sc[((n+1)//2)-1]\n",
        "else:          # 짝수\n",
        "   p1 = sorted_sc[(n//2)]\n",
        "   p2 = sorted_sc[(n//2)-1]\n",
        "   med = (p1 + p2) / 2\n",
        "\n",
        "print(sorted_sc, p1,p2,med)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[41 42 48 49 56 57 58 65 65 69] 57 56 56.5\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tGG6bXo5xEf6",
        "colab_type": "text"
      },
      "source": [
        "# 최빈값\n",
        "* 두번 이상 발생하는 자료 중에서 자주 나타나는 자료값\n",
        "* 극단값에 전혀 영향을 받지 않음\n",
        "* 존재하지 않거나 여러개 존재할 수 있음\n",
        "\n",
        "$$ M_O $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1w93qO0Gx9bh",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 107
        },
        "outputId": "78e462b9-2cfc-4414-966b-c09f35171c39"
      },
      "source": [
        "# 조선조 왕들 수명의 최빈값을 조사\n",
        "# pandas의 mode함수를 사용함\n",
        "\n",
        "print(sorted(kings))\n",
        "pd.Series(kings).mode()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[16, 22, 28, 30, 30, 32, 33, 33, 36, 37, 38, 40, 44, 45, 48, 51, 52, 53, 54, 56, 56, 59, 62, 66, 67, 73, 82]\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0    30\n",
              "1    33\n",
              "2    56\n",
              "dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "htFxLr5v3Poj",
        "colab_type": "text"
      },
      "source": [
        "# 기술통계의 또 다른 관점 : 분산, 산포\n",
        "* 자료의 흩어지거나 밀집되는 정도를 나타내는 척도\n",
        "* 범위, 사분위수, 분산, 표준편차등으로 표현"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z1K1Pag52lKF",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "fcbcb44c-351b-46e9-e85e-3f670efb316a"
      },
      "source": [
        "# 평균이 동일한 자료들의 분산\n",
        "A = [1,2,3,4,5,5,5,6,7,8,8,9,9,9,9]\n",
        "B = [4,5,5,5,6,6,6,6,6,6,6,7,7,7,8]\n",
        "\n",
        "print(np.mean(A), np.mean(B))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "6.0 6.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LTuuUUqC6Fyz",
        "colab_type": "text"
      },
      "source": [
        "# 범위\n",
        "* 수집한 자료의 가장 큰 값과 작은 값의 차이\n",
        "* 수집한 자료가 어느정도 흩어져 있는지 살펴볼 수 있는 통계치\n",
        "* 계산하기 쉽다\n",
        "* 특이값에 영향을 많이 받는다\n",
        "* 범위가 동일해도 분산정도는 크게 다를 수 있다\n",
        "\n",
        "$$ R = x_{(n)} - x_{(1)} $$\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "61Y785_x67Kr",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "943a9060-0d73-48fc-fce1-e4b7cf9833b0"
      },
      "source": [
        "# 다음 리스트의 범위를 구하세요\n",
        "nums = [3,4,6,7,7,9]\n",
        "\n",
        "max = np.max(nums)\n",
        "min = np.min(nums)\n",
        "max - min"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "6"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iiDAzqyO7ERX",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "da774877-7f1b-4cde-f60f-c891266efb28"
      },
      "source": [
        "# 조선조 왕들 수명의 범위를 조사\n",
        "max = np.max(kings)\n",
        "min = np.min(kings)\n",
        "max - min"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "66"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Hlx6DH1c8_84",
        "colab_type": "text"
      },
      "source": [
        "# 분산\n",
        "* 평균을 중심으로 밀집되거나 퍼짐 정도를 나타내는 척도\n",
        "* 모분산 $ \\sigma^2 $ : 모집단을 구성하는 모든 자료값과 모평균의 편차제곱에 대한 평균\n",
        "* 표본분산 $ s^2 $: 표본을 구성하는 모든 자료값과 표본평균의 편차의 제곱합을 n-1로 나눈 수치\n",
        "\n",
        "![분산설명이미지](https://drive.google.com/uc?id=1WRINjF2mqYuQF4zCW3FLmoERXIV0ZLIo)\n",
        "\n",
        "**편차 제곱**\n",
        "  * 각 관측값을 평균에서 뺀 값의 제곱\n",
        "  $$ (x_i - \\bar x)^2 $$ \n",
        "\n",
        "**모분산**  \n",
        "   $$ \\sigma^2 $$\n",
        "**표본분산** \n",
        "   $$ s^2 $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2SiGxcJH_V0y",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "f892029a-4aa8-46e0-bfa4-d73463b38097"
      },
      "source": [
        "# 데이터 A, B에 대한 편차제곱을 계산하세요\n",
        "# 데이터 A에 대한 편차제곱\n",
        "# [1,2,3,4,5,5,5,6,7,8,8,9,9,9,9]\n",
        "meanA = np.mean(A)\n",
        "deviA = A - meanA\n",
        "dsqrA = deviA ** 2\n",
        "print(meanA, deviA, dsqrA) "
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "6.0 [-5. -4. -3. -2. -1. -1. -1.  0.  1.  2.  2.  3.  3.  3.  3.] [25. 16.  9.  4.  1.  1.  1.  0.  1.  4.  4.  9.  9.  9.  9.]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yuLb_VE8AgtO",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "359c4bba-266a-47b7-f61d-88044247f6e3"
      },
      "source": [
        "# 데이터 B에 대한 편차제곱\n",
        "# [4,5,5,5,6,6,6,6,6,6,6,7,7,7,8]\n",
        "meanB = np.mean(B)\n",
        "deviB = B - meanB \n",
        "dsqrB = deviB ** 2\n",
        "print(meanB, deviB, dsqrB) "
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "6.0 [-2. -1. -1. -1.  0.  0.  0.  0.  0.  0.  0.  1.  1.  1.  2.] [4. 1. 1. 1. 0. 0. 0. 0. 0. 0. 0. 1. 1. 1. 4.]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1WfCrHP8BJGL",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "b6c63238-270d-43db-d73f-f54189dd30ea"
      },
      "source": [
        "# 데이터 A, B에 대한 표본분산을 계산하세요\n",
        "# 분산은 numpy의 var함수를 사용함\n",
        "# 단, 표본분산을 구할려면 var함수에 ddof옵션을 추가함\n",
        "varA1 = np.mean(dsqrA)  \n",
        "varB1 = np.mean(dsqrB)\n",
        "# 모분산 : 편차제곱합을 n으로 나눔\n",
        "\n",
        "varA2 = (np.sum(dsqrA)) / (len(dsqrA)-1)\n",
        "varB2 = (np.sum(dsqrB)) / (len(dsqrB)-1)\n",
        "# 표본분산 : 편차제곱합을 n-1로 나눔\n",
        "\n",
        "print(varA1, varB1, np.var(A), np.var(B))\n",
        "print(varA2, varB2, np.var(A, ddof=1), np.var(B, ddof=1))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "6.8 0.9333333333333333 6.8 0.9333333333333333\n",
            "7.285714285714286 1.0 7.285714285714286 1.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rK9VL_l0KQzP",
        "colab_type": "text"
      },
      "source": [
        "# 표준편차\n",
        "* 분산값에 제곱근을 취한 값\n",
        "* 분산은 편차를 제곱했기 때문에 결과값의 단위 역시 제곱이 됨\n",
        "* 분산의 단위를 원래 자료의 단위로 전환하기 위해 만든 값\n",
        "\n",
        "모표준편차 $$ \\sigma $$  \n",
        "표본표준편차 $$ s $$\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "P1WvENoUK4u3",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "fac3e521-b685-4105-88be-635643138e1c"
      },
      "source": [
        "# 데이터 A, B에 대한 모표준편차/표본표준편차를 계산하세요\n",
        "# 분산은 numpy의 std함수를 사용함\n",
        "# 단, 표본표준편차을 구할려면 var함수에 ddof옵션을 추가함\n",
        "stdA1 = np.sqrt(varA1)\n",
        "stdB1 = np.sqrt(varB1)\n",
        "\n",
        "stdA2 = np.sqrt(varA2)\n",
        "stdB2 = np.sqrt(varB2)\n",
        "\n",
        "print(stdA1.round(2), stdB1.round(2), np.std(A).round(2), np.std(B).round(2))\n",
        "print(stdA2.round(2), stdB2.round(2), np.std(A, ddof=1).round(2), np.std(B, ddof=1).round(2))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "2.61 0.97 2.61 0.97\n",
            "2.7 1.0 2.7 1.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6IW85OlOOSdP",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "5d760f2d-051f-43c1-9c2b-89f06eef483f"
      },
      "source": [
        "# 조선조 왕들의 수명은 1대~27대까지 모든 왕을 대상으로 했음\n",
        "print(np.mean(kings).round(2), \n",
        "      np.var(kings).round(2), np.std(kings).round(2))\n",
        "\n",
        "meanK = np.mean(kings)\n",
        "deviK = kings - meanK  \n",
        "dsqrK = deviK ** 2\n",
        "var = np.mean(dsqrK)\n",
        "std = np.sqrt(var)\n",
        "print(var.round(2), std.round(2))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "46.04 251.89 15.87\n",
            "251.89 15.87\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TcntCMg-SmMK",
        "colab_type": "text"
      },
      "source": [
        "# 결론 : 평균 수명 : $ 46 $세, 편차는 $ \\pm 15.8세 $"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wt-c_fZtVurw",
        "colab_type": "text"
      },
      "source": [
        "# 변동계수\n",
        "* 표준편차를 평균으로 나눈 값의 백분율\n",
        "* 측정단위가 동일하지만 평균이 큰 차이를 보이는 두 자료집단 또는\n",
        "* 측정단위가 서로 다른 두 자료집단에 대한 분산 정도를 비교할때 사용  \n",
        "* 즉, 두 자료집단의 평균의 상대적인 크기의 차이를 없애줌\n",
        "* 변동계수가 크면 상대적으로 넓은 분포를 이룸\n",
        "\n",
        "* 예를 들어, A가게의 한달 평균 매출이 1억이고 표준편차가 천만원이고\n",
        "  B가게의 한달 평균 매출이 천만원이고 표준편차가 500만원일때,\n",
        "  과연, B가게가 A가게보다 못번다고 할 수 있을까?\n",
        "  => A가게의 변동계수 : 1천만/1억 = 0.1\n",
        "  => B가게의 변동계수 : 500만/1천만 = 0.5\n",
        "\n",
        "** 모집단의 변동계수 **\n",
        "$$ C.V_p $$\n",
        "\n",
        "** 표본의 변동계수 **\n",
        "$$ C.V_s $$ "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z2vgzq1pWhxC",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        },
        "outputId": "f5139647-337d-4cca-a2c6-3fd33dcce7ba"
      },
      "source": [
        "# 자료 C, D 에 대해 어느 표본이 평균으로부터 \n",
        "# 상대적으로 더 넓게 분포하는지 결정하시오\n",
        "# C = [171 164 167 156 159 164]\n",
        "# D = [11.5 12.2 12.0 12.4 13.6 10.5]\n",
        "# => 평균과 표준편차를 구한 후 변동계수를 구함\n",
        "\n",
        "from scipy.stats import variation\n",
        "\n",
        "C = [171, 164, 167, 156, 159, 164]\n",
        "D = [11.5, 12.2, 12.0, 12.4 ,13.6, 10.5]\n",
        "\n",
        "print(np.std(C)/np.mean(C), np.std(D)/np.mean(D))\n",
        "print(variation(C), variation(D))\n",
        "\n",
        "meanC = np.mean(C)\n",
        "stdC = np.std(C, ddof=1)\n",
        "cvC = stdC / meanC\n",
        "\n",
        "meanD = np.mean(D)\n",
        "stdD = np.std(D, ddof=1)\n",
        "cvD = stdD / meanD\n",
        "\n",
        "print(cvC.round(3), cvD.round(3))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.03011883119815322 0.07775993821395123\n",
            "0.03011883119815322 0.07775993821395123\n",
            "0.033 0.085\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mXlFAZvvWlBQ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aZq6FydOwkw6",
        "colab_type": "text"
      },
      "source": [
        "# 사분위수\n",
        "* 데이터를 가장 작은수부터 가장 큰수까지 정렬하였을때\n",
        "  1/4, 2/4, 3/4 위치에 있는 수를 의미\n",
        "* 이 각각의 수를 1사분위수, 2사분위수, 3사분위수라고 함\n",
        "* 2사분위수는 중앙값과 같음\n",
        "* 때로 위치를 1/100단위로 나눈 경우도 있는데, \n",
        "  이때 백분위수를 사용함\n",
        "* 한편, 사분위수를 구하는 방법은 크게 9가지가 존재하는데\n",
        "  대상 데이터의 유형에 따라 적용방법이 다름\n",
        "* numpy의 percentile함수의 interpolation 속성으로\n",
        "  계산방법을 지정할 수 있음\n",
        "  (nearst, lower, higher, linear, midpoint)  \n",
        "\n",
        "$$ Q_1, Q_2, Q_3 $$\n",
        "\n",
        "![](https://drive.google.com/uc?id=1gYoesXBJTlJc9jgzRVV4RbpWOZXzaicD)\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ELj3z85ryffI",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "9d830d3e-1315-45bd-fdc6-24a0d28f8318"
      },
      "source": [
        "# 데이터 A, B의 사분위수를 구하세요\n",
        "# 백분위수는 numpy의 percentile(대상, 위치)함수 사용\n",
        "# 25분위수는 1사분위수\n",
        "# 50분위수는 2사분위수\n",
        "# 75분위수는 3사분위수\n",
        "A = [1,2,3,4,5,5,5,6,7,8,8,9,9,9,9]\n",
        "B = [4,5,5,5,6,6,6,6,6,6,6,7,7,7,8]\n",
        "\n",
        "val1stA = np.percentile(A, 25, interpolation='linear')\n",
        "val2ndA = np.percentile(A, 50, interpolation='linear')\n",
        "val3rdA = np.percentile(A, 75, interpolation='linear')\n",
        "print(val1stA, val2ndA, val3rdA)\n",
        "\n",
        "val1stB = np.percentile(B, 25, interpolation='midpoint')\n",
        "val2ndB = np.percentile(B, 50, interpolation='midpoint')\n",
        "val3rdB = np.percentile(B, 75, interpolation='midpoint')\n",
        "print(val1stB, val2ndB, val3rdB)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "4.5 6.0 8.5\n",
            "5.5 6.0 6.5\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o0micYJPz3b-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 176
        },
        "outputId": "b7a9022c-79f9-4e1b-8fc5-d2e77d7c8634"
      },
      "source": [
        "# 또는 pandas의 describe() 함수를 사용할 수 있음\n",
        "numsA = pd.Series(A)\n",
        "print(numsA.describe())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "count    15.000000\n",
            "mean      6.000000\n",
            "std       2.699206\n",
            "min       1.000000\n",
            "25%       4.500000\n",
            "50%       6.000000\n",
            "75%       8.500000\n",
            "max       9.000000\n",
            "dtype: float64\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oyNJP9Rsz3Qg",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 176
        },
        "outputId": "e54dd194-a15b-4a05-e90d-c7d7ea48847c"
      },
      "source": [
        "numsB = pd.Series(B)\n",
        "print(numsB.describe())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "count    15.0\n",
            "mean      6.0\n",
            "std       1.0\n",
            "min       4.0\n",
            "25%       5.5\n",
            "50%       6.0\n",
            "75%       6.5\n",
            "max       8.0\n",
            "dtype: float64\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "i2Dm_60l1zQM",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        },
        "outputId": "3714fa5e-6db6-47b2-d76f-6dbee0f9a6a5"
      },
      "source": [
        "# 공식을 이용해서 사분위수를 구해봄\n",
        "# [1,2,3,4,5,5,5,6,7,8,8,9,9,9,9]\n",
        "# 1사분위수 구하기 = 25백분위수\n",
        "m = (25 * len(A)) / 100   # kn/100\n",
        "pos = int(np.ceil(m))\n",
        "print(A[ pos - 1 ], m, pos)\n",
        "\n",
        "# 2사분위수 구하기 = 50백분위수\n",
        "m = (50 * len(A)) / 100 \n",
        "pos = int(np.ceil(m))\n",
        "print(A[ pos - 1 ], m, pos)\n",
        "\n",
        "# 3사분위수 구하기 = 75백분위수\n",
        "m = (75 * len(A)) / 100  \n",
        "pos = int(np.ceil(m))\n",
        "print(A[ pos - 1 ], m, pos)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "4 3.75 4\n",
            "6 7.5 8\n",
            "9 11.25 12\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H977e-Rp0LR7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "01e9a50d-41b9-4b95-848b-f1599de1acdf"
      },
      "source": [
        "# 다음 표본에 대한 사분위수를 구하세요\n",
        "# 26 31 27 38 42 26 18 17 25 29 39 38 38 40 46 38 39 41 41 40 26 19 39 28 45 34 21 41 30 30 12 22 48 34 29 26 29 58 43 16 42 44 38 44 28 43 39 42 39 46\n",
        "nums = [26,31,27,38,42,26,18,17,25,29,39,38,38,40,46,38,39,41,41,40,26,19,39,28,45,34,21,41,30,30,12,22,48,34,29,26,29,58,43,16,42,44,38,44,28,43,39,42,39,46]\n",
        "\n",
        "q1 = np.percentile(nums, 25)\n",
        "q2 = np.percentile(nums, 50)\n",
        "q3 = np.percentile(nums, 75)\n",
        "\n",
        "print(q1,q2,q3)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "27.25 38.0 41.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "84o8KVIo-5B9",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        },
        "outputId": "a5bbce17-2ca2-4f09-bd17-91e1e7bff186"
      },
      "source": [
        "m = (50*25) / 100 # n = 50, k = 25\n",
        "pos = int(np.ceil(m))\n",
        "print(sorted(nums)[pos-1], m, pos)\n",
        "\n",
        "m = (50*50) / 100 # n = 50, k = 50\n",
        "pos = int(np.ceil(m))\n",
        "print(sorted(nums)[pos-1], m, pos)\n",
        "\n",
        "m = (50*75) / 100 # n = 50, k = 75\n",
        "pos = int(np.ceil(m))\n",
        "print(sorted(nums)[pos-1], m, pos)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "27 12.5 13\n",
            "38 25.0 25\n",
            "41 37.5 38\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "96Fx6x5GApXW",
        "colab_type": "text"
      },
      "source": [
        "# 사분위수 범위\n",
        "* 수집한 자료의 1사분위수와 3사분위수인 \n",
        "   $Q_1$ 과 $Q_3$ 사이의 범위를 의미\n",
        "\n",
        "$$ I.Q.R = Q_3 - Q_1 $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "v9MLAvzmBiHn",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "fee05961-4498-48e6-e7c4-01d8e7a2e53c"
      },
      "source": [
        "# 데이터 A, B의 사분위수 범위를 구하세요\n",
        "iqrA = np.percentile(A, 75) - np.percentile(A, 25)\n",
        "iqrB = np.percentile(B, 75) - np.percentile(B, 25)\n",
        "print(iqrA, iqrB)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "4.0 1.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mOUupLxCBsmV",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "00c6c8ca-d3b7-4c2c-e7cd-7165c90852c7"
      },
      "source": [
        "# 다음 표본에 대한 사분위수 범위를 구하세요\n",
        "iqr = np.percentile(nums, 75) - np.percentile(nums, 25)\n",
        "print(iqr)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "13.75\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xiCvnyeDCfyy",
        "colab_type": "text"
      },
      "source": [
        "# 상자수염그래프boxplot\n",
        "\n",
        "* 사분위수를 포함해서 수집된 자료에 포함된 특이값등을 알려주는\n",
        "시각적 도구\n",
        "* 특이값, 이상치에 재한 정보를 제공\n",
        "* 자료의 중심위치와 흩어진 모양, 분포의 꼬리부분을 쉽게 파악"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LEEVJU5DDzLm",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 412
        },
        "outputId": "77465d10-8a07-485d-b108-7194ed20de78"
      },
      "source": [
        "# 다음 표본에 대한 상자수염그래프를 그려보세요\n",
        "# boxplot(대상)\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "plt.boxplot(nums)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'boxes': [<matplotlib.lines.Line2D at 0x7fbc13956b70>],\n",
              " 'caps': [<matplotlib.lines.Line2D at 0x7fbc1396b588>,\n",
              "  <matplotlib.lines.Line2D at 0x7fbc1396b908>],\n",
              " 'fliers': [<matplotlib.lines.Line2D at 0x7fbc138f5048>],\n",
              " 'means': [],\n",
              " 'medians': [<matplotlib.lines.Line2D at 0x7fbc1396bc88>],\n",
              " 'whiskers': [<matplotlib.lines.Line2D at 0x7fbc13956e80>,\n",
              "  <matplotlib.lines.Line2D at 0x7fbc1396b208>]}"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 58
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MLOHcALhEDZ9",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 409
        },
        "outputId": "0a80859c-d3da-4b2c-fcbb-98daa3ff71ca"
      },
      "source": [
        "plt.boxplot(nums, vert=0)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'boxes': [<matplotlib.lines.Line2D at 0x7fbc138e4be0>],\n",
              " 'caps': [<matplotlib.lines.Line2D at 0x7fbc13425630>,\n",
              "  <matplotlib.lines.Line2D at 0x7fbc134259b0>],\n",
              " 'fliers': [<matplotlib.lines.Line2D at 0x7fbc1342f0f0>],\n",
              " 'means': [],\n",
              " 'medians': [<matplotlib.lines.Line2D at 0x7fbc13425d30>],\n",
              " 'whiskers': [<matplotlib.lines.Line2D at 0x7fbc138e4ef0>,\n",
              "  <matplotlib.lines.Line2D at 0x7fbc134252b0>]}"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 59
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OFygvqq6EcEV",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 339
        },
        "outputId": "b66813de-1d8d-4f3a-cc28-8dd7ea12f200"
      },
      "source": [
        "import seaborn as sns\n",
        "sns.boxplot(nums)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fbc0918deb8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 60
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1h3iThUbKJ0s",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 463
        },
        "outputId": "f3bfdf0b-5aa7-4cf7-ec2a-927875b8d3b5"
      },
      "source": [
        "# 조선조 왕들 수명의 사분위수와 상자수염그래프를 그려보세요\n",
        "q1 = np.percentile(kings, 25)\n",
        "q2 = np.percentile(kings, 50)\n",
        "q3 = np.percentile(kings, 75)\n",
        "print(q1,q2,q3)\n",
        "\n",
        "print(pd.Series(kings).describe())\n",
        "\n",
        "sns.boxplot(kings)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "33.0 45.0 56.0\n",
            "count    27.000000\n",
            "mean     46.037037\n",
            "std      16.173296\n",
            "min      16.000000\n",
            "25%      33.000000\n",
            "50%      45.000000\n",
            "75%      56.000000\n",
            "max      82.000000\n",
            "dtype: float64\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fbc089f7d30>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 67
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PTr7dgnQ0o1V",
        "colab_type": "text"
      },
      "source": [
        "# 도수분포표\n",
        "* 단순한 숫자의 나열인 데이터 자체로는 어떠한 정보도 알 수 없음\n",
        "* \n",
        "* ex) 80명의 학생의 키를 정리한 데이터에서 무엇을 알수 있을까\n",
        "    + 각 학생들의 키는 모두 같지않고 제각각의 숫자로 나타남\n",
        "    + 다양한 수치로 나타나는 것을 '분포한다'라고 함  \n",
        "    + 분포가 생기는 이유는 어떤 불확실성(!)이 있기 때문\n",
        "    + 이러한 불확실성이 제각각인 키의 수치를 발생시킨다고 여김\n",
        "  + 하지만, 이러한 수치들에도 고유한 특징이나 반복되는 것이 존재 \n",
        "  + 분포의 특성을 도출하기 위해 통계라는 도구 사용\n",
        "\n",
        "* 분포화된 자료를 시각화하려면 히스토그램을 그려야 하는데\n",
        "* 먼저, 도수분포표를 작성해야 함\n",
        "    + 최대/최소값 \n",
        "    + 계급class 설정\n",
        "    + 계급값 설정\n",
        "    + 계급내 데이터수 파악 - 빈도/도수frequency\n",
        "    + 각 계급 빈도의 상대비율 - 상대도수\n",
        "    + 각 계급의 누적합 - 누적도수\n",
        "  \n",
        "* 히스토그램을 통해 데이터의 분포(어떻게 모여 있는지) 파악 가능"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Qrwa2tuX3xok",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 72
        },
        "outputId": "0edf5078-9372-4176-9481-7d37de80aaeb"
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import seaborn as sns\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9U7DV97U4Fpd",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 230
        },
        "outputId": "c7a9355e-faf5-4634-a242-6df1f46a1ed1"
      },
      "source": [
        "# 80명 학생 키 데이터 불러오기\n",
        "heights = pd.read_csv('height.csv')\n",
        "heights['height(cm)']"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0     151\n",
              "1     154\n",
              "2     160\n",
              "3     160\n",
              "4     163\n",
              "     ... \n",
              "75    156\n",
              "76    159\n",
              "77    156\n",
              "78    156\n",
              "79    161\n",
              "Name: height(cm), Length: 80, dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lHk9PJDg6rbb",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "1da5fe90-f9ea-4ed6-c4bf-30c5f1d771de"
      },
      "source": [
        "# 구간 파악\n",
        "max = np.max(heights['height(cm)'])\n",
        "min = np.min(heights['height(cm)'])\n",
        "# print(max)  # 169 => 170\n",
        "# print(min)  # 143 => 140\n",
        "max = int(max / 10) * 10 + 10\n",
        "min = int(min / 10) * 10\n",
        "\n",
        "bins = np.arange(min, max+1, 5)\n",
        "print(bins)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[140 145 150 155 160 165 170]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Skwy-Tl28clz",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        },
        "outputId": "ced6e886-73a5-4419-ed1c-231079190829"
      },
      "source": [
        "# 구간 별도 \n",
        "hist, bins = np.histogram(heights['height(cm)'], bins)\n",
        "print(hist)\n",
        "print(bins)\n",
        "\n",
        "mid = (bins[1]-bins[0])/2\n",
        "print(bins + mid)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[ 1  4 17 27 23  8]\n",
            "[140 145 150 155 160 165 170]\n",
            "[142.5 147.5 152.5 157.5 162.5 167.5 172.5]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cPw7rWROC2Dy",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "5cda0b6a-0493-4718-8b1c-4996e5a35412"
      },
      "source": [
        "# 계급값 - 각 계급을 대표하는 값, 계급의 중앙값\n",
        "# [140 145 150 155 160 165]\n",
        "mid = (bins[1] - bins[0]) / 2\n",
        "mdbins = bins + mid\n",
        "print(mdbins)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[142.5 147.5 152.5 157.5 162.5 167.5 172.5]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S-HDEscX9lVw",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "260fb6a2-1a12-48ff-928e-666b41fd21d0"
      },
      "source": [
        "# 상대대수 \n",
        "# 구간별 빈도수를 전체빈도수의 총합으로 나눈 값\n",
        "total = len(heights['height(cm)'])\n",
        "relfrq = hist / total\n",
        "print(relfrq)\n",
        "print(sum(relfrq)) # 상대도수의 총합은 1"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0.0125 0.05   0.2125 0.3375 0.2875 0.1   ]\n",
            "1.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rbSDSGHIEOrM",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "cb8f89e4-aa8d-46cf-b45d-ac00c966f2c3"
      },
      "source": [
        "# 누적도수/누적빈도\n",
        "# 각 구간별 도수의 누적합\n",
        "# [1,2,3,4,5] => [1,3,6,10,15]\n",
        "# [ 1  4 17 27 23  8]\n",
        "csfrq = np.cumsum(hist)\n",
        "print(csfrq)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[ 1  5 22 49 72 80]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ocCY2aMCXoBV",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "c2cc20fb-6020-4a8e-be3e-7c803d4524e6"
      },
      "source": [
        "# 도수분포표의 평균\n",
        "# 각 빈도값와 계급값의 곱의 총합을 전체도수로 나눈 값\n",
        "avghist = hist * mdbins[:-1]\n",
        "avghist = (sum(avghist) / len(heights['height(cm)'])).round(2)\n",
        "print(avghist)\n",
        "\n",
        "avg = np.mean(heights['height(cm)']) # 전체 키에 대한 평균\n",
        "avg"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "158.19\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "157.575"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 117
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XNnunPfMEwzZ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 264
        },
        "outputId": "585c9338-6cd6-4980-fa56-a7c1ef24cdc4"
      },
      "source": [
        "# 히스토그램 시각화\n",
        "plt.hist(heights['height(cm)'], bins, color='red')\n",
        "plt.grid()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wfHy-NRTV3Vi",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 264
        },
        "outputId": "a6247f11-5802-41fe-8cd3-6ecdb041395d"
      },
      "source": [
        "# 히스토그램 시각화 2\n",
        "plt.plot(mdbins[:-1], hist, color='blue')\n",
        "plt.grid()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "12lmPMQ4FqMc",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 264
        },
        "outputId": "ed7c17cd-f7da-4dc0-cdb0-0c89d2584b8a"
      },
      "source": [
        "# 누적도수/누적빈도 시각화\n",
        "plt.scatter(mdbins[:-1], csfrq, color='navy')\n",
        "plt.grid()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXAAAAD4CAYAAAD1jb0+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAT8ElEQVR4nO3df3Bld1nH8fez7S6QBne7FOJO200qLTC1O1T2WmEQJmGp1h91K9NhymScxakTdQTrb6qZEXHMCDpKGWXUaDvuH4FQa6EtAlojkXFGihugbn/AtJZm7Vq7SrcLIR26LY9/5KSm2ZvNzeb+yDf3/ZrJ3Hu+99yc5+nZfvbs955zT2QmkqTybOl0AZKkM2OAS1KhDHBJKpQBLkmFMsAlqVBnt3Nj5513Xg4MDLRzk+v2rW99i3POOafTZbSVPXcHey7HzMzM/2bmy5ePtzXABwYGOHToUDs3uW7T09MMDg52uoy2sufuYM/liIjZeuNOoUhSoQxwSSqUAS5JhTLAJalQBrgkFaqhAI+IX46I+yPivoj4aES8OCIuioh7IuLhiPhYRGxrdbGSVJKJicMMDNzEli3vY2DgJiYmDjf1968a4BFxPvCLQC0zLwPOAq4DPgB8MDMvBo4D1ze1Mkkq2MTEYUZG7mJ29gSZMDt7gpGRu5oa4o1OoZwNvCQizgZ6gMeBtwC3Va8fBK5pWlWSVLjR0Snm50++YGx+/iSjo1NN20Y08n3gEXEDMAY8DfwDcAPw+erom4i4EPh0dYS+/L0jwAhAX1/f3snJyaYV3w5zc3P09vZ2uoy2sufuYM+tNTPz+Iqv7d27a02/a2hoaCYza8vHV70SMyLOBfYDFwFPAX8DXNXohjNzHBgHqNVqWdpVUKVeubUe9twd7Lm13vnOm5idPXHKeH//dh599B1N2UYjUyhvBb6Wmf+TmSeB24E3AjuqKRWAC4CjTalIkjaBsbF99PRsfcFYT89Wxsb2NW0bjQT4EeD1EdETEQHsAx4APgtcW61zALijaVVJUuGGh/cwPn41/f3biVg48h4fv5rh4T1N28aqUyiZeU9E3AZ8EXgW+BILUyJ/B0xGxO9VYzc3rSpJ2gSGh/c0NbCXa+jbCDPzvcB7lw0/AlzR9IokSQ3xSkxJKpQBLkmFMsAlqVAGuCQVygCXpEIZ4JJUKANckgplgEtSoQxwSSqUAS5JhTLAJalQBriktmn1PSK7TUNfZiVJ67V4j8jF24wt3iMSaOk39m1mHoFLaot23COy2xjgktriyJFTby92unGtzgCX1Ba7d29f07hWt2qAR8SrI+LLS36+ERG/FBE7I+LuiHioejy3HQVLKlM77hHZbVYN8Mz8amZenpmXA3uBeeDjwI3AVGZeAkxVy5JUVzvuEdlt1noWyj7gPzJzNiL2A4PV+EFgGnhP80qTtNm0+h6R3SYys/GVI24BvpiZfxoRT2Xmjmo8gOOLy8veMwKMAPT19e2dnJxsTuVtMjc3R29vb6fLaCt77g72XI6hoaGZzKwtH284wCNiG/BfwPdm5hNLA7x6/XhmnnYevFar5aFDh9ZYemdNT08zODjY6TLayp67gz2XIyLqBvhazkL5ERaOvp+olp+IiF3VL98FHFt/mZKkRq0lwN8BfHTJ8p3Ager5AeCOZhUlSVpdQwEeEecAVwK3Lxl+P3BlRDwEvLValiS1SUNnoWTmt4CXLRv7OgtnpUiSOsArMSWpUAa4JBXKAJekQhngklQoA1ySCmWAS1KhDHBJKpQBLkmFMsAlqVAGuCQVygCXpEIZ4JJUKANckgplgEtSoQxwSSqUAS5JhWr0jjw7IuK2iPhKRDwYEW+IiJ0RcXdEPFQ9nvaGxpKk5mr0CPxDwGcy8zXAa4EHgRuBqcy8BJiqliVJbbJqgEfEduDNwM0AmflMZj4F7AcOVqsdBK5pVZGSpFNFZp5+hYjLgXHgARaOvmeAG4CjmbmjWieA44vLy94/AowA9PX17Z2cnGxqA602NzdHb29vp8toK3vuDvZcjqGhoZnMrC0fbyTAa8DngTdm5j0R8SHgG8C7lwZ2RBzPzNPOg9dqtTx06NAZNdAp09PTDA4OdrqMtrLn7mDP5YiIugHeyBz4Y8BjmXlPtXwb8DrgiYjYVf3yXcCxZhUrSVrdqgGemf8N/GdEvLoa2sfCdMqdwIFq7ABwR0sqlCTVdXaD670bmIiIbcAjwE+zEP63RsT1wCzw9taUKEmqp6EAz8wvA6fMv7BwNC5J6gCvxJSkQhngklQoA1ySCmWAS1KhDHBJKpQBLkmFMsAlqVAGuCQVygCXpEIZ4JJUKANckgplgEtSoQxwSSqUAS5JhTLAJalQBrgkFaqhGzpExKPAN4HngGczsxYRO4GPAQPAo8DbM/N4a8qUJC23liPwocy8fMmdkW8EpjLzEmCqWpYktcl6plD2Awer5weBa9ZfjiSpUZGZq68U8TXgOJDAX2TmeEQ8lZk7qtcDOL64vOy9I8AIQF9f397Jyclm1t9yc3Nz9Pb2drqMtrLn9njyyac5evSbPPPMc2zbdhbnn/9Sdu58Sdu2734ux9DQ0MyS2Y/nNXpX+h/MzKMR8Qrg7oj4ytIXMzMjou7fBJk5DowD1Gq1HBwcXFvlHTY9PU1pNa+XPbfexMRhRkbuYn7+5PNjPT1bGR+/muHhPW2pwf1cvoamUDLzaPV4DPg4cAXwRETsAqgej7WqSGmzGR2dekF4A8zPn2R0dKpDFalEqwZ4RJwTES9dfA78EHAfcCdwoFrtAHBHq4qUNpsjR06saVyqp5EplD7g4wvT3JwNfCQzPxMR/wbcGhHXA7PA21tXprS57N69ndnZU8N69+7tHahGpVo1wDPzEeC1dca/DuxrRVHSZjc2tq/uHPjYmP9LqXFeiSl1wPDwHsbHr6a/fzsR0N+/va0fYGpzaPQsFElNNjy8x8DWungELkmFMsAlqVAGuCQVygCXpEIZ4JJUKANckgplgEtSoQxwSSqUAS5JhTLAJalQBrgkFcoAl6RCGeCSVCgDXJIK1XCAR8RZEfGliPhktXxRRNwTEQ9HxMciYlvrypQkLbeWI/AbgAeXLH8A+GBmXgwcB65vZmGSpNNrKMAj4gLgx4C/qpYDeAtwW7XKQeCaVhQoSaovMnP1lSJuA34feCnwa8A7gc9XR99ExIXApzPzsjrvHQFGAPr6+vZOTk42rfh2mJubo7e3t9NltJU9dwd7LsfQ0NBMZtaWj696S7WI+HHgWGbORMTgWjecmePAOECtVsvBwTX/io6anp6mtJrXy567gz2Xr5F7Yr4R+ImI+FHgxcB3AR8CdkTE2Zn5LHABcLR1ZUqSllt1DjwzfzMzL8jMAeA64J8ycxj4LHBttdoB4I6WVSlJOsV6zgN/D/ArEfEw8DLg5uaUJElqRCNTKM/LzGlgunr+CHBF80uSJDXCKzElqVAGuCQVygCXpEIZ4JJUKANckgplgEtSoQxwSSqUAS5JhTLAJalQBrgkFcoAl6RCGeCSVCgDXJIKZYBLUqEMcEkqlAEuSYVaNcAj4sUR8YWIuDci7o+I91XjF0XEPRHxcER8LCK2tb5cSdKiRo7Avw28JTNfC1wOXBURrwc+AHwwMy8GjgPXt65MSdJyjdzUODNzrlrcWv0k8Bbgtmr8IHBNSyqUJNUVmbn6ShFnATPAxcCHgT8EPl8dfRMRFwKfzszL6rx3BBgB6Ovr2zs5Odm86ttgbm6O3t7eTpfRVvbcHey5HENDQzOZWVs+3tBNjTPzOeDyiNgBfBx4TaMbzsxxYBygVqvl4OBgo2/dEKanpymt5vWy5+5gz+Vb01komfkU8FngDcCOiFj8C+AC4GiTa5MknUYjZ6G8vDryJiJeAlwJPMhCkF9brXYAuKNVRUqSTtXIFMou4GA1D74FuDUzPxkRDwCTEfF7wJeAm1tYpyRpmVUDPDP/Hfi+OuOPAFe0oihJ0uq8ElOSCmWAS1KhDHBJKpQBLkmFMsAlqVAGuCQVygCXpEIZ4JJUKANckgplgEtSoQxwSSqUAa4NYWLiMAMDN7Fly/sYGLiJiYnDnS5J2vAauqGD1EoTE4cZGbmL+fmTAMzOnmBk5C4Ahof3dLI0aUPzCFwdNzo69Xx4L5qfP8no6FSHKpLKYICr444cObGmcUkLDHB13O7d29c0LmlBI7dUuzAiPhsRD0TE/RFxQzW+MyLujoiHqsdzW1+uNqOxsX309Gx9wVhPz1bGxvZ1qCKpDI0cgT8L/GpmXgq8HviFiLgUuBGYysxLgKlqWVqz4eE9jI9fTX//diKgv3874+NX+wGmtIpGbqn2OPB49fybEfEgcD6wHxisVjsITAPvaUmV2vSGh/cY2NIaRWY2vnLEAPA54DLgSGYu3q0+gOOLy8veMwKMAPT19e2dnJxcf9VtNDc3R29vb6fLaCt77g72XI6hoaGZzKwtH284wCOiF/hnYCwzb4+Ip5YGdkQcz8zTzoPXarU8dOjQGkvvrOnpaQYHBztdRlvZc3ew53JERN0Ab+gslIjYCvwtMJGZt1fDT0TErur1XcCxZhUrSVpdI2ehBHAz8GBm/vGSl+4EDlTPDwB3NL88SdJKGrmU/o3ATwGHI+LL1dhvAe8Hbo2I64FZ4O2tKVGSVE8jZ6H8CxArvOyJupLUIV6JKUmFMsAlqVAGuCQVygCXpEIZ4JJUKANckgplgEtSoQxwSSqUAS5JhTLAJalQBrgkFcoAl6RCGeCSVCgDXJIKZYBLUqEMcEkqVCO3VLslIo5FxH1LxnZGxN0R8VD1eNqbGUuSmq+RI/C/Bq5aNnYjMJWZlwBT1bIkqY1WDfDM/Bzw5LLh/cDB6vlB4Jom1yVJWkVk5uorRQwAn8zMy6rlpzJzR/U8gOOLy3XeOwKMAPT19e2dnJxsTuVtMjc3R29vb6fLaCt77g72XI6hoaGZzKwtH2/krvSnlZkZESv+LZCZ48A4QK1Wy8HBwfVusq2mp6cpreb1sufuYM/lO9OzUJ6IiF0A1eOx5pUkSWrEmQb4ncCB6vkB4I7mlCNJalQjpxF+FPhX4NUR8VhEXA+8H7gyIh4C3lotS5LaaNU58Mx8xwov7WtyLZKkNfBKTEkqlAEuSYUywCWpUAa4JBXKAN+AJiYOMzBwE1u2vI+BgZuYmDjc6ZIkbUDrvhJTzTUxcZiRkbuYnz8JwOzsCUZG7gJgeHhPJ0uTtMF4BL7BjI5OPR/ei+bnTzI6OtWhiiRtVAb4BnPkyIk1jUvqXgb4BrN79/Y1jUvqXgb4BjM2to+enq0vGOvp2crYmBe+SnohA3yDGR7ew/j41fT3bycC+vu3Mz5+tR9gSjqFZ6FsQMPDewxsSavyCFySCmWAS1KhNnyAe1WiJNW3oefAvSpRkla2riPwiLgqIr4aEQ9HxI3NKmqRVyVK0srOOMAj4izgw8CPAJcC74iIS5tVGHhVoiSdznqOwK8AHs7MRzLzGWAS2N+cshZ4VaIkrSwy88zeGHEtcFVm/ky1/FPAD2Tmu5atNwKMAPT19e2dnJxseBtPPvk0s7Mn+M53/r/GLVuC/v7t7Nz5kjOqe63m5ubo7e1ty7Y2CnvuDvZcjqGhoZnMrC0fb/mHmJk5DowD1Gq1HBwcXNP7JyYOMzo6xZEjJ9i9eztjY/t429va9wHm9PQ0a625dPbcHey5fOsJ8KPAhUuWL6jGmsqrEiWpvvXMgf8bcElEXBQR24DrgDubU5YkaTVnfASemc9GxLuAvwfOAm7JzPubVpkk6bTWNQeemZ8CPtWkWiRJa7DhL6WXJNVngEtSoc74PPAz2ljE/wCzbdtgc5wH/G+ni2gze+4O9lyO/sx8+fLBtgZ4iSLiUL0T6Dcze+4O9lw+p1AkqVAGuCQVygBf3XinC+gAe+4O9lw458AlqVAegUtSoQxwSSpU1wd4RNwSEcci4r46r/1qRGREnFctD0bEiYj4cvXz2+2veP3q9RwRvxMRR5f09qNLXvvN6rZ5X42IH+5M1euzlp4jYiAinl4y/uedq/zMrfRnOyLeHRFfiYj7I+IPloxvyv1cjZ/S86bYz5nZ1T/Am4HXAfctG7+QhS/qmgXOq8YGgU92uuZW9Az8DvBrdda9FLgXeBFwEfAfwFmd7qHFPQ8s//NQ4s8KPQ8B/wi8qFp+RRfs55V6Ln4/d/0ReGZ+DniyzksfBH4D2HSf8p6m53r2A5OZ+e3M/BrwMAu30yvKGnveFFbo+eeB92fmt6t1jlXjm3k/r9Rz8bo+wOuJiP3A0cy8t87Lb4iIeyPi0xHxve2urcXeFRH/Xv0z9Nxq7HzgP5es81g1tlnU6xngooj4UkT8c0S8qWPVNd+rgDdFxD1Vb99fjW/m/bxSz1D4fjbAl4mIHuC3gHrz219k4TsJXgv8CfCJdtbWYn8GvBK4HHgc+KPOltMWK/X8OLA7M78P+BXgIxHxXZ0psenOBnYCrwd+Hbg1IqKzJbXcSj0Xv58N8FO9koU5wHsj4lEWbhX3xYj47sz8RmbOwfPfhb518QPO0mXmE5n5XGZ+B/hL/v+fz225dV4nrNRzNY3w9er5DAvzwa/qXKVN9Rhwey74AvAdFr7gadPuZ1boeTPsZwN8mcw8nJmvyMyBzBxgYee/LjP/OyK+e/FoJSKuYOG/39c7WG7TRMSuJYs/CSx+in8ncF1EvCgiLgIuAb7Q7vpaYaWeI+LlEXFW9fx7WOj5kfZX2BKfYOFDPSLiVcA2Fr6db9PuZ1boeTPs55bflX6ji4iPsnB2yXkR8Rjw3sy8eYXVrwV+PiKeBZ4Grsvq4+yS1OsZGIyIy1n40PZR4GcBMvP+iLgVeAB4FviFzHyuE3Wvx1p6ZuFMht+NiJMsHK39XGYW9wHoCj3fAtxSnWb3DHCg+jO8mfdz3Z4jovj97KX0klQop1AkqVAGuCQVygCXpEIZ4JJUKANckgplgEtSoQxwSSrU/wGu46435rz8sgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b3HtrfgvH9-e",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 275
        },
        "outputId": "7c8eaba1-1c23-4fbb-9806-86496163fd43"
      },
      "source": [
        "# 빈도, 상대도수, 누적도수 모두 보기\n",
        "frqclass = [f'{i} ~ {i+5}' \n",
        "                for i in range(min, max, 5)]\n",
        "print(frqclass)\n",
        "\n",
        "hthist = pd.DataFrame({'frq': hist}, index =pd.Index(frqclass, name='class'))\n",
        "hthist['midbin'] = mdbins[:-1]\n",
        "hthist['relfrq'] = relfrq\n",
        "hthist['csfrq'] = csfrq\n",
        "hthist"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "['140 ~ 145', '145 ~ 150', '150 ~ 155', '155 ~ 160', '160 ~ 165', '165 ~ 170']\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>frq</th>\n",
              "      <th>midbin</th>\n",
              "      <th>relfrq</th>\n",
              "      <th>csfrq</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>class</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>140 ~ 145</th>\n",
              "      <td>1</td>\n",
              "      <td>142.5</td>\n",
              "      <td>0.0125</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>145 ~ 150</th>\n",
              "      <td>4</td>\n",
              "      <td>147.5</td>\n",
              "      <td>0.0500</td>\n",
              "      <td>5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>150 ~ 155</th>\n",
              "      <td>17</td>\n",
              "      <td>152.5</td>\n",
              "      <td>0.2125</td>\n",
              "      <td>22</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>155 ~ 160</th>\n",
              "      <td>27</td>\n",
              "      <td>157.5</td>\n",
              "      <td>0.3375</td>\n",
              "      <td>49</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>160 ~ 165</th>\n",
              "      <td>23</td>\n",
              "      <td>162.5</td>\n",
              "      <td>0.2875</td>\n",
              "      <td>72</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>165 ~ 170</th>\n",
              "      <td>8</td>\n",
              "      <td>167.5</td>\n",
              "      <td>0.1000</td>\n",
              "      <td>80</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "           frq  midbin  relfrq  csfrq\n",
              "class                                \n",
              "140 ~ 145    1   142.5  0.0125      1\n",
              "145 ~ 150    4   147.5  0.0500      5\n",
              "150 ~ 155   17   152.5  0.2125     22\n",
              "155 ~ 160   27   157.5  0.3375     49\n",
              "160 ~ 165   23   162.5  0.2875     72\n",
              "165 ~ 170    8   167.5  0.1000     80"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 74
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gQyZyPlwarQJ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "outputId": "1e10a542-0416-4a60-9856-a68a458bd99e"
      },
      "source": [
        "sns.distplot(heights['height(cm)'], rug=True)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f908cb6e208>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 120
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "__1xtQ27N7u0",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# 청소년 핸드폰 사용시간에 대한 도수분포표를 작성하세요\n",
        "phone = [10,37,22,32,18,15,15,18,22,15,20,25,38,28,\n",
        "         25,30,20,22,18,22,22,12,22,26,22,32,22,23,\n",
        "         20,23,23,20,25,51,20,25,26,22,26,28,28,20,\n",
        "         23,30,12,22,35,11,20,25]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ATDYKO5-Suy7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "286eab63-e44f-427c-c94d-d4cbf8aa4306"
      },
      "source": [
        "# 구간 파악\n",
        "min = 9.5\n",
        "max = 54.5\n",
        "\n",
        "bins = np.arange(min, max+1, 9)\n",
        "bins"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 9.5, 18.5, 27.5, 36.5, 45.5, 54.5])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 77
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TBHKGwRPTAXC",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "dbb92812-f873-4251-f4f2-b62f5efc43e2"
      },
      "source": [
        "# 구간 빈도\n",
        "hist, bins = np.histogram(phone, bins)\n",
        "hist"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([10, 29,  8,  2,  1])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 81
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z4i9I27STShI",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "7c4fd177-12f2-4e7c-f634-562c9ae59155"
      },
      "source": [
        "# 계급값\n",
        "# [9.5, 18.5, 27.5, 36.5, 45.5, 54.5]\n",
        "mid = (bins[1] - bins[0]) / 2\n",
        "mdbins = bins + mid\n",
        "mdbins[:-1]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([14., 23., 32., 41., 50.])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 86
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gEbvOvioTqOj",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "44f37622-2144-4ab1-bf0d-303304d9b76b"
      },
      "source": [
        "# 상대도수/상대빈도 \n",
        "total = len(phone)\n",
        "relfrq = hist / total\n",
        "print(relfrq)\n",
        "print(sum(relfrq))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0.2  0.58 0.16 0.04 0.02]\n",
            "1.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "faFMgSp0T1P2",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "88a602cf-8592-4170-fb52-2b3f48e01848"
      },
      "source": [
        "# 누적도수/누적빈도\n",
        "csfrq = np.cumsum(hist)\n",
        "csfrq"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([10, 39, 47, 49, 50])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 87
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bmv2k14DUBwa",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "outputId": "895653a4-9b9d-440f-def6-d10e66756412"
      },
      "source": [
        "# 히스토그램 시각화\n",
        "plt.hist(phone, bins, color='pink')\n",
        "plt.grid()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xqxk8MnwWq4u",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# 히스토그램 시각화 2\n",
        "plt.plot(mdbins[:-1], hist, color='blue')\n",
        "plt.grid()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nP1DV5ueUQCC",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 264
        },
        "outputId": "f3a963b5-bba6-4b9d-d818-6a8ce52a7bcf"
      },
      "source": [
        "# 누적도수/누적빈도 시각화\n",
        "plt.scatter(mdbins[:-1], csfrq, color='navy')\n",
        "plt.grid()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kRmgGYLOUi25",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 227
        },
        "outputId": "ff360912-023e-4928-f7e6-63663b928425"
      },
      "source": [
        "# 빈도, 상대도수, 누적도수 모두 보기\n",
        "frqclass = [f'{i}~{i+9}' for i in bins[:-1]]\n",
        "\n",
        "hthist = pd.DataFrame({'frq': hist},\n",
        "\tindex = pd.Index(frqclass, name='class'));\n",
        "hthist['midbin'] = mdbins[:-1]\n",
        "hthist['relfrq'] = relfrq\n",
        "hthist['csfrq'] = csfrq\n",
        "\n",
        "hthist"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>frq</th>\n",
              "      <th>midbin</th>\n",
              "      <th>relfrq</th>\n",
              "      <th>csfrq</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>class</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>9.5~18.5</th>\n",
              "      <td>10</td>\n",
              "      <td>14.0</td>\n",
              "      <td>0.20</td>\n",
              "      <td>10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18.5~27.5</th>\n",
              "      <td>29</td>\n",
              "      <td>23.0</td>\n",
              "      <td>0.58</td>\n",
              "      <td>39</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>27.5~36.5</th>\n",
              "      <td>8</td>\n",
              "      <td>32.0</td>\n",
              "      <td>0.16</td>\n",
              "      <td>47</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>36.5~45.5</th>\n",
              "      <td>2</td>\n",
              "      <td>41.0</td>\n",
              "      <td>0.04</td>\n",
              "      <td>49</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>45.5~54.5</th>\n",
              "      <td>1</td>\n",
              "      <td>50.0</td>\n",
              "      <td>0.02</td>\n",
              "      <td>50</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "           frq  midbin  relfrq  csfrq\n",
              "class                                \n",
              "9.5~18.5    10    14.0    0.20     10\n",
              "18.5~27.5   29    23.0    0.58     39\n",
              "27.5~36.5    8    32.0    0.16     47\n",
              "36.5~45.5    2    41.0    0.04     49\n",
              "45.5~54.5    1    50.0    0.02     50"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 95
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B3VIgksacfI4",
        "colab_type": "text"
      },
      "source": [
        "# 확률밀도 추정KDE\n",
        "* kernal density estimation\n",
        "* 관측된 데이터들의 분포로부터 원래 변수의 확률분포특성을 추정\n",
        "* 즉, 해당 변수에서 관측된 몇가지 데이터로부터 변수가 가질수 있는\n",
        "  모든 값들에 대한 밀도(확률)를 추정하는 것\n",
        "  + 예) 수능을 위해 모의고사를 실시함\n",
        "  + 모의고사를 통해 실제 수능시험 성적을 예측할 수 있음\n",
        "  + 몇 회의 모의고사 성적에 대한 분포를 토대로\n",
        "  + 실제로 받을 수능시험 성적에 대한 확률을 유추해 볼수 있음"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GrwUSqZmcgiy",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "outputId": "4a681f9b-4f01-45a0-ffea-06edc1d2a911"
      },
      "source": [
        "import seaborn as sns\n",
        "\n",
        "sns.distplot(heights['height(cm)'])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f908cb43668>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 122
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7tkQrcmWcvAT",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "2f2d04e3-66fb-4e54-8650-e5f01ea1f73f"
      },
      "source": [
        "sns.distplot(phone)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f908a2be940>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 123
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}