It is the sampling distribution of the sampling means approaches a normal distribution as the sample size gets larger, no matter what the shape of the data distribution. An essential component of the Central Limit Theorem is the average of sample means will be the population mean. Similarly, if you find the average of all of the standard deviations in your sample, you will find the actual standard deviation for your population.
μ_sample = μ # mean
σ_sample = σ / sqrt(n) # standard deviation
σ_sample ^2 = σ^2 / n # variance
Where, (n>= 30) and μ = Population mean, σ = Population standard deviation, μ_sample = Sample mean, σ_sample = Sample standard deviation, n = Sample size
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