Moving to quantiles or other statistics

[giacomoorsi]

It is reasonable to consider showing median delays instead of average delays.

• Median delays provide the simple intuition: half of the time the train arrives with a delay lower than the value shown
• Median is probably a concept not understood by the general population
• The average delay is very sensitive to trains delayed in exceptional cases (e.g. infrastructure failure). A delay of 500 minutes which happens once, moves the average delay a lot, but it doesn't have any impact on the median. E.g. over one month, if a train is delayed for 0 minutes every day, and one day it has a delay of 120 minutes, the average delay is 4 minutes, which would be displayed orange/red on the website

However, showing median delays reveals a good performance all over Italy, for any kind of trains, including InterCity trains, which are the most problematic (see picture below), therefore it doesn't lead to any discussion

That's why, perhaps, we should consider moving to other quantiles. For instance the quantile 0.9 would tell 90% of the trains arrive with a delay lower than this value. However, this might be hard to be explained to the general public.

Perhaps, we could also explore moving to the "percentage" of train delayed. We set a threshold of delay, for instance 3 or 5 minutes and we show the percentage.