Describing a Distribution

Four things, always four

Every description of a distribution must cover SOCS:

• Shape — symmetric, skewed right, skewed left, uniform, bimodal.
• Outliers — unusual values, checked with the $1{,}5\times\text{IQR}$ rule.
• Center — mean or median, with a number.
• Spread — standard deviation, IQR or range, with a number.

And every one must be stated in context: "the distribution of daily rainfall is skewed right", not "it is skewed right".

Which centre to report

The mean follows the tail; the median does not. So for a skewed distribution or one with outliers, report median and IQR; for a roughly symmetric one, report mean and standard deviation.