Why medians

Sentence lengths are skewed. Most federal prison terms are short (the national median is 24 months) while a small number run to decades or life. The mean is pulled upward by those few: nationally it is 51 months, about twice the median. For drug trafficking the median is 62 months and the mean 81.

What the median is

Line up every prison term in a group from shortest to longest; the median is the one in the middle. Half the terms are shorter, half longer. It moves only when the middle of the distribution moves, not when one sentence at the top changes, which makes it the right single number for "what a sentence in this group has typically been".

Quartiles and the histogram

Each page also reports the first and third quartiles, between which the middle half of terms fall, and draws the whole distribution as a histogram over fixed bins from under six months to life. The dashed line marks the median. Read the histogram before the median: a group with two clusters (say, many terms near a mandatory minimum and many short terms after cooperation motions) has a median that describes neither.

Why the mean is still shown

The Commission's Sourcebook reports both, and the mean is what many published comparisons use. Comparison tables on this site show the mean beside the median so either can be matched to other sources. Life sentences count as 470 months in the mean, following the Commission's convention.

What neither number is

A median describes cases already sentenced, in aggregate. It is not an estimate for any case, whose range depends on its own offence level, criminal history and statutory minimums, and whose sentence depends on the court's findings.