Median and mean
When does the average return misrepresent the typical week, and what does the median show instead?
In plain words
The mean is the sum of a set of weekly returns divided by the number of weeks. The median is the middle value once the returns are sorted from smallest to largest. A single extreme week shifts the mean a lot but barely moves the median.
Why it matters
Averages summarise a run of weeks, but one very large week can drag the average away from what most weeks actually looked like. Risk estimates built on a mean may then describe a market nobody traded in, while the median shows the middle experience and the dispersion shows how unusual the extremes were.
In a real week: ETH, week of 17 December 2018
ETH returned 52.37% in the week of 17 December 2018, after four straight down weeks of -33.72%, -1.75%, -20.04% and -9.21%. Across these five weeks the median weekly return is -9.21%, the middle of the sorted list, while the mean sits far closer to flat because the single extreme week pulls it upward. That week ranked at the 100.0 percentile of the 44 weeks of history on record.
A common mistake
Assuming the mean and median tell the same story. They diverge when the returns are lopsided, and a small sample of weeks makes the mean especially unstable.