Track 13 · Resampling and Statistical Reasoning · Lesson 4 of 10
Robust statistics
Measure how sensitive a statistic is to outliers, use robust alternatives (median, trimmed mean, MAD), and decide when a non-robust statistic is still the right one.
One motor-insurance claim of 480,000 SAR is larger than the next 8 largest claims combined. Whether the “average claim” is reported as about 14 000 or 7 000 SAR depends on how that one number is treated. Robust statistics make that dependence visible — and force the analyst to decide which question is being answered.
A statistic is robust (or resistant) when a few unusual observations cannot move it much. The mean and the standard deviation are not robust: one wild value can drag them anywhere. The median, trimmed means, the interquartile range and the median absolute deviation are robust.
Robustness is measured by the breakdown point: the smallest fraction of the data that, if replaced by arbitrarily bad values, can make the statistic arbitrarily wrong.
Included with a Formula Quest membership
It has 8 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Compute the median, trimmed mean, MAD and scaled MAD, and compare them with the mean and SD
- Work out how many bad values break a statistic (its breakdown point)
- Show the sensitivity of a result to extreme values with and without them
- Choose between robust and non-robust summaries according to the question, never delete genuine values silently