Robust Statistics

How are the sample statistics of the interest rate data set affected by the observation, 26.3%? What would have happened if this loan had instead been only 15%? What would happen to these summary statistics if the observation at 26.3% had been even larger, say 35%?

Interest Rate

●5% 10% 15% 20% 25% 30% 35%

Original●26.3% to 15%

●26.3% to 35%

Dot plots of the original interest rate data and two modified data sets.

robust not robust scenario median IQR x̄ s original interest rate data 9.93% 5.76% 11.57% 5.05% move 26.3% → 15% 9.93% 5.76% 11.34% 4.61% move 26.3% → 35% 9.93% 5.76% 11.74% 5.68%

A comparison of how the median, IQR, mean (x̄), and standard deviation (s) change had an extreme observations from the interest rate variable been different.

(a) Which is more affected by extreme observations, the mean or median? Figure 2.12 may be helpful. (b) Is the standard deviation or IQR more affected by extreme observations?12

The median and IQR are called robust statistics because extreme observations have little effect on their values: moving the most extreme value generally has little influence on these statistics. On the other hand, the mean and standard deviation are more heavily influenced by changes in extreme observations, which can be important in some situations.