It is well known that means are sensitive to outliers. Recently, I was asked what the effect would be on the mean if outliers from the distribution were to be removed from the analysis. Leaving aside questions of how to identify outliers and whether they should be trimmed, the question of how the mean would change if outliers are trimmed is addressed with this formula:
Consider an example with the original mean = 5.5 and the original sample size = 250. If three observations with “1” values were trimmed and another three observations with “7” values were trimmed, the change in mean would be (5.5 * 6 – 24) / (250 – 6) = .037. Therefore, the mean would increase by .037 (i.e., from 5.5 to 5.537).
– Eric DeRosia