[TowerTalk] Median vs Average

[kr2q at optimum.net]

I was recently stated here that:

[snip]
With a number of samples large enough to be statistically valid a single, significant outlier, be it
high or low can substantially skew the median, but have little effect on the average.
[end snip]

Ummm.  This is exactly backwards.  The median is often used because it is immune to outliers,
whereas the mean (average) is can be greatly impacted by the outliers.

EG: Grades in class.  Lets say your grades are 95, 95, 95, 95, 95, 95, 95, 95, 95, 95.

What grade is typical?  Well, 95!  The mean (average) is 95 and the median is 95.

But what if you failed one quiz/test and got a 15?
Now your grades are 95, 95, 95, 15, 95, 95, 95, 95, 95, 95.

Your median grade is still 95, but your average is now 87.

So clearly, median was unaffected by an outlier, while the average moved a lot.

If you make "n" larger, you will still see the same thing; median is static while average isn't.

For those who "love" using the mean (average), try using the geometric mean.  It greatly
lessens the impact of outliers.  Of course, you have to account for that when reporting out.

de Doug KR2Q