Estimation of expected value: why sample mean is usually preferred over median
Tutoring statistics, mean is used more than median. The tutor points out a reason why.
In my post from November 30, 2014, I write about why the median might be preferred to the mean in some cases. For instance, the median tends to be less sensitive to outliers. Why, then, is the mean typically preferred in academic statistics?
The estimator of the median, it turns out, has higher variance than that of the mean. In particular,
var (sample median) = (π/2)*var(x)
Therefore, if you want to estimate the true expected value of the population, a sample size of 157 is needed to estimate it as precisely from the median as you can from a sample size of 100 using the mean.
Harnett, Donald L. and James L. Murphy. Statistical Analysis for Business and Economics. Don Mills: Addison Wesley, 1986.
Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.