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 Question from Myrte: Is the median always smaller then the mean?

Hi Myrte,

Suppose you have 5 data points, 1, 2, 3, 4 and 15. The median is 3 and the mean is

$\frac{1 + 2 + 3 + 4 + 15}{5} = \frac{25}{5} = 5$

so the median is smaller than the mean. Here I had four small numbers and one quite a bit larger.

Suppose I change this to have 1 small number and four quite a bit larger. For example 1, 12, 13, 14 and 15. This time the median is 13 and the mean is

$\frac{1 + 12 + 13 + 14 + 15}{5} = \frac{55}{5} = 11$

and this time the median is larger than the mean.

For another example look at my response to a question from Kaliela.

Penny