Why is median age a better statistic than mean age?

Question

If you look at Wolfram Alpha

or this Wikipedia page List of countries by median age

Clearly median seems to be the statistic of choice when it comes to ages.

I am not able to explain to myself why arithmetic mean would be a worse statistic. Why is it so?

Answer 1

Median is what many people actually have in mind when they say "mean." It's easier to interpret the median: half the population is above this age and half are below. Mean is a little more subtle.

People look for symmetry and sometimes impose symmetry when it isn't there. The age distribution in a population is far from symmetric, so the mean could be misleading. Age distributions are something like a pyramid. Lots of children, not many elderly. (Or at least that's how it is in a sort of steady state. In the US, for example, the post-WWII baby boom generation has distorted the distribution as they age.)

With an asymmetrical distribution, it may be better to report the median because it is a symmetrical statistic in the sense that it splits the population in half. Said another way, the median is symmetrical even if the distribution isn't.

Update: I got my logic backward when I first answered and said the mean would be lower than the median. I meant the opposite.

Answer 2

The best statistic to summarize a distribution depends upon the distribution and what you want to use it for. For distributions that are nicely bell-shaped, the mean, median, and mode are close together and it doesn't matter. For skew distributions the mean is out on the skew side from the median, but it still represents the expected value of the average of a large number of samples. The median is closer to more of the individuals than the mean. For stranger distributions no one number can provide a useful summary.