# Why is median age a better statistic than mean age?

If you look at Wolfram Alpha

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?

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Just a thought: Perhaps it is so, because it easier to estimate the median as compared to the mean from a given sample? –  Aryabhata Sep 10 '10 at 20:18
@Moron: Why do you think it is easier to estimate the median? –  Lazer Sep 10 '10 at 20:23
@Lazer: It was just a thought. What I was thinking: say I gave you a random sample of 1000 people. Now if you calculate the median and mean of those, I would expect the median to be much more accurate than the mean. –  Aryabhata Sep 10 '10 at 20:27
Better for what? –  Mariano Suárez-Alvarez Sep 10 '10 at 20:41
This question has been cross-posted at stats.stackexchange.com/q/2547/159 which is a more appropriate site for it (IMO). –  Rob Hyndman Sep 11 '10 at 2:19
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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.

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Why do you say the mean should be lower than the median? While not always true, I would typically expect the mean to be higher if the distribution is positively skewed as age is. –  Larry Wang Sep 10 '10 at 21:58
You have a population of five people, four are age 5 and the other age 80. Median = 5 and mean = 20, so here we have median<mean and more young people than old people. –  Derek Jennings Sep 11 '10 at 7:27
Thank you for responding so gently! You're absolutely right. I updated my response. –  John D. Cook Sep 11 '10 at 14:03