
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?

Originally posted here because I did not know this site existed.

Statistics does not provide a good answer to this question, in my opinion.  A mean can be relevant in mortality studies for example, but ages are not as easy to measure as you might think.  Older people, illiterate people, and people in some third-world countries tend to round their ages to a multiple of 5 or 10, for instance.

The median is more resistant to such errors than the mean.  Moreover, median ages are typically 20 – 40, but people can live to 100 and more (an increasing and noticeable proportion of the population of modern countries now lives beyond 100).  People of such age have 1.5 to 4 times the influence on the mean than they do on the median compared to very young people.  Thus, the median is a bit more up-to-date statistic concerning a country's age distribution and is a little more independent of mortality rates and life expectancy than the mean is.

Finally, the median gives us a slightly better picture of what the age distribution itself looks like: when you see a median of 35, for example, you know that half the population is older than 35 and you can infer some things about birth rates, ages of parents, and so on; but if the mean is 35, you can't say as much, because that 35 could be influenced by a large population bulge at age 70, for example, or perhaps a population gap in some age range due to an old war or epidemic.

Thus, for demographic, not statistical, reasons, a median appears more worthy of the role of an omnibus value for summarizing the ages of relatively large populations of people.
