# How does the average standard FIDE rating vary by age and sex?

In my answer to this question regarding requirements for female titles I quoted the mean and standard deviation for male and female ratings for standard chess in the then current FIDE rating list. These were:

Female
Mean = 1505, standard deviation = 339

Male
Mean = 1675, standard deviation = 346

In the comments David pointed out:

I don't think the average rating of men and women is a relevant statistic at all. For starters, female players are on average much younger, so we should correct for that.

He makes a very good point.

A fairer comparison would be to look at mean and standard deviation for the two sexes for the U20, 20-50 and over 50 age groups, roughly juniors, adults and seniors

So, what are these figures for male and female for these three age groups?

Here are the statistics from the latest (February 2023) FIDE rating data:

Female all ages
Mean = 1478, standard deviation = 336

Male all ages
Mean = 1644, standard deviation = 346

Female U20
Mean = 1282, standard deviation = 237

Male U20
Mean = 1356, standard deviation = 279

Female 20-50
Mean = 1614, standard deviation = 318

Male 20-50
Mean = 1690, standard deviation = 330

Female over 50
Mean = 1644, standard deviation = 357

Male over 50
Mean = 1761, standard deviation = 300

So, David was right. The difference between the "all ages" means is about 165 but when these statistics are calculated by age range the differences decrease.

For U20 the difference is about 75.

For 20-50 it is also about 75.

For over 50 it opens up to just over 115.