# How to find the average given that you have the mean, standard deviation and amount?

I have an assignment where I'm asked to find the the average shoe number for men and women from given data:

Sum of men and women: 312

Amount of men: 239

Standard deviation of men: 1.63

Mean of shoe number for men: 43.5

Amount of women: 239

Standard deviation of women: 1.4

Mean of shoe number for women: 38.2

Variance squared: 2321

Sum of all shoe numbers: 13183

• ?! Mean of men: 43.5, Mean of women: 38.2 ?! – user2974951 Feb 6 '19 at 13:55
• It is the mean of the shoe number for men and women – Alan Rostem Feb 6 '19 at 13:56
• Isn't that what you want, the average shoe number? – user2974951 Feb 6 '19 at 13:56
• Yes, I want the average shoe number specifically for men and specifically for women. – Alan Rostem Feb 6 '19 at 13:58
• @AlanRostem average and mean are the same thing. – Lucas Farias Feb 6 '19 at 14:08

• pooled mean: $$\frac{\sum_i^n N_i \mu_i}{\sum_i^n N_i}$$
• pooled variance: $$\frac{\sum_i^n (N_i-1) \sigma_i^2}{\sum_i^n (N_i-1)}$$
$$N_i$$, $$\sigma^2_i$$ and $$\mu_i$$ stand for the number of observations, variance and mean of group $$i$$, respectively.