The gender pay gap and the problem with averages

Let's say we have a small fictional UK based company call ABC Inc. This company employs 13 people, 1 senior manager, 4 middle managers and 8 junior staff. The rate of pay for the different positions is senior = 40,000, middle = 30,000 and junior = 20,000. Let's say the senior manager is male and 3 of the four middle managers are male, the junior roles are 4 female and 4 male. The average pay in this case is:

male average = 26,250
female average = 22,000

So men are paid more than women in this company? No - for a given role all employees are paid the same. The problem here is the lack of female employees in middle and senior positions.
We can force the averages to converge just by re-arranging the distribution of male to female employees. For example let's say one of the male middle managers leaves the company and one of the female junior employees is promoted to fill that position. Now the averages are:

male average = 25,714
female average = 24,000

Averages are misleading because not everyone understands what they mean, in particular the main stream media struggle with statistics. There is sometimes an incorrect belief that if the average salary for women in a company is less than the men that means women are paid less than men for doing the same job. That may be true sometimes but as the above example shows it is not always the case. Rather than focusing on just average pay it might be better to focus on the ratio of male to female managers.