Why averages are pretty useless for telling us about individuals
Consider a population who are being selected for a role which requires the tallest candidates possible and that is the sole criterion. Within this population there are two groups, males and females.
Males have a higher average height and both males and females share a standard deviation (the difference in height from the mean of that group). The distribution would look something like this:

There is a large overlap between males and females. Therefore, you couldn’t use gender as a proxy for height/eligibility. As a result you would have to measure each individual for the role because there would be males who are not tall enough to be eligible for the role and also females who are.
This demonstrates why and when the difference in the mean of different groups is not useful information when selecting for a particular trait.
In the above example, the average height for females who are eligible for the role is below the average for males who are eligible for the role. This shows that while those females met the criterion without ‘positive discrimination’ there is not gender height equality within the eligible population. Nor is the ratio of males to females evidence of discrimination against females, necessarily.
Another quirk of normal distributions is that the tails of the distribution falls according to the negative exponential of the square of difference from the mean. This means even very very small differences in the mean of groups create significant differences at the extremes of the distribution.

When the requirements are more and more extreme the differences between the two groups become more pronounced. So for instance at the 2.5 mark the ratio of light blue (LB) individuals to dark blue (DB) is about 3:1.

However, if the cut-off point was at 3 then the ratio of LB to DB would be far far greater than 3:1 and this would be the natural result of a difference in means between two groups, not evidence necessarily of unfair discrimination.
This is a mathematical explanation of what you would expect to see if there were different average values across groups and what that would look like when fairly selected on ability/ objective criteria only.

The above shows that even when accounting for most factors the gender pay gap (in terms of equal pay for equal work) still exists, though it is smaller in the UK than in France or Germany.
This isn’t to say that unfair gender discrimination only results in a 0.8% pay discrepancy in the UK. There are certainly discriminatory factors that hinder woman from reaching the higher echelons of the workplace and reaching the professions that remunerate most generously.
The aim of this piece is to remedy misunderstandings of what the pay gap would look like without any unfair discrimination (at the point of selection). For example, if it is true that woman are more agreeable than men, then we would expect them to be out-earning men in the caring professions, for example.
I encourage you to explore the gender pay gap using the interactive data that the ONS has produced, it may well surprise you:
https://visual.ons.gov.uk/test-your-knowledge-on-the-gender-pay-gap/
