Mean and median pay gap: which number answers which question.

The mean pay gap is the difference between the average hourly rate of two groups. The median pay gap is the difference between their middle rates. The mean moves with the extremes of a distribution and the median moves with its bulk, which is why UK employers publish both and why the two can point in opposite directions inside the same company.

A worked example where they disagree

Twelve people in one team, six men and six women, hourly rates as recorded. One man sits far above everyone else.

The men's rates total 170, so their mean is 28.33. The women's total 159, so their mean is 26.50. Taking men as the reference group, the mean gap is 1.83 divided by 28.33, which is 6.5 percent in favour of men.

The men's median is the average of the two middle rates, 22 and 23, so 22.50. The women's median is the average of 26 and 27, so 26.50. The median gap is minus 4.00 divided by 22.50, which is 17.8 percent in favour of women.

One employer, one dataset, one number saying men are ahead by 6.5 percent and another saying women are ahead by 17.8 percent. Both are correct. A single high rate lifts the men's mean by enough to reverse the sign, and moves their median not at all.

Which number answers which question

The median answers what a typical man and a typical woman earn. One large salary cannot move it, which is why it is the figure most often quoted when a company's gap is reported on.

The mean answers what the pay bill does. Because it carries the extremes, it responds when the top of an organisation is unevenly distributed, and a large mean gap sitting beside a small median gap is usually a statement about who holds the most senior roles rather than about rates in the middle of the company.

Reading them together narrows down where the difference sits. A large mean gap with a small median gap points upward, at the top of the structure. A small mean gap with a large median gap points at the middle. Two gaps of similar size point at the distribution as a whole, and the quartile figures then tell you where.

The quartiles say where the people are

The UK regulations require the proportions of men and women in the lower, lower middle, upper middle and upper quartile pay bands. The guidance is to list every full-pay employee by hourly rate and divide the list into four quarters with an equal number of employees in each section.

Two details in that cut change the answer. Our engine hands the remainder to the lower bands, so ten people split as three, three, two, two rather than the other way round. Band boundaries are cut once, across the whole cohort, and each group is then asked what share of itself sits in each band. Cutting bands separately for each group would compare every group against itself and return four equal shares every time, which looks like a finding and is an artefact.

Ties on a boundary need handling. Where several people sit on exactly the same rate and that rate straddles a band boundary, we spread them across the bands the tie occupies, in proportion to how the whole cohort's copies of that rate split. Assigning all of them to one side would report a workforce where everybody is paid identically as one hundred percent lower quartile.

Rounding the median

The median of an even-sized group is the mean of the two middle values, and on money it has to stay exact. Two people on 5,000.50 and 5,001.50 have a median of 5,001.00, and rounding that is harmless right up until two similar figures move a published gap by half a currency unit in the direction somebody notices.

Ours keeps the even case exact for that reason. It is worth checking what a spreadsheet does with the same column before you publish a percentage to one decimal place, because a median rounded to whole currency units and a gap quoted to 0.1 percent do not belong in the same table.

The bonus figures have their own denominator

Three of the six UK figures concern bonuses: the mean difference, the median difference, and the proportions of men and of women who were paid one.

The proportions are the figure that explains the other two. A bonus gap calculated across the people who received a bonus says something about amounts. A bonus gap calculated across everyone folds in who received one at all. Publishing the proportions alongside is what lets a reader tell which effect is doing the work, and it is the first thing to reach for when the bonus gap is larger than the pay gap.

Our bonus measure sums payments in the 12 months ending at the snapshot, drawn from recorded bonus payments and from payslip lines coded as a bonus, with the window closed at both ends so a payment stamped at midnight on the first of a month cannot fall between two windows. Where a company records no bonus data at all, the answer is that the figure is not known, which is a different statement from everybody having received nothing.

The reference group is a choice

A gap percentage needs something to be a gap against, and the choice changes the number's sign and its size.

Our engine defaults to the largest measured group, with ties broken by key so the choice is repeatable rather than dependent on row order, and it will take a named reference group instead. The UK regulations frame the hourly and bonus figures as the difference between men and women, so the convention is fixed for those. For any cut you run yourself, by function, level or ethnicity, state the reference group next to the number, because a reader cannot recover it from the percentage.

Directive (EU) 2023/970 adds a further set of figures on the same pattern, including the median gap and the quartile proportions, plus the gap between workers by categories of workers. The arithmetic here does not change for those; the grouping does.

Pay gap reporting for employers: what to publish and when covers which of these figures your entities owe and by when. Turning a monthly salary into the hourly rate pay reporting needs covers the rate that feeds all of them, and The narrative that goes with your pay gap numbers covers explaining a mean and a median that disagree.