The Three Averages: First Contact

Opening Hook

Imagine a company with one hundred employees. Ninety-nine of them earn £30,000 a year. The chief executive earns £3 million.

You ask the HR department: what is the average salary here? They do the arithmetic honestly. They add up all one hundred salaries and divide by one hundred. The answer comes out at roughly £59,700.

Nobody at that company earns £59,700. Not one person. Fifty-seven thousand employees’ worth of arithmetic, and the result describes nobody’s life.

Now ask the same question a different way. Line up all one hundred employees in order from lowest to highest paid. Walk to the middle of the line. The person standing there earns £30,000. That is the median salary.

Same company. Same payroll. Two numbers: £59,700 and £30,000. Both technically correct. One of them tells you something true about what it is like to work there. The other one does not.

This is not a trick. It is a structural feature of the most common type of distribution in economic life. Once you see it, you will never read an “average” figure the same way again.

The Concept

The word “average” is doing a lot of quiet work in public life. Most people assume it refers to a single calculation with a single answer. In fact, it covers three different measures, each with its own logic, its own strengths, and its own vulnerabilities.

The mean is what most people picture when they hear “average.” Add up all the values in a dataset and divide by how many there are. If five people earn £20,000, £25,000, £30,000, £35,000, and £90,000, the mean is (20,000 + 25,000 + 30,000 + 35,000 + 90,000) divided by 5, which is £40,000. The mean is mathematically elegant and useful in many contexts. Its weakness is that it is sensitive to extreme values. One very large or very small number can pull it far from where most of the data actually sits.

The median is the middle value once you have sorted the data from smallest to largest. In that same five-person example, sorted in order, the middle value is £30,000. If there is an even number of values, the median is the mean of the two middle values. The median is resistant to extreme values. You can make the highest earner in a dataset earn ten times more, and the median does not move at all. This makes it a better description of the “typical” case in any dataset where a few extreme values exist.

The mode is the most common value in the dataset, the one that appears most frequently. If you surveyed house prices on a street and most were around £250,000 with a few outliers in either direction, the mode would be near the cluster. The mode is rarely used in isolation for continuous data (where every value might be unique) but becomes meaningful when data clusters around distinct values. It is most useful for categorical data, such as the most popular shoe size or the most common number of children per household.

For most of what you will encounter in public life, the choice that matters is between the mean and the median. Understanding when they diverge and why is the core skill this unit teaches.

Skewed distributions are what cause mean and median to separate. A distribution is what you get when you plot how frequently each value appears across a dataset. Many things in life produce roughly symmetric distributions: the heights of adult men in a given country, for instance, cluster around a central value with roughly equal numbers of people above and below it. For symmetric distributions, the mean and the median are close together. It usually does not matter much which one you use.

But income does not work like height. Income distributions are strongly skewed to the right. Most people earn a moderate amount. A smaller number earn a great deal more. A very small number earn astronomical sums. If you drew this as a histogram, the left side would have a tall, wide hump around typical earnings, and the right side would have a long, thin tail stretching far out toward very high incomes.

In a right-skewed distribution, the mean is always higher than the median. The long tail of high values pulls the mean upward and away from where most of the data actually lives. The median, sitting at the midpoint, stays put. The gap between the two is a direct measure of how skewed the distribution is.

This is not an obscure statistical property. It is the daily reality of income data, wealth data, house price data, executive pay data, and many other distributions you encounter in public life.

Why It Matters

In April 2024, the ONS published its Annual Survey of Hours and Earnings. The median gross annual earnings for full-time employees in the UK were £37,430. Because the ONS uses median as its headline measure, this is the figure most widely reported. It describes what someone in the middle of the UK earnings distribution actually earns.

The mean earnings figure for the same dataset is higher, pulled upward by the long tail of high earners concentrated in finance, law, technology, and senior management. The divergence is not subtle. It reflects a genuine feature of how earnings are distributed.

This matters when you read economic commentary or political claims about wages. When a politician says that wages are rising, or a think tank publishes research on earnings growth, the choice of mean or median determines whose experience is being described. If median earnings are stagnant while mean earnings rise, income growth is concentrating at the top. Describing mean growth as evidence of broad prosperity is technically defensible but substantively misleading.

House prices tell the same story. The UK House Price Index, published by the ONS and HM Land Registry, uses a mean figure as its headline “average house price.” In May 2024, this average was reported at around £285,000. But house price distributions are extremely right-skewed: a relatively small number of very expensive properties, concentrated in London and the South East, pull the mean upward. The median sold price is meaningfully lower and represents what a buyer actually faces in the typical transaction. Property developers, estate agents, and government briefings tend to cite whichever figure serves their argument about affordability or market strength.

Executive pay is where the skew becomes almost cartoonish. According to the High Pay Centre’s 2024 analysis, the median FTSE 100 CEO was paid £4.4 million in 2024, approximately 113 times the median UK full-time worker’s salary of £39,039. If you were to calculate the mean salary across a FTSE 100 company including its CEO, the result would be a number that described neither the CEO’s reality nor any worker’s. It would simply be a statistical artefact of the extreme skew at the top of the pay distribution.

The critical question, whenever someone presents you with an “average,” is always the same: which average? And why that one?

How to Spot It

In October 2012, the UK government published data on household income. The then Chancellor, George Osborne, referred in a speech to “average household income” in a context that used the mean figure. Opposition politicians citing the same dataset referred to median household income. Both figures came from the same ONS dataset. Both were arithmetically accurate. The mean was substantially higher, because household income is right-skewed by high-income households. The choice of mean made the country’s finances look healthier for more people than the median did. Neither side lied. Both sides chose.

This is the tell: in any dataset involving income, wealth, salaries, house prices, or similar economic quantities, the presenter knows that mean and median diverge. The choice between them is not a neutral technical decision. It is a decision about which part of the distribution you want to describe. When someone uses “average” without specifying which average, ask immediately. When they specify the mean for an income dataset, ask what the median is. The gap between them tells you something important about the shape of the distribution and about what the presenter is choosing to show you.

The pattern is consistent. Those who want to present economic conditions favourably tend toward the mean. Those who want to show that typical people are worse off tend toward the median. Neither calculation is wrong. But only one of them tells you about the experience of the person in the middle.

The practical test: if a claim about earnings, income, or wealth does not state which average is being used, treat it as incomplete. A number without its method is not a fact; it is a fragment.

Your Challenge

A technology company with 200 employees issues a press release announcing: “Average total compensation at our company is £95,000 per year, reflecting our commitment to rewarding our people.”

Before you decide whether to be impressed, what questions would you ask? What would you need to know about the shape of the pay distribution to assess whether that figure describes the experience of the typical employee? What additional figures would give you a genuinely useful picture of what it is like to work there?

There is no answer provided here. Sit with the question.

References

UK median household disposable income (FYE 2024): £36,700. Office for National Statistics. “Average household income, UK: Financial Year Ending 2024.” Published May 2025. https://www.ons.gov.uk/peoplepopulationandcommunity/personalandhouseholdfinances/incomeandwealth/bulletins/householddisposableincomeandinequality/financialyearending2024

UK median full-time earnings (April 2024): £37,430. Office for National Statistics. “Employee earnings in the UK: 2024.” Annual Survey of Hours and Earnings (ASHE). Published October 2024. https://www.ons.gov.uk/employmentandlabourmarket/peopleinwork/earningsandworkinghours/bulletins/annualsurveyofhoursandearnings/2024

UK average house price (May 2024): approximately £285,000 (mean). UK House Price Index. HM Land Registry and Office for National Statistics. https://landregistry.data.gov.uk/app/ukhpi/

FTSE 100 median CEO pay (2024): £4.4 million, approximately 113 times median UK worker pay of £39,039. High Pay Centre. “CEO pay in the FTSE 100 reaches record high for the third year in a row.” Published January 2026. https://highpaycentre.org/ceo-pay-in-the-ftse-100-reaches-record-high-for-the-third-year-in-a-row/

On the ONS preference for median as the headline measure of earnings: The ONS states that median earnings are used as the headline measure because they are less affected by a small number of very high earners. This methodology note appears throughout ASHE publications and ONS guidance on income statistics.