Average vs Median
Two words get used as though they mean the same thing, and the gap between them is where a great deal of misleading writing lives. The mean is the total divided by the count. The median is the middle value when everything is lined up in order.
In English, average almost always means the mean. In practice, the median is far more often the number you actually wanted.
The rule in one line
Use the median when you want to know what is typical. Use the mean when you need to multiply back up to a total. Almost every misleading statistic is one used where the other belonged.
What one outlier does
Take ten people. Nine earn $50,000.00 and one earns $500,000.00.
Nobody in that group earns $95,000.00. Not one person. The mean is a real number, correctly calculated, and it describes nobody in the room. That is not a trick example, it is what happens whenever one value sits far from the rest.
Anything with a hard floor at zero and no ceiling above will do this. Income, wealth, house prices, KiwiSaver balances, days a property takes to sell, business revenue. You cannot earn less than nothing, but you can earn a hundred times the typical figure, so the tail runs one way only. For all of these the mean sits above the median, reliably, and the median is the one that describes a typical person.
When the mean is the right tool
The mean is not the villain here. It answers a different question, and for that question the median is useless.
| Question | Which one |
|---|---|
| What does a typical household earn? | Median |
| What is a normal price for a house here? | Median |
| How much tax will this group pay in total? | Mean, times the count |
| How much power does the network need? | Mean, times the count |
| What should I expect to pay? | Median |
| What is our total wage bill? | Mean, times the count |
The distinction is clean. If you are going to multiply the number by how many there are, you need the mean, because only the mean reconstructs the total. If you are going to compare yourself to it, you want the median.
House prices are reported as medians rather than means, and the reason is exactly the distribution above. A handful of very expensive sales in a month would drag a mean upwards and make it look as though ordinary prices had risen when they had not. The median moves only when the middle of the market moves, which is what someone buying an ordinary house wants to know.
The third one, briefly
The mode is the most common value. It is rarely useful for money, because exact amounts repeat so seldom, but it is genuinely useful for categories: the most common house size, the most common reason for a claim, the most common KiwiSaver fund type. Where the thing being counted is not a number, the mode is often the only one of the three that means anything.
How the choice gets used on you
Nobody has to lie to mislead with these. They only have to pick. A claim is made with whichever of the two flatters the case, and both are technically correct, which is what makes it effective.
So the useful habit is not scepticism about statistics generally. It is a single question, asked every time: is that a mean or a median? If the source does not say, that is itself informative, and if the two are far apart, the gap is the story.
Reports about how much people have saved, or hold in KiwiSaver, or have set aside for retirement, are frequently quoted as means. Because wealth is even more skewed than income, the gap between mean and median is wider again. Someone comparing themselves to a mean savings figure is comparing themselves to a number that a large majority of people are below, and concluding they are behind when they are close to typical.
Two more things worth knowing
The first is the spread. Neither the mean nor the median tells you how varied the data is, and two groups with identical medians can be nothing alike. Where it is available, a range or a set of quartiles tells you far more than any single number, and its absence is often deliberate.
The second is what is being counted. A median house price is the median of houses that sold, not of houses that exist. A median wage is the median of people in work, not of people. The definition frequently matters more than the choice of average, and it is usually further down the page in smaller type.
Checking a number in three questions
What this guide does not cover
Weighted averages, geometric means for growth rates, standard deviation and confidence intervals all matter and are beyond this page. Every figure above is a worked example built from stated assumptions rather than data about any real group. The general point holds regardless of the numbers used to illustrate it.
Related guides and tools
- How house prices are measured guide, for why the property market reports medians.
- Inflation adjusted thinking guide, for the other adjustment that changes what a number means.
- Compound decisions guide, for another place intuition and arithmetic part company.
- Round-up apps guide, for a case where doing the sum changes the conclusion.
Test Your Knowledge
Ten questions on means, medians and which one answers your question.
Sources: arithmetic worked from stated assumptions. The convention that the Real Estate Institute of New Zealand and Statistics New Zealand report median rather than mean values for house prices and incomes reflects the distribution property described here. This guide contains no external figures requiring verification, only worked examples.
Related tools and guides
- Average salary NZ: the median against the mean on real NZ earnings data.
- Standard deviation calculator: how spread out a data set really is.
- Quartile and IQR calculator: quartiles and outliers for your own numbers.