The average hides the spread.
An 8 per cent economy can leave most people exactly where they were, and the average will not tell you. Mean and median are both honest numbers; they answer different questions. This page is about the gap between those questions.
One number, folded from millions
First principlesAsk how a country is doing and someone will quote an average: per capita income, mean wages, average inflation. An average is a compression. Hundreds of millions of experiences are folded into one number. Compression is useful, and it is where things get lost.
Five people, one doubling
A worked example, toy figuresSuppose five people earn toy incomes in lakh per year: 1.2, 3.0, 3.0, 3.0 and 4.8. Their total is ₹15 lakh. Then one person's income doubles, from ₹1.2 lakh to ₹2.4 lakh, while the other four stay flat. Watch what the two averages do.
| Person | Before | After | Change |
|---|---|---|---|
| Asha | ₹1.2 lakh | ₹2.4 lakh | Doubled |
| Bina | ₹3.0 lakh | ₹3.0 lakh | Flat |
| Chand | ₹3.0 lakh | ₹3.0 lakh | Flat |
| Dev | ₹3.0 lakh | ₹3.0 lakh | Flat |
| Esha | ₹4.8 lakh | ₹4.8 lakh | Flat |
| The meantotal ÷ five | ₹3.0 lakh | ₹3.24 lakh | Up 8 per cent |
| The medianthe middle person | ₹3.0 lakh | ₹3.0 lakh | Unmoved |
The total income of the five rises 8 per cent, and the mean rises with it: prosperity, by the average. The median does not move at all. The person in the middle earned ₹3 lakh before and earns ₹3 lakh after, and four of the five people are exactly where they started. Both numbers are honest. They are answering different questions, and the mistake is thinking they answer the same one.
Two claims, not one
Reading any average“GDP grew 8 per cent” and “Indians are better off” are different claims. The first is about a total. The second is about a distribution, and it cannot be settled by the total. An economy where the top decile takes all the growth and an economy where everyone gains 8 per cent produce the same headline. Only one of them matches the second sentence.
This is not an argument against averages. Totals and means answer real questions: how much is there, and is there more than before? It is an argument for asking the next question. When you are quoted an average, ask three things of it. Is it a mean or a median? The two part company precisely when the spread is wide. Who is in it? A national average folds farmer and banker into one person who exists nowhere. And what does the spread look like? The average plus the spread is the beginning of the truth; the average alone is the end of the conversation.
The same discipline applies to the per capita figure, which is a mean in national dress. The companion note on per capita divides the economy by its people; this page asks what that division conceals.
How to misread this concept
- i.
“The average Indian is a real person.”
No one earns the average. The mean is a property of the group, not a biography: mix a village and a boardroom and the average of the room belongs to nobody in it. The typical person is the median, and even the median is a position, not a person.
- ii.
“If the mean rises, most people are better off.”
Not necessarily. In the five-person example the mean rose 8 per cent while four people gained nothing. A rising mean tells you the total grew; who gained is a separate question, answered only by looking at the spread.
- iii.
“Talking about distribution is just politics.”
It is arithmetic first. The mean and the median are two measurements of the same data, and the gap between them is a fact, not an opinion. What to do about the gap is politics. Noticing it is accounting.