Average wealth and the household in the middle

Average net worth can rise while most households in the group see no change. The mean and median describe different features of the same figures.

The mean adds the net worth figures and divides by the number of households. The median finds the middle after ordering them from lowest to highest. With an odd number of observations, one value occupies that middle position; with an even number, take the arithmetic mean of the two middle values. NIST explains these two measures of location.

Five households, two answers

Consider five invented households at one date. Each figure is that household's total assets less its total debts, in US dollars, measured on the same basis. Every household counts once. These are the complete five observations in the example, not a sample offered as evidence about a country.

Invented household net worth, ordered from lowest to highest

Scroll across to see both columns. Use the arrow keys when the table is focused.

The combined net worth is $2 million. Divide by five and the mean is $400,000. Four of the five households have less than that amount; none has exactly $400,000.

The median is $70,000, the third value. Two households are below it and two are above it. It identifies the middle of this ordered group, rather than dividing the group's wealth into two equal amounts.

The Census Bureau's wealth definitions distinguish these calculations and explain why a small number of large wealth figures can pull the mean above the median. A high observation need not be an error to have that effect.

A rising average, with four unchanged households

Keep A through D unchanged. Suppose only E's net worth increases, from $1,760,000 to $2,760,000. The group's total is now $3 million and its mean is $600,000, a 50 percent increase.

The median remains $70,000. The statement that average net worth rose by half is correct under these assumptions. Saying that each household became 50 percent wealthier would be wrong. Four balances did not move.

The example does not say how E's increase arose. A changed asset valuation could raise it without money being received. An increase in net worth is not automatically income, saving or bank cash. Those are separate questions about the form of wealth.

The same two summaries can hide other changes

Return to the original five figures. For a separate comparison, replace them with $40,000, $60,000, $70,000, $120,000 and $1,710,000. The total is still $2 million, the mean still $400,000 and the median still $70,000.

Three households now have more than in the original list and one has less. Both summary measures are unchanged. Reporting only their stability would miss those movements.

The median is useful for locating the middle. The mean connects the combined total to the number counted. Neither is a substitute for looking across the distribution when the question concerns who gained or lost.

Read the unit before the comparison

Before comparing published figures, check whether they describe individuals, households or another defined unit. Keep the date, currency, assets included and treatment of debt consistent. A household figure cannot be compared directly with one person's figure just because both are labeled net worth.

The five-household arithmetic gives each observation equal weight. A population survey can assign different weights to sampled observations; its published estimates need the survey's methods. This miniature example does not reproduce a national wealth estimate.

When a headline says average wealth rose, ask which average, whose wealth and which period. Then ask what evidence shows the changes across that group. A larger mean can be a real increase in combined wealth without describing an improvement experienced by most of the people counted.

For the choices and responsibilities behind one founder's business life, read the opening of Vijay Sheth's Infinite Upside: Building Wealth With Room to Live. Choose an edition.