Percent of what, and compared with when?

“Cases rose 50%” may sound more informative than it is. Ask: how many cases, among whom, over what period, and counted in the same way?

The numerator is the quantity being counted. The denominator is what it is divided by. Changing the denominator changes the question.

Percentage and percentage point are different

In a hypothetical example, a share rises from 20% to 25%. That is an increase of 5 percentage points. Relative to the original 20%, it is a 25% increase: (25 − 20) / 20 × 100.

Neither calculation says that the underlying number of people rose by 25% unless the population and other necessary conditions support that conclusion.

Counts and rates can tell different stories

Imagine two hypothetical towns. Town A records 100 incidents among 100,000 residents. Town B records 150 among 300,000 residents. A has 100 recorded incidents per 100,000 residents; B has 50.

B has the larger count and the lower population rate. Before treating that rate as a risk comparison, you would still need compatible definitions, reporting practices and an appropriate population measure. Arithmetic cannot repair incomparable inputs.

A real example: unemployment

MoSPI defines the unemployment rate using unemployed people as a share of the labour force, not the whole population. Its worker population ratio uses employed people as a share of the relevant population. Confusing those denominators produces a different statistic. 1

This is why you should not read an unemployment rate as “the share of all Indians without a job”. Preserve the survey's age group, reference period and activity-status measure as well.

Read the axis and the missing values

On a chart, check whether the vertical scale begins at zero, whether time intervals are equal and whether a line connects missing observations as though they were measured. A truncated scale can be legitimate, but it needs to be obvious enough not to disguise the size of a change.

Treat “not reported” as unknown, not zero. Do not add percentages from different populations or average rates without appropriate weights.

A useful numerical caption answers: what was counted, out of what, where, when, in which unit and by what method? If those answers are missing, hold the interpretation until you find them.