Understanding numbers

Averages

Mean – The mean is calculated by dividing the sum of the observations by the number of observations. Very high or very low observations can have a lot of influence on the result.

Median – The median is calculated by identifying the exact middle point in a set of observations. When the observations are ranked from lowest to highest, the median is the value in the exact middle of the observed values.

Uses - The Office for National Statistics’ preferred measure of average earnings is the median as it is less affected by a relatively small number of very high earners than the mean.

Distribution of Data

Percentile – data divided in 100 equal parts, 1%

Deciles – data divided into 10 equal parts, 10%

Quintile – data divided into 5 equal parts, 20%

Quartile – data divided into 4 equal parts, 25%

Uses - In the Index of Multiple Deprivation, Decile 1 represents the most deprived 10% (or decile) of small areas in England, and Decile 10 represents the least deprived 10%.

What Is an IMD Decile? | IMD 2025 Explainer

Index Numbers

Base value is often set to 100.

Uses - Show relative change over time (e.g. prices, inflation) or relative to a geography (e.g. UK=100)

Percentages

Percentage = a proportion out of 100 (e.g. 20% = 20/100).

Uses -  Useful for comparing groups of different sizes.

Percentage change = The difference divided by the original × 100. Distinguish percentage points vs % change (e.g. 2% → 3% = +1 percentage point, but +50% increase).

Uses - Useful for looking at change over time.

Rounding

Rounding to the nearest 10

To round a number to the nearest 10, look at the units digit. If the units digit is 5 or more, round up. If the units digit is 4 or less, round down.

The last digit in 456 is 6. So round it up to 460.
The last digit of 452 is 2. So round it down to 450.
485 ends in a 5. Round a 5 up. So 485 rounds up to 490.

 Uses - Simplify communications and prevent disclosure of small numbers.

Advanced Concepts

Confidence Intervals

Confidence intervals are usually presented as a range around a central average or estimate; they are the standard way of expressing the statistical accuracy of an estimate based on a survey or sampling (that is, measuring something for a sample of the entire population rather than for the whole population directly). Wider confidence intervals mean the estimate value is less likely to be accurate.

If an estimate is based on sampling, the 95% confidence interval describes the range within which the true population value should fall 95% of the time when taking different samples from the same population.

Uses - Confidence intervals are used to honestly communicate uncertainty in data.