Mean, median and mode explained
Mean, median and mode are three ways to describe the centre of a set of numbers. Used together with the range and the standard deviation, they give you a quick, reliable summary of survey ratings, test scores, prices or any other numeric data.
A worked example
Take the values 12, 15, 15, 18, 20, 22 and 25.
- Mean: the sum is 127 and there are 7 values, so the mean is 127 ÷ 7 = 18.14.
- Median: the fourth of the seven sorted values is 18.
- Mode: 15 appears twice and every other value once, so the mode is 15.
- Range: the highest value minus the lowest is 25 − 12 = 13.
Mean or median: which one should I report?
Use the mean when your values are spread fairly evenly, such as ratings on a 1 to 5 scale. Use the median when a few very high or very low values would distort the picture, as with income, order value or time spent. If the mean and the median are far apart, your data is skewed and the median is usually the fairer summary.
When is the mode useful?
The mode shows the most popular answer. It is the best choice for questions where averaging makes little sense, for example “how many people live in your household?” or a rating question where you want to know which score was chosen most.
Sample or population standard deviation?
Use the sample standard deviation when your numbers come from a sample of a larger group, which is the case for almost every survey. It divides by the number of values minus one. Use the population standard deviation only when your numbers cover the entire group you want to describe.
Using this with survey data
Export the answers to a rating or number question, paste the column into the calculator and you have the key figures for your report. To check how precise a percentage from your survey is, continue with the margin of error calculator.
