Mean, Median & Mode Calculator

The three averages, mean, median and mode, each summarise a data set differently. The mean is the sum divided by the count, so it uses every value but gets dragged around by outliers. The median is the middle value once the numbers are sorted, and it shrugs those outliers off. The mode is the most frequent value, and it is the only one of the three that means much for categorical or discrete data. Take the set [2, 4, 4, 5, 8]. Its mean is 23/5 = 4.6, its median is 4 because that value sits in the middle, and its mode is 4 as well because it appears twice.

This calculator finds all three plus the range, which is the highest value minus the lowest. It sorts your data, marks the median position and identifies every mode, since a set can have several or none at all, and it shows step-by-step working for each measure. That working matters, because the three numbers can disagree sharply and knowing which one a headline is quoting is often the whole story.

Outliers are where the mean falls apart. Line up salaries of 25k, 28k, 30k, 35k, 40k and 250k and the mean lands at 68k, higher than five of the six people earn. The median is 32.5k, which describes the group honestly, and there is no mode because every value is unique. The shape of the distribution predicts the gap. Positive skew, with a long right tail, is normal for incomes, property and sales, and it leaves the median below the mean. Negative skew, where a ceiling bunches values at the top as exam scores capped at 100% do, works the other way. Only symmetric data such as heights and weights brings the three averages close together.

Choosing between them comes down to the shape of the data and the question being asked. The median suits incomes and property prices, where a small number of very large values would otherwise set the tone. The mean suits exam scores, which sit close enough to a normal distribution. The mode suits survey answers on a Likert scale of 1-5, where the most common opinion is the point of the exercise. Where the data carries genuine outliers, as sales and salary figures do, a median with the interquartile range describes it better than a mean with the standard deviation. UK government statistics generally follow that rule for incomes and property values.

Published figures show the gap in practice. UK median household income in 2024 was £35,000 against a mean of £40,000, the mean inflated by high earners. The median UK house price in 2026 is £290,000 while the mean is £370,000, skewed by London properties above £1M. Median weekly earnings for full-time work were £692 in April 2024, and median full-time gross hourly pay was £17.43. Mean private-sector rent runs at £1,200 a month across the UK and £1,750 in London.

Once the difference is clear, the wording used in news reports starts to matter. An 'average UK salary' is always worth checking, because the mean and the median tell different stories. A 'median worker' is the 50th percentile, with half earning more and half less. An 'average household pays' figure for council tax is usually a mean, pulled up by expensive boroughs, whereas an average NHS waiting time is often quoted as a median because outliers distort it. Standard deviation, where it appears, describes spread rather than position. The ONS at gov.uk/ons uses medians and the interquartile range for most income and wealth statistics, while tabloid averages tend to be whichever measure flatters the argument.