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What is mean, median and mode?

The mean, median and mode are three averages: the arithmetic average, the middle value in order, and the most frequent value.

Mean, median and mode explained

The mean uses every data value and so is affected by outliers. The median ignores extremes and is the better summary for skewed data such as house prices or salaries.
The mode is the only average that works for categorical data — favourite colour, most-sold size — and a data set can have more than one mode or none at all.

Key formula

xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}

Worked example

For 3,5,5,8,1003, 5, 5, 8, 100: mean =24.2= 24.2, median =5= 5, mode =5= 5. The median describes this data far better.

Examiner tip

When a question asks which average is most appropriate, name the average and justify it with the presence or absence of outliers.

Mean, median and mode: common questions

Which average is best?
It depends on the data. Use the median for skewed data with outliers, the mean for symmetric data, and the mode for categories.
How do I find the mean from a frequency table?
Multiply each value by its frequency, add the products, then divide by the total frequency.

Related terms

Standard deviation

Standard deviation measures the average spread of data values about the mean — a small value means tightly clustered data.

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