How to Calculate Mean, Median and Mode

The mean is the total divided by how many values there are. The median is the middle value once the data is sorted. The mode is the value that appears most often. The range, largest minus smallest, measures spread. Each "average" answers a slightly different question.

Example data

We will use: $3, 7, 7, 2, 9, 4$.

Mean

Add the values and divide by the count:

Median

1. Sort the data: $2, 3, 4, 7, 7, 9$.
2. There are 6 values (even), so the median is halfway between the 3rd and 4th:

With an odd number of values, the median is the single middle value.

Mode

$7$ appears twice and everything else once, so the mode is $7$.

A data set can have two modes (bimodal), such as $12, 15, 11, 15, 19, 11$, where both $11$ and $15$ appear twice. If every value appears equally often, there is no mode.

Range

Which average should I use?

Example of an outlier: salaries of 25, 27, 28, 30 and 190 (thousands). The mean is 60, but the median of 28 better describes a typical salary.

Another worked example

$4, 8, 15, 16, 23, 42$ has sum $108$ and count $6$, so the mean is $108 \div 6 = 18$. The median is $\frac{15 + 16}{2} = 15.5$. There is no mode.

Common mistakes

• Finding the "middle" of unsorted data.
• Dividing by the wrong count, for example forgetting a zero value.
• Saying the mode is how many times a value appears, rather than the value itself.

Practice questions

For $5, 1, 8, 3, 8, 6, 4$ find:

1. The mean.
2. The median.
3. The mode and range.

Answers: 1) $5$ 2) $5$ 3) Mode $8$, range $7$

Paste any list into the mean, median and mode calculator to see the sorted data with the mean and median marked on a chart, or use the average calculator for weighted averages. To measure spread properly, read standard deviation explained.

Frequently asked questions

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