Mean, median and mode

01Why this matters

Different summaries reveal different things. A few very high values can shift the mean while leaving the median relatively stable.

02See it

2 · 3 · 3 · 4 · 8sum 20 / count 5mean 4median & mode 3

Read left to right: 2 · 3 · 3 · 4 · 8 → sum 20 / count 5 → mean 4 → median & mode 3. Each panel connects one part of the example.

03Understand it

The mean is the total divided by the number of values. The median is the middle of an ordered list. The mode is the most frequent value.

To find the mean, include every value and divide by the count, not by the largest value. To find the median, sort first; with an even count, average the two central values. A dataset may have several modes or none. Always consider what the data describes and how it was collected.

04Guided example

Find the mean, median and mode of 2, 3, 3, 4, 8.

The total is 2 + 3 + 3 + 4 + 8 = 20. Divide by 5 values: mean = 4.
The list is already ordered. The third value is central: median = 3.
The value 3 occurs twice, more than any other: mode = 3.

05Try it

06Practise it

07Use it in the real world

For journey times of 10, 11, 11, 12 and 36 minutes, the mean is 16 minutes but the median is 11. The delayed journey affects the mean strongly.

Go a little deeper

The range is maximum minus minimum. It describes spread but depends only on the two extreme observations, so it does not describe the shape of a distribution.

08Quick check

09Summary

The mean is the total divided by the number of values. The median is the middle of an ordered list. The mode is the most frequent value. The value 3 occurs twice, more than any other: mode = 3.

Before moving on, explain the worked example in your own words. Use the hint on any question you want to revisit.

10Key idea

mean = sum of values / number of values

The mean has the same units as the values; the count is unitless and must be positive.

sum = mean × count

Find this in the formula library →