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Maths · Statistics & Probability

Mean, median, mode, range

Compute averages and range from a data set or table.

Not startedCAMBRIDGE · 7CBSE · VIIIB · MYP-1

What Are Averages and Range?

Averages help us describe a typical value in a data set. Range tells us how spread out the data is. The mean is the sum of all values divided by how many there are. The median is the middle value when data is ordered. The mode is the most common value. Range is largest minus smallest.

Finding the Mean

To find the mean, add up all the numbers in your data set. Then divide this total by how many numbers you have. For example, the mean of 3, 7, and 8 is 18 ÷ 3 = 6.

Finding the Median

First, put the numbers in order from smallest to largest. The median is the middle number. If there are two middle numbers, find their mean. For 2, 5, 9, the median is 5.

Finding the Mode and Range

The mode is the number that appears most often. A data set can have one mode, several modes, or no mode at all. Range shows spread: subtract the smallest value from the largest. For 3, 7, 7, 10, the mode is 7 and range is 7.

Worked examples

  1. 1. Find the mean, median, mode and range of: 4, 8, 6, 4, 10, 3

    1. Mean: Add all values: 4 + 8 + 6 + 4 + 10 + 3 = 35. Divide by 6: 35 ÷ 6 = 5.83 (to 2 d.p.)
    2. Median: Order the data: 3, 4, 4, 6, 8, 10. Two middle values are 4 and 6. Median = (4 + 6) ÷ 2 = 5
    3. Mode: 4 appears twice, all others once. Mode = 4
    4. Range: 10 − 3 = 7

  2. 2. A table shows test scores: 15, 18, 12, 15, 20. Find the mean and range.

    1. Mean: Add scores: 15 + 18 + 12 + 15 + 20 = 80. Divide by 5: 80 ÷ 5 = 16
    2. Range: Largest is 20, smallest is 12. Range = 20 − 12 = 8

Try it yourself

Find the median of: 7, 3, 9, 5, 11

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