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Learn Index · Data Management and Statistics Grade 6–8

Mean, median, and mode

Three ways to describe the centre of a data set.

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Describing the "typical" value

Mean, median and mode are measures of central tendency. Each gives one number that represents a whole data set, but in a different way.

Mean

The mean is what most people call the average.

Mean = sum of values ÷ number of values

Example: Test scores 72, 85, 90, 68, 85

  • Sum = 400
  • Count = 5
  • Mean = 400 ÷ 5 = 80

The mean "shares out" the total equally.

Median

The median is the middle value once the data is in order.

Example: 68, 72, 85, 85, 90 → median = 85

With an even number of values, the median is the mean of the two middle values.

Example: 4, 7, 9, 12 → (7 + 9) ÷ 2 = 8

Mode

The mode is the most frequent value.

  • 68, 72, 85, 85, 90 → mode = 85
  • A set can have no mode (all different) or more than one mode (two values tie).
  • The mode is the only measure that works for non-number data, like "favourite colour".

Which one to use?

Situation Best measure Why
Data without extreme values Mean Uses every value
Data with an outlier Median Not pulled by extremes
Categories (colours, brands) Mode Only one that works
Most popular shoe size to stock Mode Most common

The effect of outliers

Salaries at a small company (in thousands): 40, 42, 45, 48, 250

  • Mean = 425 ÷ 5 = 85
  • Median = 45

The one large salary drags the mean up. The median better describes a typical worker.

Finding a missing value

Example: The mean of 4 numbers is 15. Three are 12, 18 and 10. Find the fourth.

  • Total must be 4 × 15 = 60
  • 12 + 18 + 10 = 40
  • Fourth = 20

Worked examples

Example 1: Find the mean, median and mode of 3, 7, 7, 2, 6.

  • Ordered: 2, 3, 6, 7, 7
  • Mean = 25 ÷ 5 = 5
  • Median = 6
  • Mode = 7

Example 2: Median of 15, 9, 22, 11, 30, 18?

Ordered: 9, 11, 15, 18, 22, 30 → (15 + 18) ÷ 2 = 16.5.

Example 3: Which measure suits "most common T-shirt size sold"?

Mode.

Common mistakes

  • Finding the median without ordering the data first.
  • Forgetting to include zeros when calculating the mean.
  • Saying the mode is the frequency (how often) instead of the value.

Try it yourself

  1. Mean of 10, 12, 14, 16, 18
  2. Median of 5, 1, 9, 3
  3. Mode of 2, 4, 4, 6, 6, 6, 8
  4. The mean of 5 numbers is 20. Four are 18, 22, 15, 25. Find the fifth.
  5. House prices include one mansion. Mean or median?

Answers: 1) 14 2) 4 3) 6 4) 20 5) median

Quick recap

  • Mean = sum ÷ count; median = middle value; mode = most frequent.
  • Outliers affect the mean much more than the median.
  • Choose the measure that best fits the data.