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GCSE Maths · Topic guide

Averages

Averages summarise a set of data with a single typical value. The three types are the mean (total divided by how many values there are), the median (the middle value when data is ordered), and the mode (the most frequently occurring value). The range measures how spread out the data is - the largest value minus the smallest value.

Grade 3-4 (Foundation)Topic 2.14
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Before you start

No specific prerequisites - this is a good place to start.

Method

  1. To find the mean, add up all the values and divide by how many values there are.
  2. To find the median, put the values in order from smallest to largest, then pick the middle value, or the mean of the two middle values if there is an even number of values.
  3. To find the mode, identify the value that appears most often; there can be more than one mode, or none at all.
  4. To find the range, subtract the smallest value from the largest value.
  5. When comparing two data sets, compare an average - usually the mean or median - alongside the range, to describe both typical size and consistency.

Worked example

Find the mean, median, mode and range of the data set: 4, 7, 4, 9, 6, 4, 8.

  1. Mean: add the values, 4+7+4+9+6+4+8 = 42, then divide by 7 (how many values): 42 divided by 7 = 6.
  2. Median: order the values, 4, 4, 4, 6, 7, 8, 9. With 7 values, the middle (4th) value is 6.
  3. Mode: 4 appears three times, more than any other value, so the mode is 4.
  4. Range: largest value (9) minus smallest value (4) = 5.

Practice questions

Try each question, then tap to reveal the answer.

Exam-style questions

Written in the style of a GCSE exam paper, with a full mark scheme.

Q1[3 marks]

The test scores of 6 students are 12, 15, 18, 12, 20 and x. The mean score is 16. Work out the value of x.

Q2[4 marks]

Two runners' race times in seconds over 5 races are: Runner A: 12.1, 12.5, 12.0, 12.8, 12.6. Runner B: 12.3, 12.4, 12.3, 12.5, 12.5. Compare the two runners' performance using the mean and the range.

Next topics

Cumulative FrequencyBox Plots

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