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GCSE Maths / Edexcel

Averages and range

Find the mean, median, mode and range from a list of numbers, then choose the correct average in a GCSE-style context.

Probability and StatisticsFoundation and HigherGrades 2 to 5Focused skill

Curriculum path: GCSE Maths > Edexcel > Probability and Statistics > Averages and range

Pearson Edexcel GCSE Maths Statistics S4: use measures of central tendency and spread to interpret and compare data.

Practise this topicUpload your answerAsk AI to explain thisTry exam-style questions
Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

An average is a number that represents a typical value in a data set. The three GCSE averages are mean, median and mode.

The mean is found by adding all the values and dividing by how many values there are. It uses every number, so one very large or very small value can pull the mean away from the middle.

The median is the middle value after the data has been put in order. If there are two middle values, add them and divide by 2.

The mode is the value that appears most often. A data set can have one mode, more than one mode, or no mode.

The range is not an average. It measures spread: range = largest value - smallest value. A large range means the data is more spread out.

Foundation students should slow down at the ordering step. Many lost marks come from finding the median before putting the numbers in order.

Key ruleMean = total / number of values. Range = largest value - smallest value.

Diagram guide

478813median is middle valuerange = 13 - 4ordered datamean uses all values
Averages from a listOrder the data first, identify the middle value for the median, then use the largest and smallest values for the range.

Worked examples

Find all four measures

Find the mean, median, mode and range of 4, 7, 8, 8, 13.

478813median is middle valuerange = 13 - 4ordered datamean uses all values
Ordered listThe numbers are already in order, so the middle value is easy to spot.
  1. There are 5 values.
  2. Mean = (4 + 7 + 8 + 8 + 13) / 5 = 40 / 5 = 8.
  3. The middle value is 8, so the median is 8.
  4. 8 appears most often, so the mode is 8.
  5. Range = 13 - 4 = 9.

Answer: Mean = 8, median = 8, mode = 8, range = 9

Median with an even number of values

Find the median and range of 12, 3, 9, 5.

478813median is middle valuerange = 13 - 4ordered datamean uses all values
Averages from a listOrder the data first, identify the middle value for the median, then use the largest and smallest values for the range.
  1. Put the numbers in order: 3, 5, 9, 12.
  2. There are two middle values, 5 and 9.
  3. Median = (5 + 9) / 2 = 7.
  4. Range = 12 - 3 = 9.

Answer: Median = 7, range = 9

Choose the best average

A shoe shop records sizes 4, 5, 5, 6, 6, 6, 7. Which average best shows the most popular shoe size?

478813median is middle valuerange = 13 - 4ordered datamean uses all values
Averages from a listOrder the data first, identify the middle value for the median, then use the largest and smallest values for the range.
  1. The phrase most popular means the value that happens most often.
  2. The mode is the value that appears most often.
  3. 6 appears three times, more than any other size.

Answer: The mode, which is size 6

Common mistakes

  • Finding the median before putting the values in order.
  • Dividing by the largest number instead of by the number of values when finding the mean.
  • Calling the range an average.
  • Forgetting that a data set can have no mode if every value appears once.
  • Using the mode when the question asks for the mean because the word average is used casually.

Quick exercise

Try these before moving to the exam-style questions.

  1. Find the mean of 2, 6, 7, 9.
    478813median is middle valuerange = 13 - 4ordered datamean uses all values
    Averages from a listOrder the data first, identify the middle value for the median, then use the largest and smallest values for the range.
  2. Find the median of 10, 4, 8, 3, 5.
    478813median is middle valuerange = 13 - 4ordered datamean uses all values
    Averages from a listOrder the data first, identify the middle value for the median, then use the largest and smallest values for the range.
  3. Find the mode of 1, 4, 4, 6, 9, 9, 9.
    478813median is middle valuerange = 13 - 4ordered datamean uses all values
    Averages from a listOrder the data first, identify the middle value for the median, then use the largest and smallest values for the range.
  4. Find the range of 14, 6, 11, 3.
    478813median is middle valuerange = 13 - 4ordered datamean uses all values
    Averages from a listOrder the data first, identify the middle value for the median, then use the largest and smallest values for the range.
  5. A set has values 2, 3, 4, 100. Which average is affected most by 100?
    478813median is middle valuerange = 13 - 4ordered datamean uses all values
    Averages from a listOrder the data first, identify the middle value for the median, then use the largest and smallest values for the range.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationNon-calculator3 marks

Find the mean, median and range of 5, 9, 2, 6, 8.

478813median is middle valuerange = 13 - 4ordered datamean uses all values
Averages from a listOrder the data first, identify the middle value for the median, then use the largest and smallest values for the range.
meanmedianrangefoundation statistics
Standard exam styleFoundation and HigherEither4 marks

The numbers 3, 7, 8, 10, x have a mean of 8. Work out the value of x.

478813median is middle valuerange = 13 - 4ordered datamean uses all values
Averages from a listOrder the data first, identify the middle value for the median, then use the largest and smallest values for the range.
meanmissing valuemethod marks
ChallengeFoundation and HigherEither4 marks

Class A has a median score of 18 and a range of 12. Class B has a median score of 18 and a range of 4. Compare the two classes.

478813median is middle valuerange = 13 - 4ordered datamean uses all values
Averages from a listOrder the data first, identify the middle value for the median, then use the largest and smallest values for the range.
compare distributionsmedianrange