✅ When to use the mean
Use the mean when the scores are fairly close together. It uses every score, so it gives a fair overall picture. It is pulled by extreme scores, so be careful when one score is far from the rest.
Dealing with Data » Mean, Median, Mode and Range
What you'll learn this session
Study time: 30 minutes
Cambridge spec: 7.9.3, 7.9.4, 7.9.5, 7.9.6
Exam: Paper 1 and Paper 2
- What the mode, median and mean are, and how each is found
- How to choose the best measure of central tendency for a set of data
- What the range shows about how spread out the data is
- How to use these measures in a new scenario
A table can hold a lot of numbers. Researchers often need one number that sums up the whole set. They may also want to know how much the scores differ from each other. This lesson covers both. The spec says candidates will not be expected to find these measures, so the exam asks you to choose, read and interpret them. The small examples here show you where the numbers come from, so that you understand what they mean.
🔒 Unlock Full Course Content
Sign up to access the complete lesson and track your progress!
Unlock This CourseMeasures of central tendency
Key terms:
- Measure of central tendency: a value that shows a typical score in a set of data.
- Mode: the value that appears most frequently in a set of data.
- Median: the value in the middle of a set of data, when the scores are arranged from the smallest to the largest.
- Mean: the value found by adding all the scores and then dividing by the number of scores in the set.
Five pupils each did as many press-ups as they could in one minute. The numbers were 12, 15, 9, 15 and 14.
🔢 Mode
15 appears twice and every other number appears once. The mode is 15 press-ups.
📏 Median
Arrange the numbers: 9, 12, 14, 15, 15. The middle value is 14 press-ups.
➕ Mean
Add them: 12 + 15 + 9 + 15 + 14 = 65. Divide by 5 scores. The mean is 13 press-ups.
Learn this
Mode = most common. Median = middle once the scores are in order. Mean = total divided by the number of scores. If there is an even number of scores, the median is halfway between the two middle ones. For 4, 6, 8, 10 it is 7.
Choosing the right measure
The three measures can give different answers for the same data, so you need to pick the one that best shows a typical score. A question may give you a new scenario and ask which measure is most suitable, and why.
Here is a set of data. Five pupils counted how many text messages they sent in one day: 8, 10, 9, 11 and 72.
The mean is 110 divided by 5, which is 22. But four of the five pupils sent about 10 messages. A mean of 22 is not typical of anyone. The one extreme score of 72 pulled the mean up. The median is 10, which is a much better picture of a typical pupil.
🎯 When to use the median or mode
The median is not pulled by an extreme score, so it is a good choice when there is one. The mode is useful for the most common result, such as the most popular choice in a survey.
The mode can also be used for data that is not numbers. If pupils choose a favourite revision method, the mode is the method chosen most often. You cannot add up methods, so a mean would make no sense.
The range
Key terms:
- Measure of spread: a value that shows how similar or different the values are in a set of data.
- Range: the difference between the highest value and the lowest value in a set of data.
To find the range, take the lowest value away from the highest value. For the press-ups, 15 − 9 = 6 press-ups. For the text messages, 72 − 8 = 64 messages.
The range tells you about spread, not about a typical score. A small range means the scores are close together, so they are similar. A large range means the scores are far apart, so they are very different.
Worked example
Two classes took a quiz out of 20. Class P scored 10, 10, 10 and 10. Class Q scored 2, 18, 3 and 17. What do the means and ranges show? [3 marks]
Both classes have a mean of 10 (1). Class P has a range of 0, so every pupil scored the same (1). Class Q has a range of 16, so the scores were very different, with some pupils doing well and some doing badly (1). The means are the same, but the range shows that the two classes are not alike.
This is why researchers often give a measure of central tendency and a measure of spread together. One tells you what is typical. The other tells you how much the scores vary. You may be asked to read both from a table, or to use them to compare two conditions in a study. The results can also be shown on a bar chart, which is covered in the next lesson, Bar Charts.
Common mistakes
Common mistakes
- Finding the median without putting the scores in order first. Always arrange them from the smallest to the largest.
- Saying the mean is always the best measure. If there is an extreme score, the median is usually better.
- Muddling the range with the highest score. The range is the highest minus the lowest.
- Saying a large range means a high mean. The range shows spread, not whether the scores are high or low.
- Giving an answer with no reason. Say why, for example: "the median, because one extreme score pulls the mean up".
Exam-style question
A researcher asked five pupils to remember a list of words. The numbers of words recalled were 5, 8, 6, 8 and 18. The mean is 9 and the median is 8.
(a) The mode of this data is 8. State what is meant by the mode. [1 mark]
(b) The mean is higher than the median. Explain why. [1 mark]
(c) A second group of pupils had a range of 3 and the first group had a range of 13. What does this tell the researcher about the two groups? [2 marks]
Model answer
(a) The value that appears most often in a set of data (1).
(b) The extreme score of 18 pulls the mean up (1).
(c) The second group's scores were closer together, or more similar (1). The first group's scores were more spread out, or more different from each other (1).
Exam tip
When asked to compare a mean with a median, look for an extreme score in the data. Name it, and say it pulls the mean up or down.