7.1 Mean and Range

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: working out the mean and the range, and using them to compare data. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

• Calculate the mean of a set of data, including decimals and negative numbers
• Find the range of a set of data and explain what it tells you
• Use the total to find a missing value when the mean is known
• Compare two sets of data using the mean and the range

Key words

• Data: A collection of values, such as test scores or temperatures.
• Average: One value that represents a whole set of data. The mean is one type of average.
• Mean: Add up all the values, then divide by how many values there are.
• Range: Largest value − smallest value. It measures how spread out the data is.
• Consistent: Values that are close together, so the range is small.

Finding the mean

The mean shares the total out equally. Add every value (include zeros!), then divide by the number of values.

Key fact: Mean = total of the values ÷ number of values

Worked example: books read

Six pupils read 3, 7, 2, 5, 8 and 5 books over the summer. Find the mean.
Total = 3 + 7 + 2 + 5 + 8 + 5 = 30. There are 6 values.
Mean = 30 ÷ 6 = 5

Answer: 5 books

Worked example: decimals

Four parcels weigh 1.6 kg, 2.3 kg, 0.9 kg and 3.2 kg. Find the mean weight.
Total = 1.6 + 2.3 + 0.9 + 3.2 = 8.0 kg. 8.0 ÷ 4 = 2

Answer: 2 kg

The mean does not have to be one of the values, and it does not have to be a whole number.

Finding the range

The range is not an average. It tells you how spread out the values are. A small range means the data is consistent.

Key fact: Range = largest value − smallest value

Worked example: temperatures

The midnight temperatures in a town on five nights were 4 °C, −2 °C, 7 °C, 1 °C and −5 °C. Find the range.
Largest = 7. Smallest = −5.
7 − (−5) = 7 + 5 = 12

Answer: 12 °C

Always give the range as a single number with units, not “from −5 to 7”.

Using the total to find missing values

If you know the mean and how many values there are, you can find the total: total = mean × number of values.

Worked example: a missing value

The mean of four numbers is 12. Three of the numbers are 10, 15 and 9. Find the fourth number.
Total of all four = 12 × 4 = 48. Total of the three = 10 + 15 + 9 = 34.
Fourth number = 48 − 34 = 14

Answer: 14

Worked example: a new value changes the mean

The mean height of 3 plants is 20 cm. A fourth plant is added and the mean becomes 22 cm. How tall is the fourth plant?
Old total = 3 × 20 = 60 cm. New total = 4 × 22 = 88 cm.
Fourth plant = 88 − 60 = 28 cm

Answer: 28 cm

Comparing two sets of data

To compare, make one comment about the average and one comment about the spread, both in context.

• Team A; 1 12; 2 15; 3 9; 4 14; 5 10; Mean 12; Range 6
• Team B; 1 5; 2 20; 3 11; 4 18; 5 6; Mean 12; Range 15

Worked example: which team is better?

Team A: total 60, mean 60 ÷ 5 = 12, range 15 − 9 = 6.
Team B: total 60, mean 60 ÷ 5 = 12, range 20 − 5 = 15.
The means are the same, so on average both teams score the same. Team A has the smaller range.

Answer: Same average score; Team A is more consistent (smaller range)

Exam tip: A smaller range means more consistent. A bigger mean means higher on average – that is only “better” if high values are good.

Common mistakes

• Dividing by the wrong number of values, or forgetting to count a value of 0.
• Giving the range as “9 to 15” instead of working out 15 − 9 = 6.
• Getting the range wrong with negative numbers: 7 − (−5) is 12, not 2.
• Comparing only the means and forgetting to comment on the range (or the other way round).
• Not writing the comparison in context, for example “Team A is more consistent”.

Revision questions

Try these, then check your answers below each one.

Question 1. Find the mean of 6, 9, 4, 11, 5

Answer: 7

Working: 6 + 9 + 4 + 11 + 5 = 35 and 35 ÷ 5 = 7.

Question 2. Find the range of 18, 7, 25, 13, 9

Answer: 18

Working: 25 - 7 = 18.

Question 3. The midday temperatures (°C) on five days were −4, 3, −1, 6, 1. Find the range.

Answer: 10 °C

Working: 6 - (-4) = 6 + 4 = 10 °C.

Related lessons

• Previous lesson: 6.6 Geometrical Problems
• Next lesson: 7.2 Mode, Median and Range
• In this chapter: 7.3 Types of Average
• In this chapter: 7.4 Estimating the Mean
• In this chapter: 7.5 Sampling

Continue in the full course

This lesson is section 7.1 (EGCMF0701) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.