# Find the Range

In this worksheet, students find the range from both lists and tables

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Statistics

Curriculum subtopic:   Statistics, Analysing Data

Difficulty level:

### QUESTION 1 of 10

When you initially learn about averages, four topics are normally learnt together. Mean, Median, Mode and Range.

While the first three are averages (they give one number to represent the set of data), Range is a measure of spread.

The Range doesn't give a number to represent the others, it gives a measure of how consistent the data is, the smaller the range, the more consistent the data is.

How to find the range.

The range is found by subtracting the smallest piece of data from the largest.

Range = Largest - Smallest

Example 1: Find the range of 4, 8, 7, 5, 9, 4, 8, 3

Largest Value in the list if 9

Smallest Value in the list is 3

Range = 9 - 3 = 6

Example 2: I collect the shoe sizes of a group of people and put it into a frequency table. What is the range of the shoe sizes?

 Shoe Size 3 4 5 6 7 8 9 10 11 12 Number of people 5 7 9 14 21 28 16 6 5 1

We need to be careful here, the largest number that appears in the table is 28, but this is a frequency, not a shoe size. We never use frequency when we are finding the range.

The largest shoe size that appears is 12

The smallest shoe size that appears is 3

The range of shoe sizes is 12 - 3 = 9

To find the range...

The range is a measure of consistency. The...

I am finding the range for 3, 8, 7, 4, 5, 9, 10, 6, 7, 4

A - B = C

What numbers need to go in A, B and C

 Value A B C

Find the range for 6, 16, 14, 8, 10, 18, 20, 12, 14, 8

James says 'The range must be a positive number'

Is this statement...

True

False

What is the range for 2, -1, 0, 3, -1, -2, 1, -4, 2, 3, 0, 2, -2, 0, -3

James and John both play 8 rounds of golf.

James scores are 75, 92, 80, 73, 72, 88, 66, 90

John scores 80, 87, 85, 76, 85, 79, 84, 66

Who is the more consistent player?

James

John

Match the data sets with their ranges

## Column B

6, 10, 3, 4, 3, 6, 2, 9, 3, 4
4
6, 8, 6, 10, 6, 9, 6, 10, 6, 8
26
7, 4, 5, 3, 28, 8, 2, 4, 10, 9
8

The average minimum and maximum temperatures for three cities are shown. Which city has the least consistent climate?

 London Manchester Edinburgh Max 36 32 28 Min -5 -2 -10

London

Manchester

Edinburgh

The average minimum and maximum temperatures for three cities are shown. Which city has the most consistent climate?

 London Manchester Edinburgh Max 36 32 28 Min -5 -2 -10

London

Manchester

Edinburgh

• Question 1

To find the range...

EDDIE SAYS
The range is the difference between the largest and smallest. In Maths difference means subtract.
• Question 2

The range is a measure of consistency. The...

EDDIE SAYS
When we are looking which data is more consistent, if the numbers are all clumped together, the data will be more consistent. This will give a lower (smaller) range.
• Question 3

I am finding the range for 3, 8, 7, 4, 5, 9, 10, 6, 7, 4

A - B = C

What numbers need to go in A, B and C

 Value A B C
EDDIE SAYS
The range is always given by the largest number - the smallest. In this, the largest number is 10 and the smallest number is 3
• Question 4

Find the range for 6, 16, 14, 8, 10, 18, 20, 12, 14, 8

14
EDDIE SAYS
Did you notice that all the numbers were double the numbers from last time? If you double all the numbers in a list, you will double the range.
• Question 5

James says 'The range must be a positive number'

Is this statement...

False
EDDIE SAYS
Most of the time it will be. What about the set of numbers 1,1,1,1,1,1,1? Is this range a positive number?
• Question 6

What is the range for 2, -1, 0, 3, -1, -2, 1, -4, 2, 3, 0, 2, -2, 0, -3

7
EDDIE SAYS
The largest number here is 3 The smallest number is -4 (remember your rules for negatives) The range will be 3 - - 4 What do two negatives together make?
• Question 7

James and John both play 8 rounds of golf.

James scores are 75, 92, 80, 73, 72, 88, 66, 90

John scores 80, 87, 85, 76, 85, 79, 84, 66

Who is the more consistent player?

John
EDDIE SAYS
James has a range of 92 - 66 = 26 John has a range of 87 - 66 = 21 Because John has a lower range, he is more consistent.
• Question 8

Match the data sets with their ranges

## Column B

6, 10, 3, 4, 3, 6, 2, 9, 3, 4
8
6, 8, 6, 10, 6, 9, 6, 10, 6, 8
4
7, 4, 5, 3, 28, 8, 2, 4, 10, 9
26
EDDIE SAYS
A nice and easy one here. All you need to remember is that you need to find the largest and smallest for each data set. Once you have these, find the difference.
• Question 9

The average minimum and maximum temperatures for three cities are shown. Which city has the least consistent climate?

 London Manchester Edinburgh Max 36 32 28 Min -5 -2 -10

London
EDDIE SAYS
Its all nice and easy to find the ranges of the cities (be careful with the negatives) London = 36 - -5 = 41 Manchester = 32 - - 2 = 34 Edinburgh = 28 - - 10 = 38 But, did you notice the question asked for the least consistent? For this, we want the city with the largest range
• Question 10

The average minimum and maximum temperatures for three cities are shown. Which city has the most consistent climate?

 London Manchester Edinburgh Max 36 32 28 Min -5 -2 -10

Manchester
EDDIE SAYS
Its all nice and easy to find the ranges of the cities (be careful with the negatives) London = 36 - -5 = 41 Manchester = 32 - - 2 = 34 Edinburgh = 28 - - 10 = 38 Did you think I just repeated a question? It's vital you read the questions fully. This time, I asked for the most consistent, so we need the one with the lowest range.
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