 # Interquartile Ranges

In this worksheet, students calculate the interquartile range of a set of data. Key stage:  KS 4

Curriculum topic:  Statistics

Difficulty level:   ### QUESTION 1 of 10

The upper quartile of a set of data is the median of the higher half of the data.

The lower quartile of a set of data is the median of the lower half of the data.

The interquartile range is the difference between the upper and lower quartiles and gives an indication of the statistical dispersion or spread of the given data.

Example

Find the interquartile range of the following set of data:

3     4     5     5     7     7     7     8     9     10

Answer

Divide the data into two halves.

3     4     5     5     7     7     7     8     9     10

The lower quartile is the median of the blue lower half.

3     4     5     5     7

The lower quartile is 5.

The upper quartile is the median of the red higher half.

7     7     8     9     10

The upper quartile is 8.

The interquartile range is 8 - 5 = 3.

Find the interquartile range of the following set of data:

2     4     6     8     9     10

Find the interquartile range of the following set of data:

1     2     6     9     10     19

Find the interquartile range of the following set of data:

2     4     6    6     7     7     7     8     9     10

Find the interquartile range of the following set of data:

1     2     6     9     10     19     21

Find the interquartile range of the following set of data:

1     2     6     9     10     19     21     23

Find the interquartile range of the following set of data:

1     2     3     9     10     19     20     23

Find the interquartile range of the following set of data:

2     3     4     9     10     13     20     23

Find the interquartile range of the following set of data:

2     5     7     9     10     13     18     27

Find the interquartile range of the following set of data:

5     3     7     12     10     8     20     21

Find the interquartile range of the following set of data:

12     4     17     12     10     18     2     31    13

• Question 1

Find the interquartile range of the following set of data:

2     4     6     8     9     10

CORRECT ANSWER
5
EDDIE SAYS
Upper Quartile is the Median of 8, 9, 10, which is 9
Lower Quartile is the Median of 2, 4, 6, which is 4
Interquartile Range is 9 - 4 = 5
• Question 2

Find the interquartile range of the following set of data:

1     2     6     9     10     19

CORRECT ANSWER
8
EDDIE SAYS
Upper Quartile is the Median of 9, 10, 19 which is 10
Lower Quartile is the Median of 1, 2, 6,which is 2
Interquartile Range is 10 - 2 = 8
• Question 3

Find the interquartile range of the following set of data:

2     4     6    6     7     7     7     8     9     10

CORRECT ANSWER
2
EDDIE SAYS
Upper Quartile is the Median of 7, 7, 8, 9, 10, which is 8
Lower Quartile is the Median of 2, 4, 6, 6, 7, which is 6
Interquartile Range is 8 - 6 = 2
• Question 4

Find the interquartile range of the following set of data:

1     2     6     9     10     19     21

CORRECT ANSWER
17
EDDIE SAYS
Upper Quartile is the Median of 10, 19, 21 which is 19
Lower Quartile is the Median of 1, 2, 6,which is 2
Interquartile Range is 19 - 2 = 17
• Question 5

Find the interquartile range of the following set of data:

1     2     6     9     10     19     21     23

CORRECT ANSWER
16
EDDIE SAYS
Upper Quartile is the Median of 10, 19, 21, 23, which is 20
Lower Quartile is the Median of 1, 2, 6, 9, which is 4
Interquartile Range is 20 - 4 = 16
• Question 6

Find the interquartile range of the following set of data:

1     2     3     9     10     19     20     23

CORRECT ANSWER
17
EDDIE SAYS
Upper Quartile is the Median of 10, 19, 20, 23, which is 19.5
Lower Quartile is the Median of 1, 2, 3, 9, which is 2.5
Interquartile Range is 19.5 - 2.5 = 17
• Question 7

Find the interquartile range of the following set of data:

2     3     4     9     10     13     20     23

CORRECT ANSWER
13
EDDIE SAYS
Upper Quartile is the Median of 10, 13, 20, 23, which is 16.5
Lower Quartile is the Median of 2, 3, 4, 9, which is 3.5
Interquartile Range is 16.5 - 3.5 = 13
• Question 8

Find the interquartile range of the following set of data:

2     5     7     9     10     13     18     27

CORRECT ANSWER
9.5
EDDIE SAYS
Upper Quartile is the Median of 10, 13, 18, 27, which is 15.5
Lower Quartile is the Median of 2, 5, 7, 9, which is 6
Interquartile Range is 15.5 - 6 = 9.5
• Question 9

Find the interquartile range of the following set of data:

5     3     7     12     10     8     20     21

CORRECT ANSWER
10
EDDIE SAYS
First place the numbers in order to get:
3, 5, 7, 8, 10, 12, 20, 21
Upper Quartile is the Median of 10, 12, 20, 21, which is 16
Lower Quartile is the Median of 3, 5, 7, 8, which is 6
Interquartile Range is 16 - 6 = 10
• Question 10

Find the interquartile range of the following set of data:

12     4     17     12     10     18     2     31    13

CORRECT ANSWER
10.5
EDDIE SAYS
First place the numbers in order to get:
2, 4, 10, 12, 12, 13, 17, 18, 31

Upper Quartile is the Median of 13, 17, 18, 31, which is 17.5
Lower Quartile is the Median of 2, 4, 10, 12, which is 7
Interquartile Range is 17.5 - 7 = 10.5
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

### What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Start your £1 trial