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Lower and Upper Quartiles

In this worksheet, students must calculate the upper and lower quartiles of a set of data.

'Lower and Upper Quartiles' worksheet

Key stage:  KS 4

Curriculum topic:  Statistics

Curriculum subtopic:  Interpret, Analyse and Compare the Distributions of Data Sets from Univariate Empirical Distributions

Difficulty level:  

down

Worksheet Overview

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.

 

Example 1

Find the lower quartile 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.

 

Example 2

Find the upper quartile of the following set of data:

3     4     5    5     7     7     7     8     9

 

Answer

There are an odd number of numbers so divide the data into two halves, ignoring the middle number, 7.

3     4     5    5     7     7     7     8     9

 

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

7     7     8     9

 

The median here is the mean of 7 and 8.

The upper quartile is.

Find the upper quartile of the following set of data:

 

3     4     5    5     7     7     7     8     9     10

Find the upper quartile of the following set of data:

 

5     7     7     7     8     9     10

Find the lower quartile of the following set of data:

 

5     7     7     7     8     9     10

Find the lower quartile of the following set of data:

 

5     7     8     9     10

Find the upper quartile of the following set of data:

 

5     7     8     9     10

Find the upper quartile of the following set of data:

 

7     8     9     10     12     14

Find the lower quartile of the following set of data:

 

7     8     9     10     12     14

Find the upper quartile of the following set of data:

 

15     9     6     12    14        10

Find the lower quartile of the following set of data:

 

17     9     3     10    14        10

Find the lower quartile of the following set of data:

 

16     9     1    15     11    14        10    4    3

  • Question 1

Find the upper quartile of the following set of data:

 

3     4     5    5     7     7     7     8     9     10

CORRECT ANSWER
8
EDDIE SAYS
Median of 7, 7, 8, 9, 10 is 8
  • Question 2

Find the upper quartile of the following set of data:

 

5     7     7     7     8     9     10

CORRECT ANSWER
9
EDDIE SAYS
Median of 8, 9, 10 is 9
  • Question 3

Find the lower quartile of the following set of data:

 

5     7     7     7     8     9     10

CORRECT ANSWER
7
EDDIE SAYS
Median of 5, 7, 7 is 7
  • Question 4

Find the lower quartile of the following set of data:

 

5     7     8     9     10

CORRECT ANSWER
6
EDDIE SAYS
Median of 5 and 7 is 6
  • Question 5

Find the upper quartile of the following set of data:

 

5     7     8     9     10

CORRECT ANSWER
9.5
EDDIE SAYS
Median of 9 and 10 is 9.5
  • Question 6

Find the upper quartile of the following set of data:

 

7     8     9     10     12     14

CORRECT ANSWER
12
EDDIE SAYS
Median of 10, 12, 14 is 12
  • Question 7

Find the lower quartile of the following set of data:

 

7     8     9     10     12     14

CORRECT ANSWER
8
EDDIE SAYS
Median of 7, 8, 9 is 8
  • Question 8

Find the upper quartile of the following set of data:

 

15     9     6     12    14        10

CORRECT ANSWER
14
EDDIE SAYS
Put the numbers in order first to get 6, 9, 10, 12, 14, 15.
Median of 12, 14, 15 is 14
  • Question 9

Find the lower quartile of the following set of data:

 

17     9     3     10    14        10

CORRECT ANSWER
9
EDDIE SAYS
Put the numbers in order first to get 3, 9, 10, 10, 14, 17.
Median of 3, 9, 10 is 9
  • Question 10

Find the lower quartile of the following set of data:

 

16     9     1    15     11    14        10    4    3

CORRECT ANSWER
3.5
EDDIE SAYS
Put the numbers in order first to get 1, 3, 4, 9, 10, 11, 14, 15, 16.
Median of 1, 3, 4, 9 is 3.5
---- OR ----

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