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Stem and Leaf Diagrams

In this worksheet, students understand and answer questions on information contained in Stem and Leaf Diagrams.

'Stem and Leaf Diagrams' 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 distribution of data can be displayed on a Stem and Leaf Diagram.

 

The Stem part is often the tens digit of each value.

The Leaf part is often the units digit of each value.

 

Ih this way we can easily see the distribution of our data.

 

 

Example

The marks gained by 15 students in a maths test are:

7, 9, 11, 14, 14, 17, 20, 22, 23, 25, 29, 30, 34, 37, 40

 

These can be represented on a Stem and Leaf Diagram as follows:

 

Stem    Leaf
  7   9
  1   4   4   7
  0   2   3   5   9
  0   4   7
  0

 

This diagram makes it easier for us to see the following:

The modal group is 20-29 because this it the one with the highest frequency (most entries).

The mode or the modal mark is 14, because this is the value that occurs most often.

The median result is the 8th value (middle of 15), which is 22.

The range is 40 - 7 = 33.

The marks of 15 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

Work out the modal mark.

 

Stem 
  Leaf
  7   9
  1   4   4   7
  0   3   3   3   9
  0   4   4
  4

 

The marks of 15 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

Work out the range of marks.

 

Stem 
  Leaf
  7   9
  1   4   4   7
  0   3   3   3   9
  0   4   4
  4

 

The marks of 15 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

Work out the median mark.

 

Stem 
  Leaf
  7   9
  1   4   4   7
  0   3   3   3   9
  0   4   4
  4

 

The marks of 15 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

How many children scored more than 30 marks?

 

Stem 
  Leaf
  7   9
  1   4   4   7
  0   3   3   3   9
  0   4   4
  4

 

The marks of 15 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

How many children scored exactly 33 marks?

 

Stem 
  Leaf
  7   9
  1   4   4   7
  0   3   3   3   9
  0   4   4
  4

 

The marks of 20 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

How many children scored exactly 35 marks?

 

Stem 
  Leaf
  7   7   9
  1   2   4   4   4   4   7
 1   3   3   3   9
  0   4   5
  4   8

 

The marks of 20 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

How many children scored less than 25 marks?

 

Stem 
  Leaf
  7   7   9
  1   2   4   4   4   4   7
 1   3   3   3   9
  0   4   5
  4   8

 

The marks of 20 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

Work out the modal mark.

 

Stem 
  Leaf
  7   7   9
  1   2   4   4   4   4   7
  1   3   3   3   9
  0   4   5
  4   8

 

The marks of 20 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

Work out the median mark.

 

Stem 
  Leaf
  7   7   9
  1   2   4   4   4   4   7
  1   3   3   3   9
  0   4   5
  4   8

 

The marks of 20 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

Select the modal group.

 

Stem 
  Leaf
  7   7   9
  1   2   4   4   4   4   7
  1   3   3   3   9
  0   4   5
  4   8

 

0 to 9

10 to 19

20 to 29

30 to 39

40 to 50

  • Question 1

The marks of 15 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

Work out the modal mark.

 

Stem 
  Leaf
  7   9
  1   4   4   7
  0   3   3   3   9
  0   4   4
  4

 

CORRECT ANSWER
23
EDDIE SAYS
23 occurs 3 times.
  • Question 2

The marks of 15 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

Work out the range of marks.

 

Stem 
  Leaf
  7   9
  1   4   4   7
  0   3   3   3   9
  0   4   4
  4

 

CORRECT ANSWER
37
EDDIE SAYS
44 - 7
  • Question 3

The marks of 15 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

Work out the median mark.

 

Stem 
  Leaf
  7   9
  1   4   4   7
  0   3   3   3   9
  0   4   4
  4

 

CORRECT ANSWER
23
EDDIE SAYS
The eighth data entry is 23.
  • Question 4

The marks of 15 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

How many children scored more than 30 marks?

 

Stem 
  Leaf
  7   9
  1   4   4   7
  0   3   3   3   9
  0   4   4
  4

 

CORRECT ANSWER
3
EDDIE SAYS
Those who scored 34, 34 and 44.
  • Question 5

The marks of 15 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

How many children scored exactly 33 marks?

 

Stem 
  Leaf
  7   9
  1   4   4   7
  0   3   3   3   9
  0   4   4
  4

 

CORRECT ANSWER
0
EDDIE SAYS
Those who scored in the 30s scored 30, 34 and 34.
  • Question 6

The marks of 20 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

How many children scored exactly 35 marks?

 

Stem 
  Leaf
  7   7   9
  1   2   4   4   4   4   7
 1   3   3   3   9
  0   4   5
  4   8

 

CORRECT ANSWER
1
EDDIE SAYS
Those who scored in the 30s scored 30, 34 and 35.
  • Question 7

The marks of 20 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

How many children scored less than 25 marks?

 

Stem 
  Leaf
  7   7   9
  1   2   4   4   4   4   7
 1   3   3   3   9
  0   4   5
  4   8

 

CORRECT ANSWER
14
EDDIE SAYS
Those who scored less than 25, scored 7, 7, 9, 11, 12, 14, 14, 14, 14, 17, 21, 23, 23, 23.
  • Question 8

The marks of 20 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

Work out the modal mark.

 

Stem 
  Leaf
  7   7   9
  1   2   4   4   4   4   7
  1   3   3   3   9
  0   4   5
  4   8

 

CORRECT ANSWER
14
EDDIE SAYS
14 was the most frequently occurring mark.
  • Question 9

The marks of 20 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

Work out the median mark.

 

Stem 
  Leaf
  7   7   9
  1   2   4   4   4   4   7
  1   3   3   3   9
  0   4   5
  4   8

 

CORRECT ANSWER
19
EDDIE SAYS
With 20 people, we are looking for the 10th and 11th mark when placed in order. These are 17 and 21, the mean of which is 19.
  • Question 10

The marks of 20 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

Select the modal group.

 

Stem 
  Leaf
  7   7   9
  1   2   4   4   4   4   7
  1   3   3   3   9
  0   4   5
  4   8

 

CORRECT ANSWER
10 to 19
EDDIE SAYS
This is the group with most entries.
---- OR ----

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