Drawing Stem and Leaf Drawing Stem and Leaf DiagramsDiagrams

Teach GCSE Maths

Petrol Consumption (mpg)

8765 8

087

Key: 5 7 means 57 mpg

3

9 91 1 6

"Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages"

© Christine Crisp

DrawingDrawingStem and Leaf Stem and Leaf

DiagramsDiagrams

Data from the Office for National Statistics which is included in this presentation is reproduced under the terms of the click-use licence.

58585959

6061616683

57

e.g.1 The table gives the 10 “best” petrol consumption figures (mpg) for cars in 2006.

Draw a stem and leaf diagram to display the data.1. Decide on the size of numbers in the

stem:A spread from 57 to 83 suggests a stem in tens, from 5 tens to 8 tens.

Petrol Consumption (mpg)

8765 8

087

Key: 5 7 means 57 mpg

3

2. Check the numbers are in order before writing the leaves. Start with the smallest.

9 91 1 6

3. Give a title and key.

Crown Copyright 1997 - 2006Source: Vehicle Certification Agency (VCA)

e.g.2. The table gives the body mass index (BMI) of 18 army recruits. (a) Draw a stem and leaf diagram to show the data.(b) Find the median.

25·4 25·7 26·0 26·8 26·9 27·1

27·6 27·6 27·7 28·1 28·2 28·7

28·8 28·9 29·3 29·6 29·8 31·1

BMI is given by weight (kg) / (height

(m))2

e.g. weight = 74 kg, height = 1·69 mBMI = 74 ÷ (1·69)2 = 25·9

In 2006, the maximum for army recruits was increased from 28 to 32.

Tell your partner what numbers you would choose for the stem.

Ans: The best choice is 25, 26, . . . 31The leaves will show the

tenths.

25·4 25·7 26·0 26·8 26·9 27·1

27·6 27·6 27·7 28·1 28·2 28·7

28·8 28·9 29·3 29·6 29·8 31·1Solution:

Key: 25 4 means 25·4

Body Mass Index of 18 army recruits

1

863

98721

980

74

31

30

29

28

27

26

25

1 6 6 7

(a)

e.g.2. The table gives the body mass index (BMI) of 18 army recruits. (a) Draw a stem and leaf diagram to show the data.(b) Find the median.

Key: 25 4 means 25·4

Body Mass Index of 18 army recruits

1

863

9872

980

74

31

30

29

28

27

26

25

1 6 6

1

7

Solution:

The total frequency is even so we need the mean of the 2 middle values:

(b) Find the median.

Median is ½(27·7 + 28·1)

= 27·9

Tell your partner which values we need.

We need the mean of the 9th and 10th . . . 27·7 and 28·1

SUMMARY

1. Decide on the size of numbers in the stem.

2. Check the numbers are in order before writing the leaves. Start with the smallest and work away from the stem.

3. Give a title and key.

Exercise

1. Stem and leaf diagrams are to be drawn for the following data set which gives the ages of 27 people in a restaurant.

42 45 51 53 57 57 57 59 60

61 61 61 62 63 63 65 65 66

67 67 68 70 70 70 71 71 73

(a) Write down sensible numbers to use in the stem.(b) State the size of the numbers in the leaves.

Answer:

For example, (a) 4, 5, 6, 7(b) Units(c) Draw the diagram. If you had a different

answer to (a), use your numbers and decide if they work well.

Exercise

42 45 51 53 57 57 57 59 60

61 61 61 62 63 63 65 65 66

67 67 68 70 70 70 71 71 73

Key: 4 2 represents 42

52

7

6

5

4

731 977

0 1 1 1 2 3 3 5 5 6 7 7 8

11000 3

Ages of 27 people in a Restaurant

(c)

Answer

Exercise

2. Stem and leaf diagrams are to be drawn for the following data set which gives the temperatures of 18 towns (C) on 21st February 2007.

7·2 7·5 7·7 8·3 8·7 8·7 8·7 8·9 9·0

9·3 9·7 10·1 10·6 10·9 10·9 11·1 11·4 11·6

(a) Write down sensible numbers to use in the stem.(b) State the size of the numbers in the leaves.

Answer:

(a) For example, 7, 8, 9, 10, 11(b) Tenths

Now draw the diagram. If you had a different answer to (a), use your numbers and decide if they work well.

Adapted from Crown copyright data supplied by the Met Office.

Exercise

7·2 7·5 7·7 8·3 8·4 8·4 8·5 8·8 9·0

9·3 9·7 10·1 10·6 10·9 10·9 11·1 11·4 11·6

0 3 7

443 85

February temperatures ( 18 towns )

(c)

10

987

11

52 7

1 4 6

Answer

Key: 7 2 represents 7·2C

9961