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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