Stem and Leaf Stem and Leaf DiagramsDiagrams

Teach GCSE Maths

Key: 3 5 means 35 hours

Hours worked in 1 week by 30

men

15654

2114665555553

4443332222110038212

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Stem and Leaf Diagrams

Key: 3 5 means 35 hours

Hours worked in 1 week by 30 men

2 1

2 8

3 0 0 1 1 2 2 2 2 3 3 3 4 4 4

3 5 5 5 5 5 5 6 6

4 1 1 2

4 5 6

5 1

A stem and leaf diagram is used to display small data sets where the data are not grouped.e.g. The diagram below gives the number of

hours worked in a particular week by a sample of 30 men.

stem

leaves

tells us that the stem gives tens and the leaves give units.

35 is 3 tens and 5 units, so the key . . .

Key: 3 5 means 35 hours

Hours worked in 1 week by 30 men

15

654

2114

665555553

444333222211003

82

12

Decide with your partner how many hours are shown here.Ans: 46 ( the stem gives 40 and the leaf 6

)The numbers on a stem and leaf diagram are always in order and increase away from the

stem.

Key: 3 5 means 35 hours

Hours worked in 1 week by 30 men

1 13

Ans: 2

How many men worked 31 hours during the week?

What is the mode of the hours worked?

2 1

2 8

0 0 2 2 2 2 3 3 3 4 4 4

3 5 5 5 5 5 5 6 6

4 1 1 2

4 5 6

5 1

Ans: Mode is most, so mode = 35

Key: 6 2 means 62 mm

Rainfall data

1098

7

317

765 6

02

50

7

Remind your partner how to find the median of a data set. Can you find the median here?

e.g The diagram shows the average rainfall (mm) for Newton Rigg ( UK ) from 1971 – 2000 for Jan. to Nov.

3

Ans: Median rainfall is 73 mm

The numbers are in order and there are 11 of them, so the median is the 6th.

1 2 3

4

5 6

Tip: Check there are the same number of numbers before and after the median. (Here there are 5 before

and 5 after)

Adapted from Crown copyright data supplied by the Met Office

Suppose I now add December’s rainfall ( 109

mm ) to the rainfall data.

Key: 6 2 means 62 mm

Rainfall data

1098

7

317

7765 6

302

50

9

109

mm

Tell your partner what the frequency is now.

Ans: 12

The median is the average of the 6th and 7th values !

Median annual rainfall for Newton Rigg = ½( 73 + 77 ) = 75 mm

Decide with your partner what the median is.

Stem and Leaf diagrams are used for small, raw data sets (not grouped data).

continued

SUMMARY

The key gives the size of the numbers in the stem and the leaves. The stem here gives tens and the leaves give units.

e.g.

Key: 6 2 means 62 mm

Rainfall data

1098

7

317

7765 6

302

50

9

The median is found by counting out from the stem. If the frequency is an even number, we have to find the average of 2 numbers.

There are always the same number of numbers before and after the median.

Key: 6 2 means 62 mm

Rainfall data: 11 months

1098

7

317

7765 6

02

50

3

Median = 73 mm

Key: 6 2 means 62 mm

1098

7

317

7765 6

302

50

9

Rainfall data: 12 months

Median = 75 mm

(a) Find the median time taken.

(b) Find the range.(c) Find the mode.

Exercise

1. The stem and leaf diagram shows the time taken for 15 students to walk to school.

0 5 7 7 8

1 0 0 2 5 6 6 8

2 5 5 5

3 8Key: 1 6 represents 16 mins

(a)

Exercise

1. The stem and leaf diagram shows the time taken for 15 students to walk to school.

The median is 15

mins.

0 5 7 7 8

1 0 0 2 5 6 6 8

2 5 5 5

3 8Key: 1 6 represents 16 mins

Solution:

1 2 3 4

5 6 7

(a)

Exercise

1. The stem and leaf diagram shows the time taken for 15 students to walk to school.

The median is 15

mins.(b)The mode is 25

mins.

0 5 7 7 8

1 0 0 2 5 6 6 8

2 5 5 5

3 8Key: 1 6 represents 16 mins

Solution:

(a)

Exercise

1. The stem and leaf diagram shows the time taken for 15 students to walk to school.

The median is 15

mins.(b)The mode is 25

mins.(c) The range is ( 38 – 5 ) = 33

mins.

0 5 7 7 8

1 0 0 2 5 6 6 8

2 5 5 5

3 8Key: 1 6 represents 16 mins

Solution:

Exercise

January Max Temperatures for Sheffield 1985 to 2005

Key: 8 1 represents 8·1C

3 4 7

4

5 0 2 3 4

6 4 5 9

7 1 2 2 4 8

8 1 2 4 5 9

9 0

2.

(a) What was the lowest temperature ? (b)Find the median temperature.

Adapted from Crown copyright data supplied by the Met Office

Exercise

January Max Temperatures for Sheffield 1985 to 2005

Key: 8 1 represents 8·1C

3 4 7

4

5 0 2 3 4

6 4 5 9

7 1 2 2 4 8

8 1 2 4 5 9

9 0

(b)

(a) The lowest temperature is 3·4C

Solution:

1 2

3 4 5 6

7 8 9

There are 20 temperatures so the median is the average of the 10th and 11th.

Exercise

January Max Temperatures for Sheffield 1985 to 2005

Key: 8 1 represents 8·1C

3 4 7

4

5 0 2 3 4

6 4 5 9

7 1 2 2 4 8

8 1 2 4 5 9

9 0

(b)

The median = 7·15C

(a) The lowest temperature is 3·4C

Solution: