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Maths Age 14-16. D4 Moving averages and cumulative frequency. D4 Moving averages and cumulative frequency. D4.1 Moving averages. A. Contents. D4.2 Plotting moving averages. A. D4.3 Cumulative frequency. A. D4.5 Box-and-whisker diagrams. D4.4 Using cumulative frequency graphs. A. A.

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maths age 14 16

Maths Age 14-16

D4 Moving averages and cumulative frequency

contents

D4 Moving averages and cumulative frequency

D4.1 Moving averages

  • A

Contents

D4.2 Plotting moving averages

  • A

D4.3 Cumulative frequency

  • A

D4.5 Box-and-whisker diagrams

D4.4 Using cumulative frequency graphs

  • A
  • A
a box and whisker diagram

100

90

80

70

60

50

Cumulative frequency

40

30

20

10

0

30

35

40

45

50

55

60

Time in seconds

A box-and-whisker diagram

A box-and-whisker diagram, or boxplot, can be used to illustrate the spread of the data in a given distribution using the highest and lowest values, the median, the lower quartile and the upper quartile.

These values can be found from a cumulative frequency graph.

For example, for this cumulative frequency graph showing the results of 100 people holding their breath,

Minimum value = 30

Lower quartile = 42

Median = 47

Upper quartile = 51

Maximum value = 60

a box and whisker diagram1

Minimum value

Median

Maximum value

Lower quartile

Upper quartile

30

42

47

51

60

A box-and-whisker diagram

The corresponding box-and-whisker diagram is as follows:

lap times

th

378 + 1

value ≈

2

Lap times

James takes part in karting competitions and his Dad records his lap times on a spreadsheet.

In 2004, 378 of James’ lap times were recorded.

The track is 1108 metres long. James’ fastest time in a race was 51.8 seconds.

In which position in the list would the median lap time be?

There are 378 lap times and so the median lap time will be the

190th value

lap times1

th

3 ×

th

value ≈

378 + 1

378 + 1

value ≈

4

4

Lap times

In which position in the list would the lower quartile be?

There are 378 lap times and so the lower quartile will be the

95th value

In which position in the list would the upper quartile be?

There are 378 lap times and so the upper quartile will be the

284th value

lap times at shenington karting circuit

400

350

300

250

200

Cumulative frequency

150

100

50

0

52

54

56

58

60

62

64

66

68

70

72

74

76

78

80

82

84

86

88

90

92

Lap times in seconds

Lap times at Shenington karting circuit

James’ lap times are displayed in the following cumulative frequency graph.

box and whisker plot for james race times
Box and whisker plot for James’ race times

Minimum value

Maximum value

Lower quartile

Median

Upper quartile

52

54

58

91

53

What conclusions can you draw about James’ performance?

comparing sets of data

James’ lap times

52

54

58

91

53

Shabnum’s lap times

52

54

60

65

86

Comparing sets of data

Here are box-and-whisker diagrams representing James’ lap times and Shabnum’s lap times.

Who is better and why?