Cambridge International Mathematics

356 Continuous data (Chapter 17)

Height (cm) Frequency (f)

1006 h< 110 1

1106 h< 120 1

1206 h< 130 4

1306 h< 140 19

1406 h< 150 25

1506 h< 160 24

1606 h< 170 13

1706 h< 180 5

1806 h< 190 1

Consider the continuous data opposite which summarises the heights

of girls in year 9. The data is continuous, so we can graph it using a

histogram.

In this case the width of each class interval is the same, so we can

construct afrequency histogram. The height of each column is the

frequency of the class, and themodal classis simply the class with the

highest column.

In some situations we may have class intervals with different widths. There are a couple of reasons why

this may happen:

Height (cm) Frequency (f)

1006 h< 130 6

1306 h< 140 19

1406 h< 150 25

1506 h< 160 23

1606 h< 170 13

1706 h< 190 6

² We may wish to collect small numbers of data at the extremities

of our data range.

For example, to make the table of girls’ heights easier to display,

we may combine the smallest three classes and also the tallest two

classes:

² The data may be naturally grouped in the context of the problem.

For example, a post office will charge different rates depending on the weight of the parcel being sent.

The weight intervals will probably not be equally spaced, but it makes sense for the post office to record

the number of parcels sent in each class.

So, the post office may collect the following data of parcels sent over a week:

Mass (mkg) 06 m< 1 16 m< 2 26 m< 5 56 m< 20

Number of parcels 18 22 24 11

In either case, the histogram we draw isnota frequency histogram. The frequency of each class is not

represented by theheightof its bar, but rather by itsarea. The height of each bar is called thefrequency

densityof the class.

Since frequency=frequency density£class interval width,

frequency density=

frequency

class interval width

0

10

20

30

100 110 120 130 140 150 160 170 180 190

height (cm)

frequency

Themodal classis the class with the highest frequency density, and so it is the highest bar on the histogram.

It is not necessarily the class with the highest frequency.

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Y:\HAESE\IGCSE01\IG01_17\356IGCSE01_17.CDR Tuesday, 18 November 2008 11:48:37 AM PETER