Cambridge International Mathematics

362 Continuous data (Chapter 17)

EXERCISE 17C

Times (min) Frequency

206 t< 25 18

256 t< 30 45

306 t< 35 37

356 t< 40 33

406 t< 45 19

456 t< 50 8

1 In a running race, the times (in minutes) of 160 competitors were

recorded as follows:

Draw a cumulative frequency graph of the data and use it to estimate:

a the median time

b the approximate number of runners whose time was not more than

32 minutes

c the approximate time in which the fastest 40 runners completed

the course

d the interquartile range.

2

3 The lengths of 30 trout (lcm) were measured. The following data was obtained:

Length (cm) 306 l< 32326 l< 34346 l< 36366 l< 38386 l< 40406 l< 42426 l< 44

Frequency 1 1 3 7 11 5 2

a Construct a cumulative frequency curve for the data.

b Estimate the percentage of trout with length less than 39 cm.

c Estimate the median length of trout caught.

d Estimate the interquartile range of trout length and explain what this represents.

e Estimate the 35 th percentile and explain what this represents.

f Use a calculator to estimate the mean of the data.

g Comment on the shape of the distribution of trout lengths.

0

20

40

60

80

100

120

0 102030405060 70

weight ( kg)w

cumulative frequency The cumulative frequency

curve shows the weights of

Sam’s goat herd in kilograms.

How many goats does

Sam have?

Estimate the median goat

weight.

Any goats heavier than

the th percentile will

go to market. How many

goats will go to market?

What is the IQR for

Sam’s herd?

60

a

b

c

d

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y:\HAESE\IGCSE01\IG01_17\362IGCSE01_17.CDR Thursday, 23 October 2008 12:19:05 PM PETER