Cambridge International Mathematics

294 Analysis of discrete data (Chapter 13)

2 A randomly selected sample of small businesses

has been asked, “How many full-time employees

are there in your business?”. A bar chart has been

constructed for the results.

a How many small businesses gave data in the

survey?

b How many of the businesses had only one or two full-time employees?

c What percentage of the businesses had five or more full-time employees?

d Describe the distribution of the data.

e Find the mean of the data.

29 14 23 32 28 30 9 24 31

30 18 22 27 15 32 26 22 19

16 23 38 12 8 22 31

3 The data alongside are the number of call-outs each day for

a city fire department over a period of 25 days:

a Construct a tally and frequency table for the data using

class intervals 0 - 9 , 10 - 19 , 20 - 29 , and 30 - 39.

b Display the data on a vertical bar chart.

c On how many days were there are least 20 call-outs?

d On what percentage of days were there less than 10 call-outs?

e Find the modal class for the data.

4 For the following data set of the number of points scored by a rugby team, find:

a the mean b the mode c the median d the range

e the upper and lower quartiles f the interquartile range.

28 , 24 , 16 , 6 , 46 , 34 , 43 , 16 , 36 , 49 , 30 , 28 , 4 , 31 , 47 , 41 , 26 , 25 , 20 , 29 , 42

25 18 35 32 34 28 24 39 29 33

22 34 39 31 36 35 36 33 35 27

26 25 20 18 9 19 32 23 28 27

5 The test score out of 40 marks was recorded for a

group of 30 students:

a Construct a tally and frequency table for this data.

b Draw a bar chart to display the data.

c How many students scored less than 20 for the test?

d If an ‘A’ was awarded to students who scored 30 or more for the test, what percentage of

students scored an ‘A’?

6 Eight scores have an average of six. Scores of 15 andxincrease the average to 7. Findx.

Stem Leaf

1 24468

2 2377799

3 002458

4 023 4 j 0 represents 40

7 For the data set given, find the:

a minimum value b maximum value

c median d lower quartile

e upper quartile f range

g interquartile range.

8 Using the bar chart alongside:

a construct a frequency table

b determine the total number of:

i games played ii goals scored

c find the:

i mean ii median

iii mode iv range.

0

2

4

6

8

10

12

12345678

no. of full time employees

frequency

0

2

4

6

8

0123

no. of goals

frequency

Goals per game by a footballer

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Y:\HAESE\IGCSE01\IG01_13\294IGCSE01_13.CDR Friday, 26 September 2008 10:20:06 AM PETER