Cambridge International Mathematics

Analysis of discrete data (Chapter 13) 289

Example 6 Self Tutor

Score Number of students

5 1

6 2

7 4

8 7

9 4

10 2

Total 20

Each student in a class of 20 is assigned a number between 1 and

10 to indicate his or her fitness.

Calculate the: a mean b median

c mode d range

of the scores.

a Score (x) Frequency (f) Product (fx)

5 1 5 £1=5

6 2 6 £2=12

7 4 7 £4=28

8 7 8 £7=56

9 4 9 £4=36

10 2 10 £2=20

Total 20 157

The mean score=

P

fx

P

f

=^15720

=7: 85

b There are 20 scores, and so the median is the average of the 10 th and 11 th.

Score Number of students

5 1 1 st student

6 2 2 nd and 3 rd student

7 4 4 th, 5 th, 6 th and 7 th student

8 7 8 th, 9 th,10th,11th, 12 th,

9 4 13 th, 14 th student

10 2

The 10 th and 11 th students both scored 8 ) median=8.

c Looking down the ‘number of students’ column, the highest frequency is 7.

This corresponds to a score of 8 , so the mode=8.

d The range=highest data value¡lowest data value=10¡5=5

EXERCISE 13E

1

Number of instruments Frequency

1 18

2 14

3 6

4 4

Total 42

Calculate the:a mode b median c mean d range.

STATISTICS

PACKAGE

The members of a school band were each asked how many musical instruments they played.

The results were:

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y:\HAESE\IGCSE01\IG01_13\289IGCSE01_13.CDR Thursday, 16 October 2008 9:41:25 AM PETER