Cambridge International Mathematics

Analysis of discrete data (Chapter 13) 291

Example 7 Self Tutor

Class interval Frequency

0 - 9 2

10 - 19 31

20 - 29 73

30 - 39 85

40 - 49 28

The table summarises the marks received by students for a Physics

examination out of 50.

a Estimate the mean mark.

b What is the modal class?

c Can the range of the data be found?

Class interval f Mid-point (x) fx

0 - 9 2 4 : 5 9 : 0

10 - 19 31 14 : 5 449 : 5

20 - 29 73 24 : 5 1788 : 5

30 - 39 85 34 : 5 2932 : 5

40 - 49 26 44 : 5 1157 : 0

217 6336 : 5

a Mean =

P

fx

P

f

=

6336 : 5

217

¼ 29 : 2

b The modal class is 30 - 39 marks.

c

3

85 £^10 is the

fraction of the

interval in which

the median is

found.

No, as we do not know the smallest

and largest score.

This formula is

.

not

examinable

THE MEDIAN

We can estimate the median of a grouped data set by using acumulative

frequency graphorogive. This is done inChapter 17.

The approximate median can also be calculated using a formula:

median¼L+

N

F

£I

whereL=the lower boundary for the class interval containing the

median

N=the number of scores in the median class needed to arrive

at the middle score

F=the frequency of the class interval containing the median

I=the class interval length.

For example, inExample 7we notice that n= 217, so the median is the

217 + 1

2

= 109th score.

There are2 + 31 + 73 = 106 scores in the first 3 classes, so the median

class is 30 - 39.

For discrete data, the lower and upper boundaries for the

class interval 30 - 39 are 29 : 5 and 39 : 5 , ) L=29: 5.

N= 109¡106 = 3, F=85and I=10

) the median¼ 29 :5+ 853 £ 10 ¼ 29 : 9

Totals

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y:\HAESE\IGCSE01\IG01_13\291IGCSE01_13.CDR Thursday, 16 October 2008 9:47:27 AM PETER