Cambridge International Mathematics

284 Analysis of discrete data (Chapter 13)

Example 2 Self Tutor

Solve the following problems:

a The mean of six scores is 78 : 5. What is the sum of the scores?

b Findxif 10 , 7 , 3 , 6 andxhave a mean of 8.

a

sum

6

=78: 5

) sum=78: 5 £ 6

= 471

) the sum of the scores is 471 :

b There are 5 scores.

)

10+7+3+6+x

5

=8

)

26 +x

5

=8

) 26 +x=40

) x=14

EXERCISE 13C

1 Find the i mean ii median iii mode for each of the following data sets:

a 12 , 17 , 20 , 24 , 25 , 30 , 40

b 8 , 8 , 8 , 10 , 11 , 11 , 12 , 12 , 16 , 20 , 20 , 24

c 7 : 9 , 8 : 5 , 9 : 1 , 9 : 2 , 9 : 9 , 10. 0 , 11 : 1 , 11 : 2 , 11 : 2 , 12 : 6 , 12 : 9

d 427 , 423 , 415 , 405 , 445 , 433 , 442 , 415 , 435 , 448 , 429 , 427 , 403 , 430 , 446 , 440 , 425 , 424 , 419 ,

428 , 441

2 Consider the following two data sets:

Data set A: 5 , 6 , 6 , 7 , 7 , 7 , 8 , 8 , 9 , 10 , 12 Data set B: 5 , 6 , 6 , 7 , 7 , 7 , 8 , 8 , 9 , 10 , 20

a Find the mean for each data set.

b Find the median for each data set.

c Explain why the mean ofData set Ais less than the mean ofData set B.

d Explain why the median ofData set Ais the same as the median ofData set B.

3 The selling price of nine houses are:

$158 000, $290 000, $290 000, $1: 1 million, $900 000, $395 000,

$925 000, $420 000, $760 000

a Find the mean, median and modal selling prices.

b Explain why the mode is an unsatisfactory measure of the middle in this case.

c Is the median a satisfactory measure of the middle of this data set?

4 The following raw data is the daily rainfall (to the nearest millimetre) for the month of February 2007

in a city in China: 0 , 4 , 1 , 0 , 0 , 0 , 2 , 9 , 3 , 0 , 0 , 0 , 8 , 27 , 5 , 0 , 0 , 0 , 0 , 8 , 1 , 3 , 0 , 0 , 15 , 1 , 0 , 0

a Find the mean, median and mode for the data.

b Give a reason why the median is not the most suitable measure of centre for this set of data.

c Give a reason why the mode is not the most suitable measure of centre for this set of data.

IGCSE01

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Y:\HAESE\IGCSE01\IG01_13\284IGCSE01_13.CDR Thursday, 25 September 2008 4:42:02 PM PETER