Cambridge International Mathematics

Analysis of discrete data (Chapter 13) 287

Example 5 Self Tutor

For the data set: 6 , 10 , 7 , 8 , 13 , 7 , 10 , 8 , 1 , 7 , 5 , 4 , 9 , 4 , 2 , 5 , 9 , 6 , 3 , 2 find the:

a median b lower and upper quartiles c interquartile range.

The ordered data set is: 12234455667778899101013 ( 20 of them)

a As n=20,

n+1

2

=10: 5

) median=

10 th value+11th value

2

=

6+7

2

=6: 5

b As the median is not a data value we split the data into two:

lower

z }| {

1223 44|{z}

Q 1 =4

5566

upper

z }| {

7778 89|{z}

Q 3 =8: 5

9101013

c IQR=Q 3 ¡Q 1

=8: 5 ¡ 4

=4: 5

Note: Some computer packages (for example,MS Excel)

calculate quartiles in a different way from this example.

EXERCISE 13D

1 For each of the following data sets, make sure the data is ordered and then find:

i the median ii the upper and lower quartiles

iii the range iv the interquartile range.

a 5 , 6 , 6 , 6 , 7 , 7 , 7 , 8 , 8 , 8 , 8 , 9 , 9 , 9 , 9 , 9 , 10 , 10 , 11 , 11 , 11 , 12 , 12

b 11 , 13 , 16 , 13 , 25 , 19 , 20 , 19 , 19 , 16 , 17 , 21 , 22 , 18 , 19 , 17 , 23 , 15

c 23 : 8 , 24 : 4 , 25 : 5 , 25 : 5 , 26 : 6 , 26 : 9 , 27 , 27 : 3 , 28 : 1 , 28 : 4 , 31 : 5

2 The times spent (in minutes) by 24 people in a queue at a supermarket, waiting to be served at the

checkout, were:

1 : 45 : 22 : 42 : 83 : 43 : 82 : 21 : 5

0 : 80 : 83 : 92 : 34 : 51 : 40 : 50 : 1

1 : 64 : 81 : 90 : 23 : 65 : 22 : 73 : 0

a Find the median waiting time and

the upper and lower quartiles.

b Find the range and interquartile range of the waiting time.

c Copy and complete the following statements:

i “50%of the waiting times were greater than ......... minutes.”

ii “75%of the waiting times were less than ...... minutes.”

iii “The minimum waiting time was ........ minutes and the maximum waiting time was .....

minutes. The waiting times were spread over ...... minutes.”

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Y:\HAESE\IGCSE01\IG01_13\287IGCSE01_13.CDR Thursday, 25 September 2008 4:51:42 PM PETER