Page 107 - Mathematics Coursebook

10.1 Average and range

2 Tom recorded the midday temperatures, in degrees 7 2 −1 3 2 −2 0 2 6 6
Celsius, each day for three weeks. His results are shown
on the right. 3 4 6 6 5 3 8 9 6 6 2
Work out: a the mode b the median c the range.

3 These are the masses, in kilograms, of nine members of 75 78 82 83 85 88 90 92 93
a slimming club.
a Work out the median mass. b Work out the range.
c After three months, they had all lost 4 kg. Work out the new median and the new range.
d How will the median change if everyone loses 10 kg?
e How will the range change if everyone loses 10 kg?

4 The table shows the populations of seven countries. The numbers are in millions.

Country Nigeria Saudi Arabia Egypt India Indonesia Malaysia New Zealand
Population 112 22 69 1013 213 22 4
(millions)

a Which country has the median population?
b Work out the range of the populations.
9 11 11 11 11 12 12 13 14 14
5 The ages of ten students are shown in the box.
Work out: a the mode b the median c the range.

6 These are the heights (in metres) of six members of 1.40 1.45 1.55 1.65 1.65 1.80
a swimming club.
a Work out: i the median height ii the range.
b One more person joins the club. The range is now 0.45 m and the median is 1.55 m. Find the
height of the seventh person.

7 This table shows how long a group of 92 holiday-makers are planning to stay in New Zealand.

Length of stay (days) 1–7 8–14 15–21 22–28 29–42
Frequency 6 14 22 35 15

a Find the modal class. Give a reason for your answer.
b It is not possible to find the range.
i Explain why the smallest possible value of the range is 22 days.
ii What is the largest possible value of the range?

8 A group of 25 children were asked how many sisters they had.
The frequency table shows the results.
Number of sisters 0 1 2 3 4 5

Frequency 4 8 6 2 4 1

a From the table, four children have no sisters. How many children have more than two sisters?
b What is the modal number of sisters? c What is the median number of sisters?

106 10 Averages