year 8 maths

580 Chapter 9 Data collection, representation and analysis
Example 15
Interpreting survey results
A survey is conducted asking 100 randomly selected
adults how many children they have. The results
are shown in this histogram.
a Assume that this sample is representative of
the population.
i What proportion of the adult population
has two or more children?
0
ii In a group of 9000 adults, how many would
0 1 2 3
Number of children
you expect to have four children?
b Which of the following methods of conducting the survey could lead to bias?
Method 1 Asking people waiting outside a childcare centre
Method 2 Randomly selecting people at a night club
Method 3 Choosing 100 adults at random from the national census and noting how many
children they claimed to have.
Frequency
60
50
40
30
20
10
4
SOLUTION
a
i
3
10
ii 450
b Methods 1 and 2 could both lead to bias.
EXPLANATION
15 + 10 + 5 = 30 adults have two or more children.
Proportion = 30
100 = 3 10
5
In the survey
100 = 1 of the population have four
20
1
children. × 9000 = 450
20
If someone is waiting outside a childcare centre they
are more likely to have at least one child.
If someone is at a night club they are likely to be a
younger adult, and so less likely to have a child.
Exercise 9J
UNDERSTANDING AND FLUENCY
1–4 2–5
3–7
1 Marieko wishes to know the average age of drivers in her city. She could survey 10 of her friends,
or survey 1000 randomly selected drivers.
a Which of these options would give a more accurate result?
b Which would be easier for Marieko to perform?
Example 15a
2 Ajith looks at a random sample of penguins and notes that of the 50 he sees, 20 of them have spots
on their bodies.
a What proportion of the population has spots?
b If there are 5000 penguins in a region, on the basis of this sample how many would you expect
to have spots on their bodies?
c If there are 500 penguins in a region, how many would you expect to not have spots on their
bodies?
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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