year 8 maths

9J
Surveying and sampling
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9J Surveying and sampling
To find information about a large number of people it is generally not possible to ask everybody to
complete a survey, so instead a sample of the population is chosen and surveyed. It is hoped that the
information given by this smaller group is representative of the larger group of people. Choosing the right
sample size and obtaining a representative sample is harder than many people realise.
Let’s start: Average word length
To decide how hard the language is in a book, you could try to calculate the average length of the words
in it. Because books are generally too large, instead you can choose a smaller sample. For this exercise,
you must decide or be assigned to the ‘small sample’, ‘medium sample’ or ‘large sample’ group. Then:
1 Pick a page from the book at random.
2 Find the average (mean) length of any English words on this page, choosing the first 10 words if you
are in the ‘small sample’ group, the first 30 words for the ‘medium sample’ group and the first
50 words for the ‘large sample’ group.
Discuss as a class:
• Which group would have the best estimate for the average word length in the book?
• What are the advantages and disadvantages of choosing a large sample?
• Does this sample help to determine the average length of words in the English language?
• How could the results of a whole class be combined to get the best possible estimate for average word
length in the book?
• If all students are allowed to choose the page on which to count words, rather than choosing one at
random, how could this bias the results?
■ A population is the set of all members of a group that is to be studied.
For example: All the people in a town, looking at which local beach they prefer.
All the kangaroos in a park, looking at the presence of any diseases.
■ A sample is a subset (selected group) of a population.
For example: 20 students selected from all Year 8 students in a school, looking at what their
favourite football team is.
One thousand people selected and called via telephone regarding their preferred
political party.
Key ideas
■A survey can be conducted to obtain information about a large group by using a smaller sample.
A survey conducted on an entire population is called a census .
■ The accuracy of the survey’s conclusion can be affected by:
• the sample size (number of participants or items considered)
• whether the sample is representative of the larger group, or biased , which can result in a
sample mean significantly different from the population mean
• whether there were any measurement errors , which could lead to outliers —values that are
noticeably different from the other values.
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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