year 8 maths

584 Chapter 9 Data collection, representation and analysis
School food survey
Investigation
A new food company, GoodCheapFood, is thinking of taking over the running of your school’s cafeteria.
Before they invest in your school, they would like to know the eating and drinking habits of high school
students, in particular:
• how much money students spend in the cafeteria (per week)
• how many drinks they purchase (per week)
• how many days of the week students use the cafeteria
• how happy students are with the current cafeteria, on a scale from 1 to 5 .
1 Design a survey for GoodCheapFood that could be used to get the data they would like. Think about
how the questions should be phrased to ensure that you get accurate results that are free of bias.
2 Explain why you cannot conduct a census of the school population and describe at least three different
ways you could choose random samples of 20 students. For each sample, comment on whether a
bias would be introduced and give an explanation for why selecting only Year 7 girls might result in
significantly different results from selecting only Year 12 boys.
3 Conduct the survey on at least three different random samples of size 20 from within the school
population and use a spreadsheet to tabulate the results. A separate sheet should be used for each of
the samples and could be filled out as given below.
4 GoodCheapFood is interested in the range of the amount of money spent in the cafeteria in a week.
Use a formula like = MAX(A2:A21)–MIN(A2:A21) to calculate the range for each of your samples,
and give the results.
5 The company wishes to know the median number of drinks purchased. Explain why the median rather
than the mean would be preferred by referring to any possible outliers, and then use a formula
like = MEDIAN(B2:B21) to find the medians for each sample.
6 Find the mode number of days used in each of the samples and explain what this signifies, in plain
English.
7 Find the mean happiness of students in each sample with a formula like = AVERAGE(D2:D21) .
8 Explain why your three or more different random samples drawn have different summary statistics
(mean, median, mode and range) even though they are all drawn from the school population.
9 GoodCheapFood is grateful that you have gone to this much effort. Present your findings as a brief
summary, combining your samples to answer the four questions in which they were interested.
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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