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Multivariate Data Investigation

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Multivariate Data Investigation

A local youth council wants to make a safer, easier journey to activities for rangatahi. Use the survey results below to investigate how travel choices relate to year level and journey time. Answer in complete sentences where appropriate. The results are fictional.

The survey

Twenty-three students were asked anonymously how they usually travel to an after-school activity and how long the journey takes. Each student chose one travel method and one journey-time category.

Year level and travel method

Under 15 minutes

15–30 minutes

Over 30 minutes

Year 7: Walk or bike

Year 7: Bus

Year 8: Walk or bike

Year 8: Bus

Investigate the data

1.What does multivariate data mean? Select the best description.

Data about one variable only
Data that records several variables for each person or item
Data collected only from a large group
Data that must be shown in a pie chart

2.Name the three variables recorded in the survey. State whether each is categorical or numerical.

3.How many Year 8 students usually travel by bus? Show how you found the total.

4.Among Year 7 students who walk or bike, what fraction have a journey under 15 minutes? Give the fraction in simplest form.

5.Compare the travel methods of Year 7 and Year 8 students. What difference do you notice? Support your comparison with totals from the table.

6.Which travel method has the largest number of journeys over 30 minutes? Use the table to justify your answer.

7.Find the total number of surveyed journeys that take over 30 minutes. What percentage of the 23 students is this?

8.A student says, “Taking the bus causes longer journeys.” Is this conclusion justified by these results? Explain one reason for your answer.

9.Suggest one ethical way to collect more information for this investigation, and name one piece of personal information the survey should avoid collecting.

10.Choose a useful display for comparing travel method, journey time and year level. Describe how you would organise it and name one pattern it could help readers see.

11.Write one follow-up survey question that could help explain why some students have journeys over 30 minutes. Keep it respectful and do not ask for an exact address.