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Multivariate Statistics Investigation Worksheet

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Multivariate Statistics Investigation Worksheet

A youth group in Aotearoa New Zealand surveyed 10 teenagers about their usual journey to activities. They recorded travel group, minutes of physical activity on a typical day, and recreational screen time in minutes on a typical day. Use the sample data below to investigate how the variables compare. Show calculations where helpful. The data are fictional.

Teenager

Travel group

Activity (min)

Screen time (min)

Aisha

Walk/cycle

120

Finn

Walk/cycle

150

Cara

Walk/cycle

180

Dylan

Walk/cycle

Eli

Walk/cycle

210

Fia

Bus/car

240

George

Bus/car

180

Hana

Bus/car

300

Isaac

Bus/car

150

Jade

Bus/car

270

Explore the data

Use the data table as evidence in each response.

1.Which variable is categorical, and which two variables are numerical? Explain how the travel groups divide the sample.

2.Calculate the median daily activity time for each travel group. Which group has the higher median, and by how many minutes?

3.Calculate the median daily screen time for each travel group. What difference do you notice?

4.Find the activity-time range and screen-time range for the whole sample. Show each subtraction.

5.Make a scatter plot of activity time against screen time. Put activity time on the horizontal axis and screen time on the vertical axis. Use different symbols for the two travel groups, add a key, and label both axes.

Horizontal axis: activity (minutes), 0–80. Vertical axis: screen time (minutes), 0–320.

6.Looking across both numerical variables, describe the overall relationship between activity time and screen time. Use at least two data points to support your description.

7.Which teenager is a possible exception to the general pattern you described? State their two measurements and explain why they stand out.

8.True or false: This survey proves that travelling by bus or car causes teenagers to do less physical activity. Give one reason for your answer.

TrueFalse

9.The youth group wants to make a claim about all teenagers in the community. Name two improvements to the data collection that would make the evidence more useful.