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Categorical Data Analysis Worksheet

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Categorical Data Analysis Worksheet

A festival team wants to plan activities for next year. Use the survey results and visual displays below to investigate categorical data. Show how you know, and question claims that are not supported by the data.

What kind of data?

Categorical data sorts responses into groups or labels. Categories should be clear and fit the question being investigated.

1.The festival team records each visitor’s preferred activity (live music, food stalls, or craft tent). Is this categorical or numerical data? Explain why.

2.Which is numerical data rather than categorical data?

Preferred festival activity
Visitor’s suburb
Number of festival visits this year
Preferred music style

Organise the responses

One hundred visitors were asked to choose one preferred activity. The table shows the results. Check totals before interpreting the data.

Preferred activity

Live music

Food stalls

Craft tent

Frequency

3.Verify that the frequencies add to the number of visitors surveyed. What does this check tell you?

4.What percentage of visitors chose the craft tent? Show your calculation.

5.Use the frequency table to make a bar graph. Give the graph a title, label both axes, use a sensible scale, and draw one bar for each activity.

6.Which activity was most popular, and how many more visitors chose it than the least popular activity?

7.A festival organiser says, “Almost half of the visitors chose live music.” Is this a fair description of the results? Use the proportion to justify your answer.

Compare two groups

A second question asked visitors whether they came with family or friends. The table shows each group’s favourite activity. Compare percentages within each group, not just the raw counts.

Group

Live music

Food stalls

Craft tent

Family (60 visitors)

Friends (40 visitors)

8.Calculate the percentage of each group that preferred live music. Which group had the greater percentage?

9.A student claims, “More family visitors than friends chose live music, so family visitors were more likely to prefer it.” Explain why the claim is not supported by the counts alone.

Think critically about the survey

The survey was carried out at the festival entrance between 10 am and midday. Every fifth person entering was invited to answer one question. Some people declined.

10.Name one strength and one possible limitation of this data collection method.

11.The organiser concludes, “All people in Aotearoa New Zealand prefer live music at festivals.” Does this survey justify that conclusion? Give one reason and a more careful conclusion.