Questions: Collecting and Displaying Categorical Data

Question 1

A class surveys students about their favorite pet. The bar for 'dog' reaches the 8 mark on a bar graph. What does this tell you?

• A. There are 8 different kinds of dogs
• B. 8 students chose 'dog' as their favorite pet
• C. 'Dog' is the 8th category on the graph
• D. The word 'dog' equals 8

Answer: (B)

The bar's height represents the frequency — the count of how many responses fell into that category. 'Dog' is the label (the name of the category), and 8 is the frequency (the number of students who chose it). These are two different things: the label names the group, the bar height counts the members of the group.

Question 2

A student looks at a tally chart and says 'The most popular answer is apple.' What additional information is needed to confirm this?

• A. Nothing — if apple is listed, it must be most popular
• B. The frequency count for apple and for all other categories
• C. The exact time the survey was conducted
• D. The total number of categories in the chart

Answer: (B)

Knowing that 'apple' is a category is not enough — you need to compare its frequency (count) to the frequencies of all other categories to determine which is most popular. The category name tells you what group; the frequency tells you how many. You must look at both pieces of information and compare across categories.

Question 3

The word 'apple' in a fruit-preference survey is a category label, not a count.

• T. True
• F. False

Answer: True

Category labels name the groups (apple, banana, orange), while frequencies are the numbers telling you how many responses fell into each group. Keeping these two things distinct is the core skill in reading data displays. Confusing a label for a count is the most common error students make when interpreting graphs.

Question 4

Categorical data and numerical data are organized the same way because both can use tally charts.

• T. True
• F. False

Answer: False

Categorical data classifies objects into named groups (favorite color, type of pet) and is counted by frequency. Numerical data measures quantities on a number scale (height, temperature) and requires different analysis tools like histograms or line plots. While tally marks can be used to count responses in either case, the type of data and the questions you can ask about it are fundamentally different.

Question 5

What is the difference between a category and a frequency, and why is it important not to confuse them when reading a data display?

Model answer: A category is a named group that responses are sorted into (like 'apple' or 'dog'). A frequency is the count of how many responses belong to that category (like 7 or 12). Confusing them leads to misreading the graph — for example, thinking 'apple' itself is a number, or reporting the wrong category when asked which has the highest count.

Every data display pairs two things: a label and a value. Getting these confused is the root cause of most errors in data interpretation. The habit of always checking 'what does the label say?' and 'what does the number say?' separately prevents these mistakes at every level of statistics.