Understanding Variables in Statistics

Name:

Date:

📚 Part 1: Multiple Choice & Classification

1. Which of the following is a categorical variable?

Shoe colour

Foot length (cm)

Number of shoes owned

2. Which example is a continuous numerical variable?

Number of pets in a household

Height measured in centimetres

Favourite sport

3. Check all that are discrete numerical variables (tick any that apply):

Number of books read this year

Foot length measured in cm

Number of shoes in a cupboard

Eye colour

4. You have a class dataset of foot lengths. One student has a very long foot compared with others (an outlier). Which measure of centre is least affected by that outlier?

Mean

Median

Mode

Range

✏️ Part 2: Short Answers & Calculations

5. Identify the variable type for this measurement: Foot length in centimetres (e.g., 22.5 cm).

6. Use the following class foot-length data (cm) to calculate summary statistics. Show working:

Data: 22.5, 23.0, 22.0, 24.5, 23.0, 21.5, 22.0

a) State the variable type:

b) Calculate the mean (show steps):

c) Find the median:

d) Identify the mode(s):

e) Calculate the range:

7. Planning: For the investigative question "Are our feet the same length?", list three variables you would collect and write the variable type next to each (categorical / discrete / continuous).

8. Reflection: In one or two sentences, explain why it matters to know whether a variable is categorical or numerical when planning data collection.