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📖 Lesson 1 ⏱ ~30 min Year 10 · Unit 4 ⚡ +50 XP

Types of Data

Distinguish between categorical and numerical data, and between discrete and continuous variables.

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Core learning
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From the lesson
Worksheet

Worksheet

Use the worksheet to complete this lesson in your book or digitally.

Warm-up
Think First
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Q1 · What kinds of information can we collect about a group of people? How would you group them into categories like numbers versus words?

Q2 · If you surveyed your class about their favourite sport, what would the results look like? Would they be numbers, names, or something else?

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From the lesson
Intentions

Learning Intentions

Know

  • Categorical data uses labels or names; numerical data uses numbers. Discrete data has distinct values; continuous data can take any value in a range.

Understand

  • Why the type of data determines which statistical techniques and displays are appropriate.

Can Do

  • Classify data as categorical, discrete numerical or continuous numerical.
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From the lesson
Key Terms

Key Terms

Categorical data — Data that can be sorted into groups or categories, e.g. colours, gender.
Numerical data — Data that involves numbers and can be counted or measured.
Discrete data — Numerical data that can only take specific values, usually whole numbers.
Continuous data — Numerical data that can take any value within a range, including decimals.
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From the lesson
Misconceptions

Misconceptions to Fix

✗

Wrong: All numbers are numerical data, so shoe sizes and postcodes are continuous.

✓

Right: Shoe sizes and postcodes use numbers as labels, not measurements. They are categorical (ordinal), not continuous numerical.

✗

Wrong: Discrete data cannot include decimals.

✓

Right: Discrete data has distinct, separate values. Money ($2.50) is discrete because it jumps in 1c steps. It is not continuous because you cannot have $2.501.

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From the lesson
Content

Types of Data

Work through the content, activities and worked examples below. Test your understanding with the questions in the Questions phase.

Remember The key question: Are the values labels (categorical) or measurements/counts (numerical)? If numerical, can the variable take any value in a range (continuous) or only specific values (discrete)?
HSC Note NESA expects you to classify data correctly before choosing summary statistics or displays. A common exam trap is presenting continuous data in a bar chart or categorical data in a histogram.
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From the lesson
Activity
✏ Activity 1 — Classify These

Classify each variable as categorical, discrete numerical or continuous numerical. Justify your choice.

  1. The number of pets owned by each student in a class.
  2. The time taken to run 100 metres.
  3. The brand of mobile phone used by each student.
  4. The temperature recorded at noon each day for a month.
  5. The shoe size of each student.
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From the lesson
Worked Example

Worked Example

Step-by-step
A survey records the following for 50 students: height (cm), number of siblings, favourite subject, and time spent on homework (hours). Classify each variable.
  1. 1
    Height (cm): This is measured and can take any value in a range (e.g., 165.3 cm). It is continuous numerical.
  2. 2
    Number of siblings: This is counted and can only be whole numbers (0, 1, 2, ...). It is discrete numerical.
  3. 3
    Favourite subject: These are labels/names (Maths, English, etc.). It is categorical.
  4. 4
    Time on homework: Time is measured and can take any value (e.g., 2.5 hours). It is continuous numerical.
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From the lesson
Revisit

Revisit Your Thinking

Look back at your Think First response. What new understanding do you have now?

Reflect
Revisit your thinking
reflect

Earlier you were asked: What was your first thought on this topic?

Now that you've worked through the lesson, write a fuller answer. What changed in your thinking?

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From the lesson
Multiple Choice

Multiple Choice

Select the best answer for each question.

1 mark The number of students in a classroom is:

1 mark The height of students measured to the nearest centimetre is:

1 mark Eye colour recorded as blue, brown or green is:

1 mark Which of the following is discrete numerical?

1 mark Which display is most appropriate for categorical data?

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From the lesson
Short Answer

Short Answer

Show all working and justify your answers.

1. 2 marks A researcher collects the following data from a group of Year 10 students: age in years, postcode, number of hours spent on social media per day, and favourite music genre. Classify each variable as categorical, discrete numerical or continuous numerical. Give a reason for each classification.

2. 3 marks A student claims that "shoe size is continuous numerical data because it uses numbers." Explain why this claim is incorrect, and state the correct classification. In your answer, distinguish between the number itself and what the number represents.

3. 3 marks For each of the following scenarios, identify the most appropriate display and justify your choice:
(a) The heights of 100 seedlings measured to the nearest millimetre.
(b) The favourite fruit chosen by 50 students from a list of 5 options.
(c) The number of text messages sent per day by 30 students.

Marking guidance: 1 mark each for MCQs. See mark allocations for each short answer question.

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