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📖 Lesson 2 ⏱ ~30 min Year 10 · Unit 4 ⚡ +50 XP

Collecting Data

Understand sampling methods, surveys, and how to identify and minimise bias in data collection.

Today's hook:
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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
+5 XP each

Q1 · If you wanted to know the average height of every Year 10 student in NSW, would you measure every single one? What might be a faster way?

Q2 · What could go wrong if you only asked your closest friends about their opinions on a new school policy?

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From the lesson
Intentions

Learning Intentions

Know

  • Common sampling methods include random, stratified, systematic and convenience sampling.

Understand

  • How bias arises from poor sampling and how it affects the reliability of conclusions.

Can Do

  • Design a simple survey, choose an appropriate sampling method, and identify sources of bias.
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From the lesson
Key Terms

Key Terms

Population — The entire group about which we want to draw conclusions.
Sample — A subset of the population selected to represent the whole group.
Random sampling — Every member of the population has an equal chance of being selected.
Bias — A systematic error that causes the sample to misrepresent the population.
Stratified sampling — Dividing the population into subgroups and randomly sampling from each.
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From the lesson
Misconceptions

Misconceptions to Fix

✗

Wrong: A larger sample always removes bias.

✓

Right: Sample size alone does not eliminate bias — the sampling method must be unbiased. A convenience sample of 10,000 people is still biased if it over-represents one group.

✗

Wrong: Voluntary response sampling gives everyone an equal chance.

✓

Right: Voluntary response sampling is self-selected and systematically over-represents people with strong opinions, creating bias regardless of size.

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From the lesson
Content

Collecting Data

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

Remember When creating class intervals, always ensure: (1) no gaps between intervals, (2) no overlap, and (3) equal width where possible.
HSC Note Examiners often test whether you can identify errors in frequency tables. Common errors include overlapping intervals, unequal widths, and gaps between intervals.
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From the lesson
Activity
✏ Activity 1 — Build a Frequency Table

The following data shows the number of hours 30 students spent on homework last week:

  1. 5, 8, 12, 15, 18, 20, 22, 25, 28, 30, 5, 8, 10, 12, 15, 18, 20, 22, 25, 28, 5, 8, 10, 12, 15, 18, 20, 22, 25, 28
  2. (a) Create a grouped frequency table using class intervals of width 10 (0-9, 10-19, 20-29, 30-39).
  3. (b) Identify the modal class.
  4. (c) Calculate the class width.
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From the lesson
Worked Example

Worked Example

Step-by-step
The ages of 40 people at a community centre are recorded. Create a grouped frequency table using class intervals of width 10, starting at 0-9.
  1. 1
    List the class intervals: 0-9, 10-19, 20-29, 30-39, 40-49, 50-59, 60-69, 70-79.
  2. 2
    Tally the data: Count how many values fall into each interval using tally marks.
  3. 3
    Write the frequency: Convert tally marks to frequencies.
  4. 4
    Check: Sum of frequencies = total number of data values (40).
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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 A teacher surveys only students in the front row. This is an example of:

1 mark Which sampling method gives every person an equal chance of selection?

1 mark Asking only Year 12 students about school uniform policy creates:

1 mark In stratified sampling, the population is divided into:

1 mark A census collects data from:

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From the lesson
Short Answer

Short Answer

Show all working and justify your answers.

1. 3 marks The following data shows the test scores of 25 students: 45, 52, 58, 62, 65, 68, 72, 75, 78, 80, 82, 85, 88, 90, 92, 48, 55, 60, 63, 67, 70, 73, 76, 79, 81. Create a grouped frequency table using class intervals of width 10 (40-49, 50-59, etc.). Identify the modal class.

2. 2 marks A student creates a frequency table with class intervals 0-5, 5-10, 10-15. Explain why this is incorrect and rewrite the class intervals correctly.

3. 3 marks A data set has values ranging from 12 to 87. You want to create a grouped frequency table with approximately 6 class intervals. Determine an appropriate class width and list the class intervals.

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

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