Mathematics • Year 7 • Unit 4 • Lesson 2

Collecting Data

Build fluency with the three collection methods (survey, observation, experiment), the difference between census and sample, and how to spot bias in a question. Pick the right method and your data actually tells you what you wanted to know.

Build · I Do / We Do / You Do

1. I do — fully worked example

Read every line. Each step asks one targeted question and shows the reasoning.

Problem. The Maths club wants to know how long the school day FEELS to Year 7 students. They draft this question: "Most Year 7s agree the school day is too long, don't you?" Identify the type of bias, then rewrite the question fairly.

Step 1 — Find the loaded language.

"Most Year 7s agree" implies a majority already thinks the day is too long.

Reason: starting a question with a claim pressures the responder to agree.

Step 2 — Find the leading add-on.

"… don't you?" is a tag that pushes the responder toward saying YES.

Reason: tag questions are a classic source of leading bias.

Step 3 — Name the bias.

This is a leading question with built-in pressure to agree.

Reason: leading bias means the wording itself nudges responders one way.

Step 4 — Rewrite it neutrally with balanced options.

"How do you feel about the length of the school day? Too short / About right / Too long."

Reason: the new question gives equal weight to all three answers and contains no opinion.

Answer: Leading bias. Fair version: "How do you feel about the length of the school day? Too short / About right / Too long."

Stuck? Revisit lesson § "Spot the Trap" — leading words include "most", "obviously", "agree" and tags like "don't you?".

2. We do — fill in the missing steps

Decide whether each situation needs a survey, an observation, or an experiment. Fill in the blanks. 4 marks

Situation A. A council wants to know how many cars use a roundabout between 8 am and 9 am on a Tuesday.

No one needs to be asked anything; nothing is changed; you just watch and record.

Method: ______________________________

Situation B. A teacher wants to know whether using flashcards each night improves spelling test scores.

The teacher will deliberately change one variable (flashcards or no flashcards) and measure the effect on scores.

Method: ______________________________

Situation C. A school wants to know students' opinions about the canteen menu.

The school needs to ask people directly — opinions can't be observed.

Method: ______________________________

Situation D. The school PE coordinator wants to know how many push-ups every Year 7 student in the whole year can do — and there are 240 students. Census or sample?

Answer: ____________    Reason: ___________________________________________

Stuck? Revisit lesson § "Census vs Sample" — use a census when the group is small and the test is non-destructive.

3. You do — independent practice

Show your reasoning, not just the answer.

Foundation — choose the method

3.1 A wildlife group wants to count how many possums visit a tree each night. Survey, observation or experiment?    1 mark

3.2 A class wants to know which superpower their friends would pick: flight, invisibility or teleportation. Survey, observation or experiment?    1 mark

3.3 A scientist wants to test whether plants grow taller with classical music playing. Survey, observation or experiment?    1 mark

3.4 Define population and sample in your own words.    2 marks

Standard — apply the ideas

3.5 A factory tests every battery to see how many hours it lasts before going flat. Each test destroys the battery. Should the factory use a census or a sample? Justify in one sentence.    2 marks

3.6 Identify the bias in this survey question and rewrite it neutrally: "Do you support our great new uniform policy?"    2 marks

Extension — push your thinking

3.7 A student stands outside the school gym and asks the next 30 people who walk out: "Do you think sport is important?" Explain why the SAMPLE is biased, even if the question itself is fair.    3 marks

3.8 Design a fair survey question to find out which sport students would like the school to add to the after-school program. Use no more than 15 words, and provide at least three answer options.    2 marks

Stuck on 3.7? A biased sample chooses people who already lean toward the answer you'll get.

How did this worksheet feel?

What I'll revisit before next class:

Answers — Do not peek before attempting

Section 2 — We do

A: Observation (just watch and record cars).
B: Experiment (deliberately change flashcards on/off and measure scores).
C: Survey (opinions must be asked).
D: Census — there are only 240 students and the push-up test is non-destructive, so every student can be tested.

3.1 — Counting possums

Observation. You watch and record without changing anything or asking anyone.

3.2 — Superpower preference

Survey. Opinions and preferences can only be collected by asking people.

3.3 — Music and plant growth

Experiment. The scientist deliberately changes one variable (music on/off) and measures the effect on another (plant height) under controlled conditions.

3.4 — Population and sample

Population: the entire group you want to draw conclusions about (e.g. all Year 7 students in Australia).
Sample: a smaller group, chosen from the population, used to represent the whole.

3.5 — Battery factory

Sample. Testing destroys each battery, so a census (test every battery) would leave the factory with nothing to sell. A representative sample is the only sensible choice.

3.6 — "Do you support our great new uniform policy?"

The word "great" is loaded — it tells the responder the policy is good before they answer. This is leading bias.
Fair version: "What is your opinion of the new uniform policy? Support / Neutral / Oppose."

3.7 — Sample bias outside the gym

The 30 people walking out of the gym are people who have just CHOSEN to play sport. They are far more likely to say "yes, sport is important" than a random Year 7 student. The sample is not representative of the whole school — it's a self-selecting group of sport lovers. This is sampling bias: the place and time of collection skewed who answered.

3.8 — Fair sports survey question (sample)

"Which sport would you most like added to the after-school program? Volleyball / Soccer / Basketball / Other ____."
Marking: 1 for neutral wording (no "great", no "agree", no "most people"); 1 for at least three balanced answer options including a way to say "none of those".