Grade 7 · Grade 7: Sampling and Probability · Sampling and Probability
Random Sampling and Comparing Populations
Use random samples to make inferences and compare two distributions using centre and spread.
Learning objectives
- Explain why random samples tend to be representative.
- Estimate a population characteristic from sample data.
- Describe how estimates vary between samples.
- Compare two distributions using overlap and variability.
AERO Mathematics alignment
AERO.M7.SP.1
Understand that statistics can gain information about a population by examining a sample, and that random sampling tends to produce representative samples.
AERO.M7.SP.2
Use data from a random sample to draw inferences about a population, generating multiple samples to gauge the variation in estimates.
AERO.M7.SP.3
Informally assess the degree of visual overlap of two numerical data distributions, measuring the difference between centres as a multiple of a measure of variability.
MYP criteria
- Criterion A — Knowing and understanding
- Criterion B — Investigating patterns
- Criterion C — Communicating
- Criterion D — Applying mathematics in real-life contexts
ENGAGE
Start here
To find the favourite sport of a whole school, one student asks only the football team.
Think about it
What is wrong with this sample, and how would you fix it?
Hint: Think about who has a chance of being asked.
EXPLAIN
Samples, inference and comparison
A population is the whole group you want to describe. A sample is the part you actually measure. In a random sample every member has an equal chance of being chosen, which is what makes the sample tend to be representative.
Estimating from a sample
If 18 out of 60 randomly chosen students walk to school, the sample proportion is 0.3, so you estimate about 30% of the 900 students, or roughly 270 people. Different samples give slightly different estimates; larger samples vary less.
Comparing two populations
| Group | Median | IQR | Interpretation |
|---|---|---|---|
| Class A | 32 | 6 | Typically higher and fairly consistent |
| Class B | 26 | 12 | Lower and much more spread out |
The medians differ by 6, which is one full IQR of Class A. A difference that is large compared with the spread is meaningful; a difference much smaller than the spread is not.
Common misconception
A big sample cannot rescue a biased method. Asking 500 people outside a stadium still over-represents sports fans.
INVESTIGATION
Try it yourself
Take three separate random samples of 10 from the same group and estimate the same quantity each time. Record how much your three estimates differ, then take one sample of 30 and compare the variability.
Watch
Basic Probability
Math Antics · 11:28
Grounds the idea that data from part of a group can describe the whole.
Before you watch: Why might asking only your friends give a biased result?
- Why does a random sample tend to represent a population?
- How does a larger sample change your estimate?
Interactive simulation · PhET
Plinko Probability
Drop 10, 100 and 1000 balls, recording the shape of the distribution each time.
While you explore
- How does sample size change the reliability of your estimate?
- Why do small samples vary so much?
Key vocabulary
- Random sample
- A sample where everyone has an equal chance of being picked.
- Population
- The whole group you want to know about.
Practice questions
0/1 correct
Level 1 · Criterion A
Which sampling method is most likely to be representative of a whole school?
MYP criterion tasks
Level 2 · Criterion D
In a random sample of 80 students, 28 cycle to school. Estimate how many of the 1000 students cycle, and state one limitation.
Reflect & track
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