GANITA MANJARI · GRADE 9 · PART I · CHAPTER 7
SAMPLE — Evidence, samples and representativeness
Think first. Use AI purposefully. Verify always.
DISCOVER
Begin with your own prediction.
Twenty of fifty surveyed students prefer mangoes. Can one class alone tell you the exact preferences of 1500 students?
Write or sketch a first attempt. Use the model to test your assumptions before accepting a rule.
Understand
A sample provides evidence about a population, not certainty. How people are selected matters. A larger sample drawn through a biased method can still be unrepresentative.
Key Ideas
n(S), the number of possible outcomes, is not the number of people in a statistical survey. Neither a large sample nor an estimate guarantees the true population count.
Visualise
Who is included in the sample?
Illustrative population, not survey data: 100 people in equal groups A and B. In A, 40 of 50 prefer mango; in B, 10 of 50 do. The population share is 50%.
Method
Separate the observed sample proportion from the population estimate. Describe selection and possible bias. Sample across the relevant groups and label extrapolations as estimates.
Worked Example
Given
20 of 50 surveyed students prefer mangoes; school population 1500 (Example 5).
To Find
Estimated number of students in the school who prefer mangoes
Reasoning
Use the sample proportion only as an estimate, with representativeness as an assumption.
Solution
- Sample share: = 0.4.
- Estimated count: 0.4 × 1500 = 600.
- Sampling across grades would provide better coverage than using one class alone.
Result
About 600 students, as an estimate—not an exact known count.
AIMS Method
- A — Attempt independently
Predict and describe what is being recorded. - I — Investigate the idea
Identify the model, evidence and assumptions. - M — Make connections
Connect outcomes, events, fractions and tree paths. - S — Scrutinise your reasoning
Check completeness, likelihoods and changing conditions.
Think first. Use AI purposefully. Verify always.
Focused Practice
In a representative sample of 30 sweets, 7 are yellow. Estimate the number of yellow sweets in a bag of 600.
Check & Feedback
Explain the model, state an assumption and identify one conclusion the information does not justify.
Textbook connection: Ganita Manjari · Grade 9 · Part I · Chapter 7 · printed page 162