Learn with Amar
Teaching video
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Grade 10 chapters and video availability01 · Read and understand
What you will learn
- Distinguish sample size from representativeness.
- Justify the method and check its domain, units, or logical conditions.
Before you start
Algebraic equations, ratios, angle and area facts, and basic coordinate geometry.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
A school asks 300 students leaving an after-school sports event about all students' preferred activities. What problem remains despite the large response count?
Why this math matters
Name the population, sampling frame, and missing groups before interpreting a survey. The example connects a stated condition to a conclusion and then checks whether the result satisfies that condition.
Set up the model
A useful answer starts with clear assumptions:
- Use the real-number system and the restrictions or data model stated in the question unless another domain is specified.
- Treat provided measurements as exact classroom-model values unless an approximation or uncertainty is stated.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
A larger sample can still miss the population
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A school asks 300 students leaving an after-school sports event about all students' preferred activities. What problem remains despite the large response count?
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the conditions
Target population: all school students
The intended conclusion reaches beyond sports-event attendees.
Develop the calculation
Sampling frame: students leaving that sports event
Students who attend other activities or leave earlier are systematically less available.
Check and interpret
Selection bias can remain despite 300 responses
A large count reduces some random variability but does not repair systematic exclusion.
The result
Selection bias can remain despite 300 responses
A large count reduces some random variability but does not repair systematic exclusion.
Common mistakes to catch
- Large sample size is not evidence that selection is unbiased.
- A survey association does not by itself establish causation.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Would inviting a random sample from the full student roster improve coverage?
Show a hint
Give each student a known selection chance.
Reveal answer and explanation
Yes, provided responses are also examined for nonresponse bias
A better sampling frame addresses the event-only selection problem, but response patterns can still matter.
Practice 2
Can this survey prove sports participation causes a particular preference?
Show a hint
The groups were observed rather than randomly assigned.
Reveal answer and explanation
No
Existing differences and self-selection can explain the association.
Take the idea with you
Name the population, sampling frame, and missing groups before interpreting a survey.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Measure how far an observation is from a fitted line
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