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Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 7 chapters and video availability01 · Read and understand
What you will learn
- Explain how to recognize who a survey leaves out.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Population and sample terminology.
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
To estimate the favourite school lunch of all 600 students, a team surveys only 40 members of the cooking club. Identify the population, sample, and a better selection method.
Why this math matters
A sample can misrepresent a population when selection systematically favours particular members. Ask who had a chance to respond and who actually responded before trusting a survey summary.
Set up the model
A useful answer starts with clear assumptions:
- The target is the preferences of all enrolled students.
- Cooking-club participation may be related to food preferences.
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.
Recognize who a survey leaves out
PausedQuestion: Start with the question. Paused.
Question
Start with the question
To estimate the favourite school lunch of all 600 students, a team surveys only 40 members of the cooking club. Identify the population, sample, and a better selection method.
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 quantities
population = 600 students; sample = 40 cooking-club members
The population follows the question, while the sample is the group actually surveyed.
Apply the relationship
selection covers only club members
Nonmembers have no chance of inclusion, so the method can systematically miss preferences.
Check and interpret
select students randomly from the full roster
Giving every student a chance of selection addresses this coverage problem; nonresponse still needs attention.
The result
select students randomly from the full roster
Giving every student a chance of selection addresses this coverage problem; nonresponse still needs attention.
Common mistakes to catch
- A large sample is not necessarily a representative sample.
- Random selection and voluntary response describe different processes.
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 surveying 200 cooking-club members from several schools automatically represent this school's students?
Show a hint
Compare the selection frame with the target population.
Reveal answer and explanation
No
Increasing a biased or mismatched sample does not repair its coverage of the intended population.
Practice 2
A school randomly chooses 60 roster names but only 20 answer. What new concern appears?
Show a hint
Consider whether responders differ from nonresponders.
Reveal answer and explanation
Nonresponse bias
The final answers may be unrepresentative if willingness to respond is related to the lunch preference.
Take the idea with you
Ask who had a chance to respond and who actually responded before trusting a survey summary.
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 spread with mean absolute deviation
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