CH08-01 lesson

Populations and Samples Learning Activity

A focused Grade 7 learning session for Populations and Samples using visual models, worked examples, strategy guidance, and a short mastery check.

Start the lesson Print practice sample
15
minutes
6
lesson parts
11
practice items
Learning goal

Students will build Grade 7 mastery of populations and samples using models, equations, and test-style reasoning.

Student goal: I can solve problems involving populations and samples.

concept

Learn the Idea

Populations and Samples is part of Grade 7 Statistics. This activity focuses on the central idea students need before they move into independent practice.

Students will build Grade 7 mastery of populations and samples using models, equations, and test-style reasoning.

visual model

See the Math

What to noticeHow to use it
Numbers, units, labels, diagrams, or graphsIdentify what each part represents before calculating.
The relationship in the problemConnect the model to an equation, comparison, or explanation.

Use the figures and worked questions in the practice set below as the visual model for this skill.

worked example

Follow a Worked Example

Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.

For Populations and Samples, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.

real world

Connect It to a Real Situation

Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.

After solving, explain what the answer means in the situation, not just the number you calculated.

strategy

Avoid Mistakes and Choose a Strategy

  • Underline the exact question before solving.
  • Label units, variables, or graph axes when they appear.
  • Estimate first so unreasonable answers are easier to catch.
  • Review missed questions and write the reason for each mistake.
summary

Remember the Key Idea

I can solve problems involving populations and samples.

Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.

Guided to independent practice

Solve before opening the answer

Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.

warmup

2 questions
G7-C08-T01-Q001 About 1 min

A principal wants to know the average number of hours students study per week at her school. Which is the BEST way to collect a representative sample?

  1. A Survey only the students in her own homeroom
  2. B Survey the first \(30\) students who arrive Monday morning
  3. C Randomly select \(30\) students from each grade
  4. D Survey only students on the honor roll
Check answer and explanation

Answer C: Randomly select \(30\) students from each grade

This is stratified random sampling: dividing the population into groups (grades) and randomly selecting from each ensures all grade levels are represented proportionally. This avoids bias toward any one grade's study habits.

G7-C08-T01-Q002 About 1 min

A school wants to know which sports are most popular among its students. Compare these two methods: Why is Method 2 more likely to produce an accurate estimate?

  1. A Method 1: Ask the students in the first period gym class
  2. B Method 2: Randomly select 30 students from a complete list of all students
Check answer and explanation

Answer B: Method 2: Randomly select 30 students from a complete list of all students

Random selection from all students ensures the sample is representative because it includes diverse students: athletes and non-athletes, different grade levels, and different interests. Method 1 only surveys gym class students, who are more likely to favor sports, making that sample biased and unrepresentative of all students.

guided

1 question
G7-C08-T01-Q003 About 1 min

A clothing store manager wants to find out which style of jeans is most popular among teenagers in her city. If she only surveys customers who shop at her store on Saturday afternoons, what type of bias is present?

  1. A Convenience sampling
  2. B Voluntary response bias
  3. C Leading question bias
  4. D Non-response bias
Check answer and explanation

Answer A: Convenience sampling

Surveying only customers at one store at one time is a convenience sample because it only includes people who are easy to reach, not a random selection of all teenagers in the city.

practice

5 questions
G7-C08-T01-Q004 About 1 min

A survey asks: "Don't you agree that our school lunch program provides terrible food?" What sampling problem does this question have?

  1. A Convenience sample
  2. B Leading question
  3. C Voluntary response bias
  4. D Insufficient sample size
Check answer and explanation

Answer B: Leading question

The question is phrased to suggest a particular answer ("terrible food") rather than remaining neutral, which influences how people respond.

G7-C08-T01-Q005 About 1 min

Which group is an example of a population in a statistical study?

  1. A \(200\) students randomly selected from all high schools in Texas
  2. B All teenagers who own a smartphone
  3. C Shoppers interviewed at one mall on Saturday
  4. D The \(50\) customers called to participate in a phone survey
Check answer and explanation

Answer B: All teenagers who own a smartphone

A population is the entire group of interest. All teenagers who own a smartphone is the complete group; the other options describe samples or parts of a larger population.

G7-C08-T01-Q006 About 1 min

A museum director wants to estimate how many visitors will spend more than one hour at the museum. She collects data by asking every \(10\)th visitor who enters. Is this a good sampling method?

  1. A No; it is a convenience sample
  2. B No; it uses voluntary response bias
  3. C Yes; it is a systematic random sample
  4. D Yes; it is a stratified sample
Check answer and explanation

Answer C: Yes; it is a systematic random sample

Asking every \(10\)th visitor is systematic random sampling. Since the pattern (every 10th) doesn't depend on characteristics of individual visitors, it provides a representative, unbiased sample of all museum visitors.

G7-C08-T01-Q007 About 1 min

A school wants to estimate the average amount of time students spend on homework per night. Which sample size is best?

  1. A \(10\) students
  2. B \(25\) students
  3. C \(100\) students
  4. D \(1000\) students
Check answer and explanation

Answer C: \(100\) students

A sample of \(100\) students balances accuracy with practicality. Samples of \(10\) and \(25\) are too small to reliably represent the whole school; \(1000\) would give similar accuracy but be costly and time-consuming to conduct.

G7-C08-T01-Q008 About 1 min

A restaurant manager posts a survey on Facebook asking customers for feedback. What bias is introduced by this sampling method?

  1. A Voluntary response bias
  2. B Stratified bias
  3. C Systematic bias
  4. D Measurement bias
Check answer and explanation

Answer A: Voluntary response bias

Only people who choose to respond to the Facebook survey are included. This typically includes people with strong opinions (positive or negative), making it non-representative.

exit

3 questions
G7-C08-T01-Q009 About 1 min

A company wants to estimate the average salary of all its employees. It randomly selects \(50\) employees and calculates the mean. The \(50\) employees are a \underline{\hspace{3cm}} of all company employees.

  1. A population
  2. B sample
  3. C statistic
  4. D parameter
Check answer and explanation

Answer B: sample

A sample is a subset of the population selected for study. The \(50\) employees are part of the entire employee population, so they form the sample.

G7-C08-T01-Q010 About 1 min

A polling company uses a phone directory to call residents and ask about voting intentions. What bias might this method have?

  1. A Neither; it is a random sample
  2. B Excludes people with unlisted phone numbers and cell-phone-only users
  3. C Only calls during evening hours
  4. D Leads respondents to lie about their voting plans
Check answer and explanation

Answer B: Excludes people with unlisted phone numbers and cell-phone-only users

Phone directories only include people with listed landline numbers, which excludes people with unlisted numbers and younger voters who use only cell phones. This coverage bias makes the sample unrepresentative of all voters in the area.

G7-C08-T01-Q011 About 1 min

A school cafeteria manager wants to know which vegetables students prefer. She surveys only students who buy lunch on a given day. What population is she actually not surveying?

  1. A Students who eat no vegetables
  2. B Students who bring lunch from home
  3. C Students who buy lunch every day
  4. D All students in the school
Check answer and explanation

Answer B: Students who bring lunch from home

By surveying only lunch-buyers that day, she misses students who bring lunch from home. This creates a non-response bias and an unrepresentative sample.

Keep the learning path connected
Previous skillCylinder Surface Area and Volume Recommended nextMaking Inferences from Random Samples Same strandMaking Inferences from Random Samples Same strandComparing Two Populations Visually
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