CH08-04 lesson

Comparing Populations with Measures of Center and Variability Learning Activity

A focused Grade 7 learning session for Comparing Populations with Measures of Center and Variability 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 comparing populations with measures of center and variability using models, equations, and test-style reasoning.

Student goal: I can solve problems involving comparing populations with measures of center and variability.

Helpful first: Comparing Two Populations Visually
concept

Learn the Idea

Comparing Populations with Measures of Center and Variability 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 comparing populations with measures of center and variability 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 Comparing Populations with Measures of Center and Variability, 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 comparing populations with measures of center and variability.

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-T04-Q001 About 1 min

Store A has a mean daily sales of \($450\) with a MAD of \($30\). Store B has a mean of \($480\) with a MAD of \($90\). Which conclusion is best supported?

  1. A Store A typically sells more than Store B
  2. B Both stores are equally consistent
  3. C Store B typically sells more, but with less consistency
  4. D Store B's sales are more predictable due to lower MAD
Check answer and explanation

Answer C: Store B typically sells more, but with less consistency

Store B has a higher mean (\($480\) vs.\ \($450\)), indicating higher center. Its larger MAD (\($90\) vs.\ \($30\)) shows greater variability, meaning less consistency. A is false (Store A's mean is lower). B is false (MADs differ). D is false (lower MAD = more predictable, but Store B has higher MAD).

G7-C08-T04-Q002 About 1 min

Two basketball teams' free-throw percentages over 10 games are shown below. Based on this data, which statement is most accurate?

Comparing Populations with Measures of Center and Variability visual for G7-C08-T04-Q002
  1. A The Sharks are more reliable free-throw shooters
  2. B The Tigers never miss a free throw
  3. C The Sharks score more points overall
  4. D Both teams have the same consistency
Check answer and explanation

Answer A: The Sharks are more reliable free-throw shooters

Although Tigers have a higher mean (75% vs.\ 72%), the Sharks have much lower MAD (4% vs.\ 8%), indicating more consistent free-throw shooting.

guided

1 question
G7-C08-T04-Q003 About 1 min

The weights (in pounds) of two dog breeds are recorded: Which breed has more consistent weight?

Comparing Populations with Measures of Center and Variability visual for G7-C08-T04-Q003
  1. A Breed A (mean 47, smaller spread)
  2. B Breed B (larger sample size)
  3. C Both have equal consistency
  4. D Cannot determine from the data
Check answer and explanation

Answer A: Breed A (mean 47, smaller spread)

Breed A ranges from 45--49 (range = 4), while Breed B ranges 35--55 (range = 20). Smaller range indicates greater consistency.

practice

5 questions
G7-C08-T04-Q004 About 1 min

Two groups of students took a math test. Group 1: mean = 82, median = 85. Group 2: mean = 82, median = 80. What does this tell us?

  1. A Group 1 has higher scores in the upper half
  2. B Group 2 performed better overall
  3. C Both groups are identical
  4. D Group 1 has outliers on the low end
Check answer and explanation

Answer D: Group 1 has outliers on the low end

Group 1 has mean 82 but median 85. Since median is higher than mean, there are likely some very low scores pulling the mean down (low outliers).

G7-C08-T04-Q005 About 1 min

A teacher recorded the number of minutes students spent on homework: Which class has more variable homework times?

Comparing Populations with Measures of Center and Variability visual for G7-C08-T04-Q005
  1. A Period 1
  2. B Period 2
  3. C Both are equally variable
  4. D The data does not support comparison
Check answer and explanation

Answer B: Period 2

Period 2 has a range of 60 minutes, much larger than Period 1's range of 20 minutes, indicating more variability in homework times.

G7-C08-T04-Q006 About 1 min

The dot plots below show the daily temperatures (in \(°\)F) for two months: Which month is more consistent in temperature?

Comparing Populations with Measures of Center and Variability visual for G7-C08-T04-Q006
  1. A Month 1 (tighter cluster)
  2. B Month 2 (wider spread)
  3. C Both have equal consistency
  4. D Cannot tell from dot plots
Check answer and explanation

Answer A: Month 1 (tighter cluster)

Month 1's dots cluster around 71--73\textdegree F (x-coordinates 1--3.5 map to 70--75\textdegree F), a narrow range of 2\textdegree F. Month 2's dots span from 71 to 82\textdegree F (x-coordinates 1--12, range \(\approx\) 11\textdegree F). Month 1 is more consistent.

G7-C08-T04-Q007 About 1 min

Two datasets have the same mean of 50. Dataset X has an IQR of 10. Dataset Y has an IQR of 25. What does this imply?

  1. A Dataset X is more spread out
  2. B Dataset Y is more spread out in the middle 50%
  3. C Both are identical except for outliers
  4. D Dataset Y has a smaller range
Check answer and explanation

Answer B: Dataset Y is more spread out in the middle 50%

IQR (Interquartile Range) measures the middle 50% of data. Dataset Y's IQR of 25 is larger than Dataset X's IQR of 10, showing greater spread in the middle half.

G7-C08-T04-Q008 About 1 min

A coach compared jump heights (in inches) of two volleyball teams: Which team has both a higher center and more consistency?

Comparing Populations with Measures of Center and Variability visual for G7-C08-T04-Q008
  1. A Team A
  2. B Team B
  3. C Both are identical
  4. D The data is insufficient
Check answer and explanation

Answer A: Team A

Team A has a higher mean (28 vs.\ 26) and lower MAD (2.5 vs.\ 4.8), meaning both a higher center and more consistent performance.

exit

3 questions
G7-C08-T04-Q009 About 1 min

Two grocery stores tracked the number of customers per hour over 5 hours: Which store had more predictable traffic?

Comparing Populations with Measures of Center and Variability visual for G7-C08-T04-Q009
  1. A Store X (mean 47, less variability)
  2. B Store Y (more customers on average means more predictable)
  3. C Both are equally predictable
  4. D Cannot determine without knowing which store is busier
Check answer and explanation

Answer A: Store X (mean 47, less variability)

Store X: 45, 46, 47, 48, 49 (mean = 47, range = 4, tightly clustered). Store Y: 31, 44, 52, 58, 65 (mean = 50, range = 34, highly variable). Predictability depends on consistency (low variability), not total customer count. Store X's tight clustering makes it far more predictable for planning staffing.

G7-C08-T04-Q010 About 1 min

A teacher gives Practice Test 1 and Practice Test 2. Both have a mean of 75. Test 1 has a range of 15 points. Test 2 has a range of 40 points. What conclusion is valid?

  1. A Test 2 is harder than Test 1
  2. B Test 1 had more consistent performance across students
  3. C Students performed identically on both tests
  4. D Test 2 is easier
Check answer and explanation

Answer B: Test 1 had more consistent performance across students

Test 1's smaller range (15 vs.\ 40) indicates students' scores were closer together, showing more consistent performance despite identical means.

G7-C08-T04-Q011 About 1 min

Which measure describes how spread out data is?

  1. A Mean
  2. B Median
  3. C Range
  4. D Mode
Check answer and explanation

Answer C: Range

Range (max \(-\) min) measures how spread out data is. Mean, median, and mode measure center, not spread.

Keep the learning path connected
Previous skillComparing Two Populations Visually Recommended nextStem-and-Leaf Plots Same strandPopulations and Samples Same strandMaking Inferences from Random Samples
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