CH08-03 lesson

Comparing Two Populations Visually Learning Activity

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

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15
minutes
6
lesson parts
11
practice items
Learning goal

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

Student goal: I can solve problems involving comparing two populations visually.

Helpful first: Making Inferences from Random Samples
concept

Learn the Idea

Comparing Two Populations Visually 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 two populations visually 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 Two Populations Visually, 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 two populations visually.

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-T03-Q001 About 1 min

Two box plots show the test scores of Class A (median \(=82\), range \(=30\)) and Class B (median \(=78\), range \(=14\)). The box plot for Class A spans from 67 to 97; Class B spans from 71 to 85. Which statement is best supported by the visuals?

  1. A Class A and Class B score ranges overlap from 71 to 85
  2. B Class A's scores varied more and its typical score was higher
  3. C Class B is always worse regardless of median
  4. D Class A has higher minimum but Class B more consistent
Check answer and explanation

Answer B: Class A's scores varied more and its typical score was higher

Class A's range of 30 (67–97) is larger than Class B's range of 14 (71–85), showing greater variability. Class A's median (82) is higher than Class B's (78). Despite overlap at 71–85, Class A is higher and more variable overall.

G7-C08-T03-Q002 About 1 min

The dot plots below show the number of text messages sent by two groups of students during a school day. Which group has a higher center (median)?

Comparing Two Populations Visually visual for G7-C08-T03-Q002
  1. A Group 1
  2. B Group 2
  3. C Both groups have the same median
  4. D Cannot be determined from the plot
Check answer and explanation

Answer B: Group 2

Group 2's dots are positioned further to the right (at 3, 3.5, 4, 5, 5.5, 6, 6.5) compared to Group 1 (at 1, 1.5, 2, 2.5, 3.5), so the median of Group 2 is higher.

guided

1 question
G7-C08-T03-Q003 About 1 min

A histogram shows heights (in inches) of students in two grades. Grade 6's histogram peaks at 60–62 inches (range 55–68 inches). Grade 7's histogram peaks at 63–65 inches (range 58–70 inches). Based on this comparison, which statement is TRUE?

  1. A Grade 7's typical height is greater, and distributions overlap from 58–68 inches
  2. B Every Grade 7 student is taller than Grade 6
  3. C Grade 6 is always shorter
  4. D Grade 6 has more height variation
Check answer and explanation

Answer A: Grade 7's typical height is greater, and distributions overlap from 58–68 inches

Grade 7 peaks at 63–65 (higher typical height) vs. Grade 6 at 60–62. The ranges (Grade 6: 55–68, Grade 7: 58–70) overlap significantly from 58–68 inches, so some Grade 6 students are taller than some Grade 7 students.

practice

5 questions
G7-C08-T03-Q004 About 1 min

A stem-and-leaf plot shows the ages of workers at two companies. Company X has data: 22, 24, 25, 26, 29; Company Y has data: 18, 19, 22, 45, 48. Which statement is best supported?

  1. A Company X has a higher median and less spread
  2. B Company Y has younger workers overall
  3. C Both companies have the same age distribution
  4. D Company X workers are older than Company Y workers
Check answer and explanation

Answer A: Company X has a higher median and less spread

Company X's median is 25, and Company Y's median is 22. Company X's range is 7 (29--22), while Company Y's range is 30 (48--18), showing less spread in Company X.

G7-C08-T03-Q005 About 1 min

Two histograms show daily temperature (in degrees Fahrenheit) over a month for City A and City B. City A's temperatures cluster at 70–75 degrees (range 5 degrees). City B's temperatures span 50–90 degrees (range 40 degrees). Where do the distributions overlap?

  1. A City A has more variable temperatures
  2. B City B is always hotter than City A
  3. C Distributions overlap at 70–75 degrees; City A is more consistent
  4. D City B never reaches City A's temperature
Check answer and explanation

Answer C: Distributions overlap at 70–75 degrees; City A is more consistent

City A clusters at 70–75 (range 5), indicating consistency. City B spans 50–90 (range 40), showing high variability. Both distributions include temperatures 70–75 degrees, so they overlap there.

G7-C08-T03-Q006 About 1 min

Two histograms compare the quiz scores of morning and afternoon classes. The morning class shows bars centered around 85\textendash 90, while the afternoon class shows bars centered around 75\textendash 80. What does this suggest?

  1. A Morning students scored higher on average
  2. B Afternoon students are smarter
  3. C Both classes performed equally well
  4. D Quiz difficulty was higher for morning students
Check answer and explanation

Answer A: Morning students scored higher on average

The histogram center (where bars cluster) indicates the typical score range. Morning (85--90) is higher than afternoon (75--80), so morning students performed better on average.

G7-C08-T03-Q007 About 1 min

A dot plot shows customer wait times (in minutes) at two restaurants. Restaurant X: 3, 4, 4, 5, 5, 5, 6, 6, 7 (minutes); Restaurant Y: 2, 5, 8, 10, 12, 15 (minutes). Which restaurant has more predictable wait times?

  1. A Restaurant X (clustered around 5 minutes)
  2. B Restaurant Y (varies from 2 to 15 minutes)
  3. C Both restaurants have equally predictable times
  4. D Restaurant Y is always faster
Check answer and explanation

Answer A: Restaurant X (clustered around 5 minutes)

Restaurant X has most data points near 5 minutes with range 4 (from 3 to 7). Restaurant Y's range is 13 (from 2 to 15) with data spread across the range, making it less predictable.

G7-C08-T03-Q008 About 1 min

Two box plots compare monthly rainfall (in inches) for Region A and Region B. Region A: IQR (Interquartile Range) = 3 inches; Region B: IQR = 8 inches. What does this comparison reveal?

  1. A Region A has more variable rainfall
  2. B Region B has a wider middle 50% of data (more variability in the middle)
  3. C Both regions have identical rainfall patterns
  4. D Region A receives more total rain annually
Check answer and explanation

Answer B: Region B has a wider middle 50% of data (more variability in the middle)

The IQR (from Q1 to Q3) represents the spread of the middle 50% of data. A larger IQR (8 vs. 3) indicates more variability in the central portion of the distribution.

exit

3 questions
G7-C08-T03-Q009 About 1 min

A histogram shows the ages of visitors at Museum A and Museum B. Museum A has visitors aged 20\textendash 30 dominating the histogram. Museum B has visitors more evenly distributed across ages 10\textendash 70. Which interpretation is valid?

  1. A Museum A appeals mainly to younger adults; Museum B attracts a broader age range
  2. B Museum B is more popular than Museum A
  3. C Museum A has older visitors overall
  4. D Both museums serve the same demographics
Check answer and explanation

Answer A: Museum A appeals mainly to younger adults; Museum B attracts a broader age range

The histogram shows where the majority of data concentrates. Museum A's concentration at 20--30 indicates younger adult appeal. Museum B's even distribution shows visitors of all ages.

G7-C08-T03-Q010 About 1 min

Two dot plots show the number of text messages sent during a study session by two groups. Group P: 5, 6, 6, 7, 7, 7, 8, 8, 9 (messages); Group Q: 1, 2, 9, 10, 11, 12 (messages). Which group was more focused (less distracted)?

  1. A Group P (consistent messaging around 7)
  2. B Group Q (sent very few messages)
  3. C Both groups sent identical messages
  4. D Group Q was more focused
Check answer and explanation

Answer A: Group P (consistent messaging around 7)

While both groups sent messages, Group P's clustering at 7 messages shows a consistent pattern during study. Group Q's extreme values (1--2, then 9--12) suggest interruptions, making Group P appear more consistently focused.

G7-C08-T03-Q011 About 1 min

A box plot compares video game scores (in points) for two players. Player A: Median = 1500, Q1 = 1200, Q3 = 1800. Player B: Median = 1400, Q1 = 1100, Q3 = 2000. Which player has more consistent performance?

  1. A Player A (smaller IQR: 600 vs. 900)
  2. B Player B (higher third quartile)
  3. C Both players have identical consistency
  4. D Player B (higher maximum score)
Check answer and explanation

Answer A: Player A (smaller IQR: 600 vs. 900)

Player A's IQR = 1800 -- 1200 = 600; Player B's IQR = 2000 -- 1100 = 900. A smaller IQR indicates less variability in the middle 50% of scores, so Player A is more consistent.

Keep the learning path connected
Previous skillMaking Inferences from Random Samples Recommended nextComparing Populations with Measures of Center and Variability Same strandPopulations and Samples Same strandMaking Inferences from Random Samples
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