Grade 7 Comparing Two Populations Visually

Visual Model 1

Question: 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)?

• A. Group 1
• B. Group 2
• C. Both groups have the same median
• D. Cannot be determined from the plot

Why it works: 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.

Answer: Group 2

Visual Model 2

Question: Looking at the dot plots of items purchased, which statement best describes the overlap?

• A. Group A typically buys fewer items; Groups overlap at 4--5
• B. Group B always buys more items than Group A
• C. No overlap exists between the groups
• D. Both groups buy identical amounts

Why it works: Group A centers at 3--5 (peak at 4). Group B centers at 5--9 (peak at 7). Overlap occurs at 4--5. Group A's lower center is clear despite overlap.

Answer: Group A typically buys fewer items; Groups overlap at 4--5

Example 1

Question: The box plots show practice hours for two soccer teams. Based on the visual, what is true about their centers and spreads?

• A. Team A: median \(\approx 4.5\); Team B: median \(\approx 6.5\); Team B more spread
• B. Team A practices more than Team B
• C. Both teams practice identically
• D. Medians cannot be compared from box plots

1. From the visual: Team A's box (2--6) has median at 4.5.
2. Team B's box (4--9) has median at 6.5.
3. Team B's box spans 5 units (4--9) vs.
4. Team A's 4 units (2--6), so Team B has more spread.

Answer: Team A: median \(\approx 4.5\); Team B: median \(\approx 6.5\); Team B more spread

Example 2

Question: 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?

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

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

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

Example 3

Question: 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?

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

1. Grade 7 peaks at 63–65 (higher typical height) vs.
2. Grade 6 at 60–62.
3. 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.

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

Problem 1

Question: 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?

• A. City A has more variable temperatures
• B. City B is always hotter than City A
• C. Distributions overlap at 70–75 degrees; City A is more consistent
• D. City B never reaches City A's temperature

Why it works: 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.

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

Problem 2

Question: 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?

• A. Morning students scored higher on average
• B. Afternoon students are smarter
• C. Both classes performed equally well
• D. Quiz difficulty was higher for morning students

Why it works: 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.

Answer: Morning students scored higher on average