Testinar Grade 7 math

Comparing Two Populations Visually

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

CH08-03 Statistics

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Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

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. Class A and Class B score ranges overlap from 71 to 85
2. Class A's scores varied more and its typical score was higher
3. Class B is always worse regardless of median
4. Class A has higher minimum but Class B more consistent
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)?
1. Group 1
2. Group 2
3. Both groups have the same median
4. Cannot be determined from the plot
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. Grade 7's typical height is greater, and distributions overlap from 58–68 inches
2. Every Grade 7 student is taller than Grade 6
3. Grade 6 is always shorter
4. Grade 6 has more height variation
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. Company X has a higher median and less spread
2. Company Y has younger workers overall
3. Both companies have the same age distribution
4. Company X workers are older than Company Y workers
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. City A has more variable temperatures
2. City B is always hotter than City A
3. Distributions overlap at 70–75 degrees; City A is more consistent
4. City B never reaches City A's temperature
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. Morning students scored higher on average
2. Afternoon students are smarter
3. Both classes performed equally well
4. Quiz difficulty was higher for morning students
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. Restaurant X (clustered around 5 minutes)
2. Restaurant Y (varies from 2 to 15 minutes)
3. Both restaurants have equally predictable times
4. Restaurant Y is always faster
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. Museum A appeals mainly to younger adults; Museum B attracts a broader age range
2. Museum B is more popular than Museum A
3. Museum A has older visitors overall
4. Both museums serve the same demographics

Teacher and parent reference

Answer key and explanations

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.
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.
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.
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.
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.
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.
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.
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.