Testinar Grade 7 math

Data Displays Extended

Students will build Grade 7 mastery of data displays extended using models, equations, and test-style reasoning.

CH08-07 Statistics

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Score: ____ / 8

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

A histogram shows the same data displayed in two different ways: Version A uses intervals of width 5 (0--5, 5--10, 10--15, etc.), while Version B uses intervals of width 10 (0--10, 10--20, 20--30, etc.). How would the two histograms appear different?
1. Version A would show more detail and variation; Version B would show a smoother pattern
2. Both histograms would look identical regardless of interval width
3. Version B would be more accurate because larger intervals are always better
4. Version A would have fewer bars but higher frequencies
A line plot shows the number of goals scored by 15 soccer players this season:
Which statement best describes the data?
1. The data shows a uniform distribution with all scores equally common
2. Most players scored between 3 and 5 goals, with one outlier at 9
3. All players scored at least 2 goals, with the median at 4
4. The mode is 4 goals, appearing 4 times
A histogram shows the frequency of ages in a fitness class: 10--20 (6), 20--30 (18), 30--40 (24), 40--50 (12). A promotional flyer claims "Our class serves ALL age groups equally." Is this supported by the histogram?
1. Yes, because four different age intervals are shown
2. No, because frequencies vary significantly (6 to 24)
3. Yes, because the highest bar represents the most popular age group
4. No, because the bar widths are all equal
A dot plot shows the number of text messages sent by 12 students in one day: 5, 8, 10, 10, 12, 12, 12, 15, 18, 20, 22, 25. Which measure BEST represents the "typical" number of messages sent?
1. The mean (approximately 14.3)
2. The median (12.5)
3. The mode (12)
4. The range (20)
Two classes have test-score distributions displayed as histograms with identical means (both 75). Class A has most scores clustered near 75 (narrow, bell-shaped); Class B has scores spread across the range (flat). What does this comparison reveal?
1. Class A has higher variability than Class B
2. Class B has lower variability than Class A
3. Class A's shape shows less variability despite the same mean
4. The mean tells you everything about variability
The test scores of 24 students are: 72, 78, 81, 75, 89, 92, 74, 80, 85, 88, 76, 91, 84, 79, 86, 83, 77, 90, 73, 87, 82, 94, 68, 95. Which display would BEST show the spread and identify outliers?
1. Circle graph
2. Box plot
3. Pictograph
4. Scatter plot
A histogram shows the ages of people visiting a museum. The x-axis shows age intervals (10--20, 20--30, 30--40, etc.), and the heights of the bars show the number of people. What does the height of each bar represent?
1. The width of each age interval
2. The frequency (count) in each age interval
3. The average age in each interval
4. The age of the oldest person
A researcher collects data on the relationship between hours of sleep and performance on a math test for 20 students. Some data points show students who slept 7 hours and scored 60, while others slept 7 hours and scored 95. What does this variation BEST indicate?
1. Sleep has no effect on test performance
2. Sleep alone does not determine test scores; other factors matter
3. The data is incorrect because the same sleep results in different scores
4. Students who sleep 7 hours have inconsistent abilities

Teacher and parent reference

Answer key and explanations

A. Version A would show more detail and variation; Version B would show a smoother pattern
Smaller intervals reveal more variability and detail in the distribution; larger intervals group data together, creating a smoother appearance. Both are valid depending on the purpose.
D. The mode is 4 goals, appearing 4 times
Counting occurrences: 2 (twice), 3 (three times), 4 (four times), 5 (twice), 6 (twice), 7 (once), 9 (once). The value 4 appears most frequently, making it the mode.
B. No, because frequencies vary significantly (6 to 24)
Equal representation would show nearly equal frequencies. The 30--40 interval (24) has 4 times as many people as the 10--20 interval (6), contradicting the "equal" claim.
C. The mode (12)
The mode (12 messages, appearing 3 times) best represents what students "typically" sent because it identifies the most common value. The mean is inflated by 25 outliers, and the median (12.5) is between two values.
C. Class A's shape shows less variability despite the same mean
Two distributions can share a mean but differ in spread (variability). Shape reveals this: a narrow cluster indicates low variability; a flat spread indicates high variability.
B. Box plot
A box plot displays the quartiles, median, and extreme values (min/max), making outliers visually apparent as points beyond the whiskers.
B. The frequency (count) in each age interval
In a histogram, the height of each bar represents the frequency (count or number of data points) in that interval.
B. Sleep alone does not determine test scores; other factors matter
A scatter plot reveals association, not causation. Variation in scores at the same sleep duration indicates that other variables (studying, prior knowledge, test anxiety) also influence performance.