Lesson 3: Comparing Data Distributions Visually — Practice Questions

1. 1. Histograms show student homework times. Group A's data is concentrated in the `45-60` minute interval. Group B's data is spread out across intervals from `30-90` minutes. Which statement about variation is true?

   • A. Group A has greater variation.
   • B. Group B has greater variation.
   • C. Both groups have equal variation.
   • D. The variation cannot be compared.

2. 2. Histograms for two libraries show the number of books checked out daily. In the `200-250` books interval, the Main Library has a frequency of 35 days and the Branch Library has a frequency of 22 days. The difference is `___` days.

3. 3. A histogram for runners in a marathon shows most runners' ages are in the `30-40` year interval. A histogram for a 5k race shows ages are spread evenly from `20-60` years. What does this suggest?

   • A. The marathon runners have a wider age variation.
   • B. The 5k runners have a wider age variation.
   • C. The age variation is the same for both races.
   • D. No conclusion can be drawn about variation.

4. 4. Two teams' basketball scores are displayed on histograms with equal intervals. In the `80-90` point interval, the Eagles have a frequency of 8 games and the Falcons have a frequency of 3 games. The Eagles had `___` more games in this interval.

5. 5. When comparing two histograms, what is the most critical first step to ensure a fair comparison of the data distributions?

   • A. Check the total number of data points
   • B. Ensure the interval widths are identical
   • C. Find the average of each dataset
   • D. Count the number of bars

6. 6. A double dot plot compares fish lengths from Pond A and Pond B. The data for Pond A is clustered from 5-9 cm, while Pond B's data is clustered from 12-16 cm. What does the minimal overlap suggest?

   • A. The ponds have a similar fish population.
   • B. There is a significant difference between the fish sizes in the ponds.
   • C. The median fish length is the same for both ponds.
   • D. Pond A has a greater spread of fish lengths than Pond B.

7. 7. A double dot plot shows points scored by two players. Player 1's scores are tightly clustered around 20. Player 2's scores are spread from 10 to 30, centered around 24. Which statement is true?

   • A. Player 1 has a higher center and greater variability.
   • B. Player 2 has a higher center and greater variability.
   • C. Player 1 has a higher center and less variability.
   • D. Player 2 has a lower center and greater variability.

8. 8. A double dot plot shows the heights of two types of plants. Type X plants have heights from 8 to 15 inches. Type Y plants have heights from 12 to 19 inches. The overall range for both is 8 to ___ inches.

9. 9. What is the primary purpose of constructing a double dot plot on a single number line?

   • A. To calculate the average of each dataset more easily.
   • B. To fit more data onto a single graph.
   • C. To directly compare the distribution, center, and spread of two populations.
   • D. To show data for one population over two different time periods.

10. 10. A double dot plot shows weekly hours worked at Store A and Store B. Store A's hours are clustered from 15-25. Store B's are from 30-40. An employee who worked 22 hours most likely works at which store?

    • A. Store A
    • B. Store B
    • C. Either store is equally likely
    • D. Cannot be determined from the information