In a distribution, how many people had scores less than X = 19? X: 20-24, 15-19,10-14, 5-9; F: 2, 5, 4, 1

In a distribution, how many people had scores less than X = 19? X: 20-24, 15-19,10-14, 5-9; F: 2, 5, 4, 1

• A. 5
• B. 10
• C. 11
• D. Cannot be determined

Answer: (D)

When data are shown as a grouped frequency distribution, you can add up whole class frequencies for values clearly below a cutoff, but you can’t split a class interval without more detail about how values are distributed inside it. In this problem, the classes are 5–9, 10–14, 15–19, and 20–24 with frequencies 1, 4, 5, and 2. The cutoff is 19, which sits inside the 15–19 class. All of the scores in the lower classes (5–9 and 10–14) are certainly below 19, contributing 1 + 4 = 5 people. But within the 15–19 class, some scores are below 19 (15–18) and some could be 19. Since we don’t know how the 5 people in that class are distributed, we can’t determine the exact number below 19. The count could range from 5 up to 10 depending on how many of those 5 scored 15–18.

When data are shown as a grouped frequency distribution, you can add up whole class frequencies for values clearly below a cutoff, but you can’t split a class interval without more detail about how values are distributed inside it.

In this problem, the classes are 5–9, 10–14, 15–19, and 20–24 with frequencies 1, 4, 5, and 2. The cutoff is 19, which sits inside the 15–19 class. All of the scores in the lower classes (5–9 and 10–14) are certainly below 19, contributing 1 + 4 = 5 people. But within the 15–19 class, some scores are below 19 (15–18) and some could be 19. Since we don’t know how the 5 people in that class are distributed, we can’t determine the exact number below 19. The count could range from 5 up to 10 depending on how many of those 5 scored 15–18.