The box plots below represent the final exam scores of four different classes.

Question

A four-box plot has numbers from 60 to 100. For the first box plot labeled Class A, the end of first whisker is at less than halfway between 60 and 70, the box starts more than halfway between 60 and 70, the line inside the box is at less than halfway between 70 and 80, the box ends at less than halfway between 80 and 90, and the end of the second whisker is at 100. For the second box plot labeled Class B, the end of first whisker is at less than halfway between 60 and 70, the box starts halfway between 60 and 70, the line inside the box is more than halfway between 60 and 70, the box ends at 90, and the end of the second whisker is at more than halfway between 90 and 100. For the third box plot labeled Class C, the end of first whisker is at halfway between 60 and 70, the box starts at more than halfway between 60 and 70, the line inside the box is halfway between 70 and 80, the box ends at halfway between 80 and 90, and the end of the second whisker is at halfway between 90 and 100. For the first box plot labeled Class D, the end of first whisker is at 60, the box starts more than halfway between 60 and 70, the line inside the box is at halfway between 70 and 80, the box ends at more than halfway between 80 and 90, and the end of the second whisker is at more than halfway between 90 and 100.

Which class shows the smallest spread in scores?

A.
Class A

B.
Class B

C.
Class C

D.
Class D

Answer 1

To determine which class shows the smallest spread in scores based on the descriptions of the box plots, we can analyze the range of scores for each class, which is defined by the minimum score (the end of the first whisker) and the maximum score (the end of the second whisker).

1. Class A:

   • Minimum (first whisker): < 65 (boundary between 60 and 70)
   • Maximum (second whisker): 100
   • Range: Less than 65 to 100

2. Class B:

   • Minimum (first whisker): < 65 (boundary between 60 and 70)
   • Maximum (second whisker): > 95 (between 90 and 100)
   • Range: Less than 65 to more than 95

3. Class C:

   • Minimum (first whisker): 65 (between 60 and 70)
   • Maximum (second whisker): 95 (halfway between 90 and 100)
   • Range: 65 to 95

4. Class D:

   • Minimum (first whisker): 60
   • Maximum (second whisker): > 95 (between 90 and 100)
   • Range: 60 to more than 95

Now, let's examine the ranges we have for each class:

• Class A: > 65 score range to 100 = > 35 unit spread.
• Class B: > 65 score range to > 95 = > 30 unit spread is uncertain.
• Class C: 65 to 95 = 30 unit spread.
• Class D: 60 to > 95 = > 35 spread as well.

From the above analysis, Class C has the most clearly defined range with a fixed spread of 30 points (from 65 to 95), while the others have uncertain overlapping ranges, but potentially larger spreads.

Therefore, the answer is C. Class C shows the smallest spread in scores.