A mathematics teacher wants to compare the test scores of her 1st period class and her 2nd period class. In order to compare the test scores, the teacher creates the following box plots.
Which of the following statements are true regarding the box plots above?
I. The range of 1st period's test scores is equal to the range of 2nd period's test scores.
II. There is a greater percentage of test scores between 85 and 95 in 1st period than in 2nd period.
III. The interquartile range of 1st period's test scores is less than the interquartile range of 2nd period's test scores.
IV. The median of 1st period's test scores is less than the median of 2nd period's test scores.
A.
I and IV
B.
I and III
C.
II and IV
D.
II and III
B. I and III
Explanation:
I. The range of the 1st period's test scores is approximately 75 to 100, while the range of the 2nd period's test scores is approximately 65 to 95. Therefore, the range of the 1st period's test scores is greater than the range of the 2nd period's test scores.
II. The box plot for the 1st period class shows a larger box between 85 and 95 compared to the box plot for the 2nd period class. Therefore, there is a greater percentage of test scores between 85 and 95 in the 1st period class than in the 2nd period class.
III. The interquartile range (IQR) of the 1st period's test scores is smaller than the IQR of the 2nd period's test scores because the length of the box in the box plot for 1st period is shorter than the length of the box in the box plot for 2nd period.
IV. The median of the 1st period's test scores is higher than the median of the 2nd period's test scores as shown in the box plots. Therefore, this statement is false.