Question

question #9 the final exam scores of two groups of students in a class are plotted as shown. group a 40 50 75 85 92 group b 45 55 70 85 95 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 final exam scores which statement correctly compares the two data sets? a most of the students in group a obtained final exam scores between 50 and 75, while most of the students in group b obtained final exam scores between 70 and 85. b the lower quartile of the final exam scores obtained by students in group b is greater than the lower quartile of the final exam scores obtained by students in group a c the interquartile range of the final exam scores obtained by students in group b is greater than the interquartile range of the final exam scores obtained by students in group a d the upper quartile of the final exam scores obtained by students in group b is greater than the upper quartile of the final exam scores obtained by students in group a

Explanation:

Step1: Identify quartiles for Group A

For Group A, the lower - quartile ($Q_1$) is 50, the upper - quartile ($Q_3$) is 85. The inter - quartile range (IQR) for Group A is $IQR_A=Q_3 - Q_1=85 - 50 = 35$.

Step2: Identify quartiles for Group B

For Group B, the lower - quartile ($Q_1$) is 55, the upper - quartile ($Q_3$) is 85. The inter - quartile range (IQR) for Group B is $IQR_B=Q_3 - Q_1=85 - 55 = 30$.

Step3: Analyze option A

The box of Group A is from 50 to 75, and the box of Group B is from 55 to 85. Most of the data (the middle 50% represented by the box) for Group A is between 50 and 75, and for Group B is between 55 and 85. Option A is incorrect as it mis - states the range for Group B.

Step4: Analyze option B

The lower quartile of Group A is 50 and the lower quartile of Group B is 55. Since 55>50, the lower quartile of the final exam scores obtained by students in Group B is greater than the lower quartile of the final exam scores obtained by students in Group A.

Step5: Analyze option C

$IQR_A = 35$ and $IQR_B=30$, so the inter - quartile range of Group B is less than that of Group A. Option C is incorrect.

Step6: Analyze option D

The upper quartile of Group A is 85 and the upper quartile of Group B is 85. They are equal. Option D is incorrect.

Answer:

B. The lower quartile of the final exam scores obtained by students in Group B is greater than the lower quartile of the final exam scores obtained by students in Group A.