Question

question #9
the final exam scores of two groups of students in a class are plotted as shown.
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

The box - and - whisker plot for Group A: lower quartile ($Q_1$) = 50, upper quartile ($Q_3$)=85.

Step2: Identify quartiles for Group B

The box - and - whisker plot for Group B: lower quartile ($Q_1$) = 55, upper quartile ($Q_3$)=85.

Step3: Analyze option A

For Group A, the inter - quartile range (IQR) is from 50 to 75, but we can't say most students are in this range just from the box - and - whisker plot. For Group B, the IQR is from 55 to 85, and we can't say most students are in the 70 - 85 range. So option A is incorrect.

Step4: Analyze option B

The lower quartile of Group A is 50 and 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. This option is correct.

Step5: Analyze option C

IQR for Group A: $IQR_A=85 - 50=35$. IQR for Group B: $IQR_B=85 - 55 = 30$. Since $30<35$, option C is incorrect.

Step6: Analyze option D

The upper quartile of Group A is 85 and of Group B is 85. They are equal, so 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.