Question

two data sets are summarized in the box plots shown.
plot a
number line from 4 to 16 with a box plot
plot b
number line from 4 to 14 with a box plot
which statements comparing the two box plots are correct? choose all the correct statements.
a. the mean of plot b is greater than the mean of plot a.
b. the range of plot b is greater than the range of plot a.
c. the median of plot b is the same as the median of plot a.
d. the interquartile range of plot b is the same as the interquartile range of plot a.

Explanation:

Step1: Analyze Option A

Box plots show median, quartiles, and range, but not mean. So we can't compare means from box plots. Eliminate A.

Step2: Analyze Option B

Range = Max - Min. For Plot A: Max=10, Min=4? Wait, no, Plot A's whiskers: left whisker to 4? Wait, no, Plot A: the box is from 5 to 9? Wait, no, the x - axis for Plot A: the left whisker is at 4, right whisker at 10? Wait, no, the box plot for Plot A: the minimum is 4, maximum is 10? Wait, no, looking at the plot: Plot A has left whisker at 4, right whisker at 10? Wait, no, the box is from 5 to 9? Wait, no, the x - axis labels: 4,5,6,7,8,9,10,11,...16. Plot A: the left whisker is at 4, the box starts at 5, ends at 9, right whisker at 10? Wait, no, maybe I misread. Wait Plot B: left whisker at 8, right whisker at 14, box from 9 to 13. Wait, let's recalculate range. Range of A: Max - Min. If Plot A's min is 4, max is 10? Wait no, maybe the top plot (Plot A) has min at 4, max at 10? Wait no, the vertical line (whisker) for Plot A: left at 4, right at 10? And Plot B: left at 8, right at 14. Then range of A: 10 - 4 = 6. Range of B:14 - 8 = 6. Wait, no, that can't be. Wait maybe I made a mistake. Wait Plot A: the box is from 5 to 9, median at 7. Plot B: box from 9 to 13, median at 11. Wait, min of A: 4, max of A:10 (since whisker ends at 10). Min of B:8, max of B:14 (whisker ends at 14). Then range of A:10 - 4 = 6. Range of B:14 - 8 = 6. So range of B is not greater than range of A. Eliminate B.

Step3: Analyze Option C

Median of Plot A: the line inside the box. For Plot A, the box is from 5 to 9, the median line is at 7. For Plot B, the box is from 9 to 13, median line is at 11. 7≠11. So median of B is not same as A. Eliminate C.

Step4: Analyze Option D

Interquartile range (IQR)=Q3 - Q1. For Plot A: Q1 is the lower quartile (start of box), Q3 is upper quartile (end of box). If Plot A's box is from 5 (Q1) to 9 (Q3), then IQR = 9 - 5 = 4. For Plot B: box from 9 (Q1) to 13 (Q3), IQR = 13 - 9 = 4. So IQR of B is same as IQR of A. So D is correct.

Answer:

D. The interquartile range of plot B is the same as the interquartile range of plot A.