Question

which statement is true about the box plots?
number of incorrect questions on exams
marcs class
sues class
0 1 2 3 4 5 6 7 8 9 10 11 12 13
both the ranges and the interquartile ranges for the data sets are the same.
neither the ranges nor the interquartile ranges for the data sets are the same.
the interquartile ranges for the box plots are the same, but their ranges are different.
the ranges for the box plots are the same, but their interquartile ranges are different.

Explanation:

Step1: Recall Range and IQR Formulas

Range is calculated as \( \text{Range} = \text{Maximum} - \text{Minimum} \). Interquartile Range (IQR) is \( \text{IQR} = Q_3 - Q_1 \), where \( Q_3 \) is the third quartile and \( Q_1 \) is the first quartile.

Step2: Analyze Marc's Class Box Plot

• Minimum: 1, Maximum: 10. So Range = \( 10 - 1 = 9 \).
• \( Q_1 \): 3, \( Q_3 \): 9. So IQR = \( 9 - 3 = 6 \).

Step3: Analyze Sue's Class Box Plot

• Minimum: 3, Maximum: 12. So Range = \( 12 - 3 = 9 \).
• \( Q_1 \): 5, \( Q_3 \): 10. So IQR = \( 10 - 5 = 5 \)? Wait, no—wait, looking at the box plot: Wait, maybe I misread. Wait, Marc's class: the whiskers go from 1 to 10? Wait, no, the plot: Marc's class has min at 1, max at 10? Wait, no, the x-axis: 0,1,2,3,4,5,6,7,8,9,10,11,12,13. Wait, Marc's class: left whisker at 1, right whisker at 10? Wait, no, the box for Marc's class: left end (Q1) at 3, right end (Q3) at 9? Wait, no, the box is from 3 to 9? Wait, no, the first box (Marc's) has left whisker to 1, box from 3 to 9, right whisker to 10? Wait, no, the plot: Marc's class: min is 1, Q1 is 3, median is 5 (mid of box), Q3 is 9, max is 10. So range: 10 - 1 = 9. IQR: 9 - 3 = 6.

Sue's class: min is 3, Q1 is 5, median is 7 (mid of box), Q3 is 10, max is 12. So range: 12 - 3 = 9. IQR: 10 - 5 = 5? Wait, no, wait the boxes: Marc's box is from 3 to 9 (length 6), Sue's box is from 5 to 10 (length 5)? Wait, no, maybe I messed up. Wait, the problem's box plots: Marc's class box: left at 3, right at 9 (so Q1=3, Q3=9, IQR=6). Sue's class box: left at 5, right at 10 (Q1=5, Q3=10, IQR=5)? Wait, but range: Marc's max - min = 10 - 1 = 9. Sue's max - min = 12 - 3 = 9. So ranges are same (both 9). IQRs: Marc's 9-3=6, Sue's 10-5=5? Wait, no, maybe the boxes are different. Wait, the options: "The ranges for the box plots are the same, but their interquartile ranges are different." Let's recheck:

Wait, maybe the max for Marc's is 10, min 1: range 9. Sue's max 12, min 3: range 9. So ranges same. Now IQR: Marc's Q3 - Q1: if Q1 is 3, Q3 is 9: IQR 6. Sue's Q1 is 5, Q3 is 10: IQR 5? Wait, no, maybe the boxes are: Marc's box from 3 to 9 (IQR 6), Sue's from 5 to 10 (IQR 5). So ranges same (9), IQRs different. So the correct option is "The ranges for the box plots are the same, but their interquartile ranges are different."

Answer:

The ranges for the box plots are the same, but their interquartile ranges are different. (The option corresponding to this statement, e.g., if it's the fourth option, then: D. The ranges for the box plots are the same, but their interquartile ranges are different.)