Question

65 70 75 80 85

Brand A
HIH
15
50
60
70
85
Brand B
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Price ($)
Which statement is the most appropriate comparison of the spreads?
O A. The interquartile range (IQR) for brand A, $20, is less than the IQR
for brand B. $70.
O B. The median for brand A, $75, is greater than the median for brand
B, $60.
O C. The interquartile range (IQR) for brand A, $10, is less than the IQR
brand B. $20.
O D. The interquartile ranges (IQRs) for brands A and B are both $20.

Answer 1

Given:

Two box plots for Brand A and Brand B.

To find:

The correct statement for the given box plots.

Solution:

In a box plot, the left end of the box represents the first quartile
`(Q_1)`, right end of the box represents the third quartile
`Q_3` and the line inside the box represents the median.

The interquartile range of a data set is:

`IQR=Q_3-Q_1`

From the box plot of Brand A, it is clear that

`Q_1=70`

`Median=75`

`Q_3=80`

So, the interquartile range (IQR) for brand A is:

`IQR=80-70`

`IQR=10`

From the box plot of Brand B, it is clear that

`Q_1=50`

`Median=60`

`Q_3=70`

So, the interquartile range (IQR) for brand B is:

`IQR=70-50`

`IQR=20`

The median for brand A, $75, is greater than the median for brand B, $60.

The interquartile range (IQR) for brand A, $10, is less than the IQR

brand B. $20.

Therefore, the correct options are B and C.