Megan constructed two box-and-whisker plots, shown below.

Question

A double box plot has numbers from 0 to 120. For the first box plot, the end of first whisker is at halfway between 0 and 20, the box starts halfway between 60 and 80, the line inside the box is at halfway between 80 and 100, the box ends at 100, and the end of the second whisker is at 120. For the second box plot, the end of first whisker is at halfway between 0 and 20, the box starts halfway between 20 and 40, the line inside the box is at 40, the box ends at 60, and the end of the second whisker is at halfway between 80 and 100.

What is the difference in the medians of the two box-and-whisker plots?

A.
0

B.
70

C.
110

D.
50

Answer 1

To find the difference in the medians of the two box-and-whisker plots, we need to identify the median value for each box plot based on the provided descriptions.

First Box Plot:

1. First whisker: The end of the whisker is at halfway between 0 and 20, which is \( \frac{0 + 20}{2} = 10 \).
2. Box starts: The box starts halfway between 60 and 80, which is \( \frac{60 + 80}{2} = 70 \).
3. Median (line inside the box): The line inside the box is at halfway between 80 and 100, which is \( \frac{80 + 100}{2} = 90 \).
4. Box ends: The box ends at 100.
5. Second whisker: The end of the second whisker is at 120.

Median of the first box plot = 90.

Second Box Plot:

1. First whisker: The end of the whisker is again at halfway between 0 and 20, which is \( \frac{0 + 20}{2} = 10 \).
2. Box starts: The box starts halfway between 20 and 40, which is \( \frac{20 + 40}{2} = 30 \).
3. Median (line inside the box): The line inside the box is at 40.
4. Box ends: The box ends at 60.
5. Second whisker: The end of the second whisker is at halfway between 80 and 100, which is \( \frac{80 + 100}{2} = 90 \).

Median of the second box plot = 40.

Difference in Medians:

Now we calculate the difference in the medians of the two box plots: \[ \text{Difference} = \text{Median of first box plot} - \text{Median of second box plot} = 90 - 40 = 50. \]

Thus, the difference in the medians of the two box-and-whisker plots is 50.

The answer is D. 50.