Question

use the box - and - whisker plot to answer the questions below.
(a) what is the difference of the largest number and the smallest number of people served by the tours? (that is, what is the range of the data?)
24
(b) which of these best describes the numbers of people served by the tours?
the number of people served was below 33 for more tours than it was above 33.
the number of people served was above 33 for more tours than it was below 33.
the number of people served was below 33 for the same number of tours that it was above 33.
(c) which of the following intervals gives the highest 25% of the data?
33 to 42 33 to 49 42 to 49 49 to 60

Explanation:

Step1: Analyze the box - and - whisker plot for range

The range is calculated as \( \text{Range}=\text{Maximum}-\text{Minimum} \). From the box - and - whisker plot, the minimum value is \( 25 \) and the maximum value is \( 49 \). So, \( 49 - 25=24 \).

Step2: Analyze the box - and - whisker plot for part (b)

In a box - and - whisker plot, the median divides the data into two halves. The median of the data is \( 33 \). The left half of the box (below the median) and the right half of the box (above the median) represent \( 50\%\) of the data each. So, the number of people served was below \( 33 \) for the same number of tours that it was above \( 33 \).

Step3: Analyze the box - and - whisker plot for part (c)

In a box - and - whisker plot, the upper \( 25\%\) of the data lies above the upper quartile. The upper quartile is \( 42 \) and the maximum is \( 49 \). So, the interval \( 42 \) to \( 49 \) gives the highest \( 25\%\) of the data.

Answer:

(a) \( 24 \)
(b) The number of people served was below \( 33 \) for the same number of tours that it was above \( 33 \).
(c) \( 42 \) to \( 49 \)