Question

use the box - and - whisker plot to answer the questions below.
(a) which of the following intervals gives the middle 50% of the data?
24 to 40
24 to 29
29 to 40
21 to 29
(b) what is the difference of the largest number and the smallest number of waves jessica surfed in a day? (that is, what is the range of the data?)
(c) which of these best describes the numbers of waves jessica surfed last summer?
the number of waves she surfed was below 29 on more days than it was above 29.
the number of waves she surfed was above 29 on more days than it was below 29.
the number of waves she surfed was below 29 for the same number of days that it was above 29.

Explanation:

Step1: Recall the concept of box - and - whisker plot

In a box - and - whisker plot, the middle 50% of the data lies between the first quartile (\(Q_1\)) and the third quartile (\(Q_3\)).

Step2: Analyze the given box - and - whisker plot

Looking at the box - and - whisker plot, we can see that the box (which represents the middle 50% of the data) is from 29 to 40.

Step3: Calculate the range

The range is calculated as \( \text{Range}=\text{Maximum value}-\text{Minimum value}\). From the plot, the maximum value is 50 and the minimum value is 21. So, \( \text{Range}=50 - 21=29\).

Step4: Analyze the quartiles for part (c)

The median of the lower half (first quartile \(Q_1 = 29\)) and the median of the upper half (third quartile \(Q_3=40\)). The number of data points below \(Q_1\) (25% of the data) and above \(Q_3\) (25% of the data). The number of data points between \(Q_1\) and \(Q_3\) (50% of the data). Since \(Q_1 = 29\), the number of days the number of waves was below 29 is 25% of the data and above 29 is 75% of the data.

Answer:

(a) 29 to 40
(b) 29
(c) The number of waves she surfed was above 29 on more days than it was below 29.