Question

jane is a surfer. she kept track of the number of waves she surfed each day last summer. the box-and-whisker plot (sometimes called a boxplot) summarizes the data.
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 waves jane surfed in a day? (that is, what is the range of the data?)
(b) which of these best describes the numbers of waves jane surfed last summer?
the number of waves she surfed was below 32 on more days than it was above 32.
the number of waves she surfed was above 32 on more days than it was below 32.
the number of waves she surfed was below 32 for the same number of days that it was above 32.
(c) which of the following intervals gives the highest 25% of the data?
32 to 42 42 to 49 32 to 49 49 to 60

Explanation:

Part (a)

Step1: Identify min and max

From the box - and - whisker plot, the minimum number of waves is 23 (leftmost whisker) and the maximum is 50 (rightmost whisker).

Step2: Calculate range

Range = Maximum - Minimum = \(50 - 23=27\)

The median (middle line of the box) is 32. In a box - and - whisker plot, the median divides the data into two equal parts (50% below and 50% above). So the number of days with waves below 32 is equal to the number of days with waves above 32.

In a box - and - whisker plot, the highest 25% of the data lies between the third quartile (\(Q_3\)) and the maximum value. From the plot, the third quartile seems to be around 49 and the maximum is 50 (and the whisker goes to 60? Wait, re - checking: the right whisker goes to 50? Wait, no, the x - axis has 20,25,30,35,40,45,50,55,60. The box - and - whisker plot's right whisker end is at 50? Wait, no, the plot's right end (maximum) is at 50? Wait, no, the original plot: the left whisker starts at 23, the box starts at \(Q_1\), median at 32, \(Q_3\) at 42? Wait, no, maybe I misread. Wait, the key is that the highest 25% is from \(Q_3\) to max. Looking at the options, 49 to 60: wait, maybe the third quartile is 49 and max is 60? Wait, the x - axis has 60 as the end. So the interval for the highest 25% (from \(Q_3\) to max) is 49 to 60.

Answer:

27

Part (b)