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 waves jessica surfed in a day? (that is, what is the range of the data?)
(b) which of these best describes the numbers of waves jessica 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 43
32 to 49
43 to 49
49 to 60

Explanation:

Step1: Recall the formula for range

The range of a data set is calculated as \( \text{Range}=\text{Maximum value}-\text{Minimum value}\).

Step2: Identify maximum and minimum values from the box - and - whisker plot

From the box - and - whisker plot, the minimum value (the left - most end of the whisker) is \(25\) and the maximum value (the right - most end of the whisker) is \(49\).

Step3: Calculate the range

Substitute the values into the range formula: \( \text{Range}=49 - 25=24\). But wait, this is wrong. Wait, no, looking at the axis: the minimum value is \(25\) and the maximum value is \(60\). So \( \text{Range}=60 - 25 = 35\). No, wait, no. Wait, the box - and - whisker plot: the left - most whisker is at \(25\), the right - most whisker is at \(60\). So \( \text{Range}=60 - 25=35\). But wait, no, wait the options for part (a) is not about calculation. Wait, no, part (a) asks "What is the difference of the largest number and the smallest number of waves Jessica surfed in a day (i.e., what is the range of the data)". From the box - and - whisker plot, the minimum (smallest) value is \(25\) and the maximum (largest) value is \(60\). So \( \text{Range}=60 - 25 = 35\). But wait, no, looking at the vertical axis: the scale. Each mark is \(5\) units. The left - most whisker is at \(25\), the right - most whisker is at \(60\).

For part (b):

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

In a box - and - whisker plot, the box represents the inter - quartile range (\(IQR\), from \(Q_1\) to \(Q_3\)). The whiskers represent the range (from minimum to \(Q_1\) and from \(Q_3\) to maximum). The median is the line inside the box. The number of data points below \(Q_1\) is \(25\%\) of the total data points, between \(Q_1\) and median is \(25\%\), between median and \(Q_3\) is \(25\%\), and above \(Q_3\) is \(25\%\).
Let's assume the value \(32\). If we check the position:
If we assume the box - and - whisker plot: \(Q_1\) (first quartile) is the value such that \(25\%\) of the data is below it. If \(32\) is \(Q_1\), then the number of days with waves below \(32\) is \(25\%\) of the total days. But we need to check the options.
Option: "The number of waves she surfed was below 32 on more days than it was above 32" is incorrect. Because in a box - and - whisker plot, the median divides the data into two halves. If \(32\) is \(Q_1\) (first quartile), the number of data points below \(Q_1\) is \(25\%\) and above \(Q_1\) is \(75\%\).
Option: "The number of waves she surfed was above 32 on more days than it was below 32" is correct. Because if \(32\) is \(Q_1\) (first quartile), \(75\%\) of the data is above \(Q_1\) (i.e., above \(32\)) and \(25\%\) is below \(Q_1\) (below \(32\))

For part (c):

Step1: Recall the definition of the upper \(25\%\) of the data

In a box - and - whisker plot, the upper \(25\%\) of the data is from \(Q_3\) (third quartile) to the maximum. From the box - and - whisker plot, \(Q_3 = 49\) and the maximum is \(60\).

Answer:

(a) The range is \(60 - 25=35\). But if we consider the options (assuming there was a mis - understanding in the initial range calculation due to problem formatting, but based on the box - and - whisker plot structure where range is max - min, and from the plot min = \(25\), max=\(60\)).
(b) The number of waves she surfed was above 32 on more days than it was below 32.
(c) \(49\) to \(60\)