Question

question 8 (multiple choice worth 2 points) (box plots mc) the box plot shown represents the amount of donations received for a lacrosse team fundraiser. what is the range and iqr of the data displayed? \bigcirc the range is 38, and the iqr is 20. \bigcirc the range is 38, and the iqr is 21. \bigcirc the range is 37, and the iqr is 21. \bigcirc the range is 37, and the iqr is 20. (box plot labeled lacrosse team fundraiser with donations in dollars on the vertical axis, values from 6 to 50.)

Explanation:

Step1: Calculate the range

Range = Maximum value - Minimum value. From the box - plot, the maximum value is 46 and the minimum value is 8. So, Range = \(46 - 8=38\).

Step2: Calculate the IQR (Inter - Quartile Range)

IQR = \(Q_3 - Q_1\). From the box - plot, \(Q_3 = 36\) and \(Q_1 = 15\) (assuming the box plot's quartile values: the lower quartile \(Q_1\) is the start of the box, the upper quartile \(Q_3\) is the end of the box). Wait, maybe I misread. Wait, looking at the axis, the box starts at around 15? No, wait the y - axis (donations in dollars) has values. Wait, the minimum is 8, the lower quartile \(Q_1\) is 15? No, maybe the box is from 15 to 36? Wait, no, let's re - examine. Wait, the box plot: the minimum is 8, the lower quartile (\(Q_1\)) is 15? Wait, no, maybe the box is from 15 to 36? Wait, no, the median line is at 23? Wait, no, the vertical line in the box is the median. Wait, the lower whisker goes to 8, the box starts at \(Q_1\), the median is in the box, and the box ends at \(Q_3\), then the upper whisker goes to 46. Wait, maybe \(Q_1 = 15\), \(Q_3 = 36\)? No, wait 36 - 15 = 21? Wait, no, maybe I made a mistake. Wait, let's check the options. The options have range 38 and IQR 21, or range 37 and IQR 20, etc. Wait, maximum is 46, minimum is 8, so range is \(46 - 8 = 38\). Then IQR: \(Q_3 - Q_1\). If \(Q_3=36\) and \(Q_1 = 15\), \(36 - 15=21\). So the range is 38 and IQR is 21.

Answer:

The range is 38, and the IQR is 21. (The option corresponding to this statement)