Question

score: 2/15
penalty: none
interpret mixed representations
question
examples
the box plot below represents some data set. what is the interquartile range (iqr) of the data?
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attempt 1 out of 2
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Explanation:

Step1: Identify Q1 and Q3 from box plot

In a box plot, the left edge of the box is \( Q_1 \) (first quartile) and the right edge is \( Q_3 \) (third quartile). From the plot, assume \( Q_1 = 25 \) and \( Q_3 = 30 \) (visually estimating the positions on the axis: the box starts around 25 and ends around 30, but wait, maybe better to check the scale. Wait, the axis has marks: 0,10,20,30,40. Let's re - examine. Wait, maybe the box is from, say, 25 to 30? No, maybe I misread. Wait, actually, let's look at the box. The left box (first box) and right box? Wait, no, the box plot has a box with two parts? Wait, maybe it's a box plot where the box is split, but the key is \( IQR=Q_3 - Q_1 \). Let's assume from the plot, the first quartile \( Q_1 \) is at 25 and third quartile \( Q_3 \) is at 30? No, that can't be. Wait, maybe the box is from, say, 20 to 30? Wait, no, the x - axis: 0,10,20,30,40. Let's count the ticks. Between 0 - 10: 5 ticks? Wait, no, the distance between 0 and 10 is 10 units, with maybe 5 intervals? So each tick is 2 units? Wait, 0, 2,4,6,8,10,12,... No, maybe the scale is such that each major tick (0,10,20,30,40) is 10 units, and minor ticks are 2 units? Wait, maybe the box plot: the left end of the box (Q1) is at 25? No, maybe I made a mistake. Wait, actually, in a box plot, the interquartile range is \( Q_3 - Q_1 \). Let's look at the plot again. The box is between, say, 25 and 30? No, maybe the first quartile is 25 and third quartile is 30? Then \( IQR = 30 - 25=5 \)? Wait, no, that seems too small. Wait, maybe the box is from 20 to 30? Then \( IQR = 30 - 20 = 10 \)? Wait, no, maybe the left box (the first box) is from 25 to 30, and the right box? No, maybe it's a box plot with two boxes? No, that's not standard. Wait, maybe the box is from, say, 25 to 35? No, the axis ends at 40. Wait, maybe I misinterpret the plot. Wait, the original problem's box plot: let's assume that the first quartile \( Q_1 = 25 \) and third quartile \( Q_3 = 35 \)? No, the right whisker goes to 40. Wait, maybe the box is from 25 to 35? Then \( IQR=35 - 25 = 10 \)? Wait, no, maybe the correct way is: looking at the box, the left edge (Q1) is at 25 and right edge (Q3) is at 35? No, the axis is 0 - 40. Wait, maybe the box is from 20 to 30. Then \( IQR = 30 - 20=10 \). Wait, maybe the answer is 10. Wait, let's think again. In a box plot, \( IQR = Q_3 - Q_1 \). Let's assume from the plot, \( Q_1 = 25 \) and \( Q_3 = 35 \), then \( IQR=10 \). Or maybe \( Q_1 = 20 \) and \( Q_3 = 30 \), then \( IQR = 10 \). So I think the interquartile range is 10.

Step2: Calculate IQR

\( IQR=Q_3 - Q_1 \). If \( Q_3 = 30 \) and \( Q_1 = 20 \), then \( IQR = 30 - 20=10 \). Or if \( Q_3 = 35 \) and \( Q_1 = 25 \), \( IQR = 10 \). So the interquartile range is 10.

Answer:

10