Refer to the box-and-whisker plot shown. Determine the interquartile range (IQR) of the data set.

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BlackTom AI · Accepted Answer

To determine the interquartile range (IQR), I first identify the quartiles shown on the box-and-whisker plot.
Option a: 1. This would imply a very small spread between Q1 and Q3, which does not match the visual distance of the box itself in the plot.
Option b: 3. The left edge of the box corresponds to Q1 and the right edge to Q3. In the plot, Q1 is at 4 and Q3 is at 7, so the distance is 7 − 4 = 3, which matches this choice.
Option c: 7. An IQR of 7 would require Q3 to be 7 units above Q1, which is far larger than the span of the box in the diagram; the box length is noticeably shorter than that.
Option d: 2. If the IQR were 2, the box would be noticeably narrower than what is shown; the observed box length corresponds to a larger spread between Q1 and Q3.

Carefully compare the Q1 and Q3 positions indicated by the box: the left side aligns with 4 and the right side with 7, giving an IQR of 3. The other options do not reflect the actual box width on the plot.

MDM4U - Mathematics of Data Management 12 (2025-26) - A

Refer to the box-and-whisker plot shown. Determine the interquartile range (IQR) of the data set.

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