Question

9 multiple choice 7 points
with the given boxplot below, what are the iqr’s for each set of data?
boxplot: top for males, bottom for females; x - axis from 0 to 8, labeled times per week eating at a fast food restaurant
what is the most correct answer?

• the iqr’s between males and females are the same
• the sample of males are less than the females
• the females don’t have outliers compared to men?
• both male and female have a wide spread of data

Explanation:

To determine the IQR (Interquartile Range), we look at the length of the box in a boxplot, which represents the range between the first quartile ($Q_1$) and the third quartile ($Q_3$), so $IQR = Q_3 - Q_1$. For both the male and female boxplots, the length of the blue box (representing the interquartile range) appears to be the same. Let's analyze the options:

• Option 1: "The IQR’s between males and females are the same" – The box length (IQR) for both genders looks equal (e.g., for males, the box spans from around 2 to 5? Wait, no, looking at the x - axis: the male box has two parts? Wait, no, the box is divided into two, but the total length of the box (from the start of the first blue rectangle to the end of the second) for males: let's see the x - axis. The male box: the first blue part starts at 2, ends at 3? Wait, no, maybe the box is from $Q_1$ to $Q_3$. Wait, the female box: from 0 to 3? No, the female box is two blue rectangles, from 0 to 3? Wait, no, the x - axis is 0 - 8. For females, the box (the blue part) is from, say, 0 to 3? Wait, no, the male box: the blue part is from 2 to 5? Wait, no, maybe the key is that the length of the box (IQR) for both is the same. Let's check the other options:
• Option 2: "The sample of males are less than the females" – This is about IQR, not the sample size or the center, so incorrect.
• Option 3: "The females don’t have outliers compared to men?" – The question is about IQR, not outliers, so incorrect.
• Option 4: "Both male and female have a wide spread of data" – The spread of data is about the range (whiskers), but the question is about IQR. Also, the IQR is about the middle 50% of data, not the overall spread. So the correct option is the first one as the box lengths (IQR) are the same.

Answer:

The IQR’s between males and females are the same