Question

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

Step1: Recall IQR Definition

IQR (Interquartile Range) is \( Q_3 - Q_1 \), where \( Q_1 \) is the first quartile (25th percentile) and \( Q_3 \) is the third quartile (75th percentile). In a boxplot, the box spans from \( Q_1 \) to \( Q_3 \), so the length of the box is the IQR.

Step2: Analyze Males' Box

For males, the box starts at \( Q_1 = 2 \) and ends at \( Q_3 = 5 \). So \( \text{IQR}_{\text{males}} = 5 - 2 = 3 \).

Step3: Analyze Females' Box

For females, the box starts at \( Q_1 = 0 \) and ends at \( Q_3 = 3 \). So \( \text{IQR}_{\text{females}} = 3 - 0 = 3 \).

Step4: Evaluate Options

• Option 1: "The IQR’s between males and females are the same" – Since both IQRs are 3, this is correct.
• Option 2: "The sample of males are less than the females" – IQR is about spread, not sample size or central tendency comparison here, incorrect.
• Option 3: "The females don’t have outliers compared to men?" – The question is about IQR, not outliers, and the plot doesn't show outliers (whiskers extend without dots), so irrelevant, incorrect.
• Option 4: "Both male and female have a wide spread of data" – IQR is 3 for both, which isn't necessarily "wide" (context-dependent, but the key is IQR equality, so this is not the focus, incorrect).

Answer:

The IQR’s between males and females are the same