Question

1. jeffrey is tracking the number of miniature ceramic sculptures he makes each month. the following modified boxplot represents the data jeffrey has collected so far.

boxplot image with axis 0,10,20,30,40,50,60,70,80,90,100, label miniature ceramic sculptures
which of the following statements about jeffrey’s data is false?
a the mean of the data is 40.
b 80 is an outlier.
c the minimum of the data is 10.
d the interquartile range is around 24.

Explanation:

• Option A: In a boxplot, the line inside the box is the median (here, 40), not the mean. The mean is affected by outliers (like 80), so we can't say the mean is 40. This statement is false.
• Option B: The modified boxplot has a dot at 80, which represents an outlier (since it's outside the whiskers). So 80 is an outlier, this is true.
• Option C: The leftmost dot (or the start of the left whisker) is at 10, so the minimum is 10, this is true.
• Option D: The interquartile range (IQR) is \( Q_3 - Q_1 \). From the boxplot, \( Q_1 \approx 26 \) and \( Q_3 \approx 50 \), so \( IQR \approx 50 - 26 = 24 \), this is true.

Answer:

A. The mean of the data is 40.