Question

1. A five-number summary of a univariate data set is determined to be [10, 15, 25, 45, 85]. These data are to be used to construct a (modified) boxplot. Which of the following statements are true?

I. The mean is probably greater than the median.
II. There is at least one outlier.
III. The data are skewed to the right.

(A) I only
(B) II only
(C) III only

Answer 1

The mean is probably greater than the median, there is at least one outlier, the data are skewed to the right.

Step-by-step explanation:

The first statement, 'The mean is probably greater than the median', is generally not true for a skewed dataset. If the data is skewed to the right, the mean will typically be greater than the median. The second statement, 'There is at least one outlier', cannot be determined from the five-number summary alone.

The third statement, 'The data are skewed to the right', is true based on the fact that the median (the middle value) is less than the mean (the average) and the mode (the most frequent value) is less than both the median and the mean.