Question

Consider the following box plot statistics for a data set: minimum at 33, Q1 at 40, median at 52, Q3 at 55, maximum at 78, and an outlier at 86. Which statement about the data set and its outliers is true?

a. If the outliers were included in the data, the mean would increase significantly.
b. If the outliers were included in the data, the box plot would be significantly skewed.
c. If the outliers were included in the data, the median would not significantly change.
d. If the outliers were included in the data, the length of the tails would not change.

Answer 1

Including outliers in the data set can significantly affect the mean and length of tails, but the median remains relatively unaffected. The statement about the box plot being significantly skewed is false.

Step-by-step explanation:

The box plot statistics for the data set are as follows: minimum = 33, Q1 = 40, median = 52, Q3 = 55, maximum = 78, and an outlier at 86.

Regarding the statements:

1. If the outliers were included in the data, the mean would increase significantly. This statement is true. The mean is sensitive to outliers, so including the outlier of 86 would increase the mean significantly.
2. If the outliers were included in the data, the box plot would be significantly skewed. This statement is false. The presence of outliers does not affect the skewness of a box plot, as the positioning and shape of the boxes and whiskers are determined by quartiles and median.
3. If the outliers were included in the data, the median would not significantly change. This statement is true. The median is resistant to outliers and would not be significantly affected by the inclusion of the outlier.
4. If the outliers were included in the data, the length of the tails would not change. This statement is false. Including outliers can affect the length of the tails, as outliers can extend the range of the data.