The five-number summary of credit hours for 24 students in a statistics class is:
$\begin{array}{|c|c|c|c|c|}
\hline Min & Q1 & Median & Q3 & Max \
\hline 13.0 & 15.0 & 16.5 & 18.0 & 22.0 \
\hline
\end{array}$

Which statement is true?
A) There is at least one high outlier in the data.
B) There are no outliers in the data.
C) There is at least one low outlier in the data.
D) None of these.
E) There are both low and high outliers in the data.

Question

The five-number summary of credit hours for 24 students in a statistics class is: 
$\begin{array}{|c|c|c|c|c|}
\hline Min & Q1 & Median & Q3 & Max \
\hline 13.0 & 15.0 & 16.5 & 18.0 & 22.0 \
\hline
\end{array}$

Which statement is true?
A) There is at least one high outlier in the data.
B) There are no outliers in the data.
C) There is at least one low outlier in the data.
D) None of these.
E) There are both low and high outliers in the data.

Quizplus · Accepted Answer

To determine if there are any outliers, we calculate the interquartile range (IQR) and then use it to find the lower and upper bounds for outliers. IQR = Q3 - Q1 = 18.0 - 15.0 = 3.0. Lower bound = Q1 - 1.5*IQR = 15.0 - 1.5*3.0 = 10.5. Upper bound = Q3 + 1.5*IQR = 18.0 + 1.5*3.0 = 22.5. Since the minimum (13.0) and maximum (22.0) values are within these bounds, there are no outliers.

The Five-Number Summary of Credit Hours for 24 Students in a Statistics