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The five-number summary for the number of males (in thousands an a company's fleet of cars is {7, 49, 66, 72, 98}. Are there any outliers? Explain.


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Given five-number summary: 7, 49, 66, 72, 98

The five-number summary\textbf{five-number summary} consists of the minimum, the first quartile, the median, the third quartile and the maximum.

Minimum=7Q1=49Median=66Q3=72Maximum=98\begin{align*} \text{Minimum}&=7 \\ Q_1&=49 \\ \text{Median}&=66 \\ Q_3&=72 \\ \text{Maximum}&=98 \end{align*}

The interquartile range\textbf{interquartile range} IQR is the difference of the upper and lower quartile:


Outliers\textbf{Outliers} are observations that are more than 1.5 times the IQR above Q3Q_3 or below Q1Q_1.

Q3+1.5IQR=72+1.5(23)=106.5Q11.5IQR=491.5(23)=14.5\begin{align*} Q_3+1.5IQR&=72+1.5(23)=106.5 \\ Q_1-1.5IQR&=49-1.5(23)= 14.5 \end{align*}

We then note that the minimum of 7 is less than 14.5 and thus the data set contains an outlier (as the minimum is an outlier).

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