## Related questions with answers

The five-number summary for the weights (in pounds) of the players on a high school soccer team is {113, 143, 152, 165, 210} Are there any outliers? Explain.

Solution

VerifiedGiven five-number summary: 113, 143, 152, 165, 210

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

$\begin{align*} \text{Minimum}&=113 \\ Q_1&=143 \\ \text{Median}&=152 \\ Q_3&=165 \\ \text{Maximum}&=210 \end{align*}$

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

$IQR=Q_3-Q_1=165-143=21$

$\textbf{Outliers}$ are observations that are more than 1.5 times the IQR above $Q_3$ or below $Q_1$.

$\begin{align*} Q_3+1.5IQR&=165+1.5(21)=196.5 \\ Q_1-1.5IQR&=143-1.5(21)= 111.5 \end{align*}$

We then note that the maximum of 210 exceeds 196.5 and thus the data set contains an outlier (as the maximum is an outlier).

## Create a free account to view solutions

## Create a free account to view solutions

## Recommended textbook solutions

#### Precalculus: Graphical, Numerical, Algebraic

10th Edition•ISBN: 9780134781945Demana, Foley, Kennedy, Waits## More related questions

- college algebra
- college algebra

1/4

- college algebra
- college algebra

1/7