Try the fastest way to create flashcards
Question

# 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

Verified
Step 1
1 of 2

Given 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).

## Recommended textbook solutions

#### Precalculus

2nd EditionISBN: 9780076602186Carter, Cuevas, Day, Malloy
8,886 solutions

#### Precalculus: Graphical, Numerical, Algebraic

10th EditionISBN: 9780134781945Demana, Foley, Kennedy, Waits
8,108 solutions

#### Nelson Functions 11

1st EditionISBN: 9780176332037Chris Kirkpatrick, Marian Small
1,275 solutions

#### Precalculus with Limits

3rd EditionISBN: 9781133962885 (3 more)Larson
11,068 solutions