Name:
Practice - FNS
Date: [tex]$\qquad$[/tex]
1. The following data contain the weights in grams of 24 male sparrows that perished in a severe winter storm:
[tex]\[
\begin{array}{llllllllllll}
24.6 & 24.6 & 24.9 & 25.0 & 25.0 & 25.1 & 25.5 & 25.6 & 25.6 & 25.8 & 25.9 & 26.0 \\
26.0 & 26.0 & 26.0 & 26.1 & 26.5 & 26.5 & 27.1 & 27.5 & 27.6 & 28.3 & 28.3 & 31.1
\end{array}
\][/tex]
a) Determine the five-number summary of the weights of the 24 sparrows that perished to the nearest tenth.
[tex]\[
\begin{tabular}{|l|l|l|l|l|}
\hline
Minimum & Lower quartile (Q1) & Median & Upper quartile (Q3) & Maximum \\
\hline
24.6 & 25.4 & 26.0 & 26.7 & 31.1 \\
\hline
\end{tabular}
\][/tex]
b) Use this information to conduct the outlier test for the weights of the sparrows that perished.
First, calculate the interquartile range (IQR):
[tex]\[
IQR = Q_3 - Q_1 = 26.7 - 25.4 = 1.3
\][/tex]
Next, determine the bounds for outliers using the formula [tex]\(1.5 \times IQR\)[/tex]:
[tex]\[
1.5 \times IQR = 1.5 \times 1.3 = 1.95
\][/tex]
Lower bound:
[tex]\[
Q_1 - (1.5 \times IQR) = 25.4 - 1.95 = 23.45
\][/tex]
Upper bound:
[tex]\[
Q_3 + (1.5 \times IQR) = 26.7 + 1.95 = 28.65
\][/tex]
Weights below 23.45 or above 28.65 are considered outliers.
c) How many outliers, if any, are there? What is/are the weight(s) of the outlier(s)?
Examine the weights to find outliers:
The only weight that falls outside the bounds is 31.1 grams because it is greater than 28.65 grams.
Thus, there is 1 outlier weight:
[tex]\[
\begin{tabular}{|l|}
\hline
Outlier Weight(s) \\
\hline
31.1 \\
\hline
\end{tabular}
\][/tex]
Therefore, there is 1 outlier with a weight of 31.1 grams.
