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]\[
\begin{tabular}{|l|l|l|l|l|}
\hline
Minimum & Lower Quartile (Q1) & Median & Upper Quartile (Q3) & Maximum \\
\hline
& & & & \\
\hline
\end{tabular}
\][/tex]

b) Use this information to conduct the outlier test for the weights of the sparrows that perished.

Perform the outlier test:
[tex]\[
\left(Q_3 - Q_1\right) * 1.5
\][/tex]

c) How many outliers, if any, are there? What is/are the weight(s) of the outlier(s)?



Answer :

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.