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A teacher was looking through her grade book at her students' test scores. Which score in the data set would be considered an outlier?

Test Scores

87
78
90
81
100

93
82
87
45
74

A 45
B 74
C 78
D 81

$3$ . A teacher was looking through her grade book at her students' test scores. Which score in the data set would be considered an outlier? $\newline$ \begin{tabular}{|c|c|c|c|c|} $\newline$ \hline \multicolumn{ $5$ }{|c|}{ Test Scores } \\ $\newline$ \hline $87$ & $78$ & $90$ & $81$ & $100$ \\ $\newline$ \hline $93$ & $82$ & $87$ & $45$ & $74$ \\ $\newline$ \hline $\newline$ \end{tabular} $\newline$ A $45$ $\newline$ B $74$ $\newline$ C $78$ $\newline$ D $81$

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Calculate quartiles and interquartile range

Full solution

Q.

3

. A teacher was looking through her grade book at her students' test scores. Which score in the data set would be considered an outlier?

\newline

\begin{tabular}{|c|c|c|c|c|}

\newline

\hline \multicolumn{

5

}{|c|}{ Test Scores } \\

\newline

\hline

87

&

78

&

90

&

81

&

100

\\

\newline

\hline

93

&

82

&

87

&

45

&

74

\\

\newline

\hline

\newline

\end{tabular}

\newline

A

45

\newline

B

74

\newline

C

78

\newline

D

81

List test scores: List all the test scores in ascending order. $45, 74, 78, 81, 82, 87, 87, 90, 93, 100$
Calculate IQR: Calculate the interquartile range (IQR). $\newline$ First, find the median, which is the average of the $5$ th and $6$ th scores: $(82 + 87) / 2 = 84.5$ $\newline$ Then, find the medians of the first half and the second half to get $Q1$ and $Q3$ . $\newline$ First half: $45, 74, 78, 81, 82$ . Median ( $Q1$ ) is $78$ . $\newline$ Second half: $87, 87, 90, 93, 100$ . Median ( $Q3$ ) is $90$ . $\newline$ $IQR = Q3 - Q1 = 90 - 78 = 12$
Determine outlier boundaries: Determine the outlier boundaries. $\newline$ Lower boundary = $Q1 - 1.5 \times IQR = 78 - 1.5 \times 12 = 78 - 18 = 60$ $\newline$ Upper boundary = $Q3 + 1.5 \times IQR = 90 + 1.5 \times 12 = 90 + 18 = 108$
Identify outliers: Identify any scores outside the boundaries. $\newline$ The score of $45$ is below the lower boundary of $60$ , so it's an outlier.

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