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Select the outlier in the data set. $\newline$ $8, 71, 79, 80, 85, 89, 94, 98, 99$

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Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

\newline

8, 71, 79, 80, 85, 89, 94, 98, 99

Arrange Data Set: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $8, 71, 79, 80, 85, 89, 94, 98, 99$ .
Calculate Quartiles: Calculate the first quartile ( $Q_1$ ), the median ( $Q_2$ ), and the third quartile ( $Q_3$ ) of the data set. $\newline$ To find $Q_1$ , we take the median of the first half of the data set (excluding the median if there is an odd number of data points). For $Q_3$ , we take the median of the second half of the data set. $\newline$ $Q_1$ is the median of $8$ , $71$ , $79$ , $80$ , which is $Q_2$ $0$ . $\newline$ $Q_3$ is the median of $Q_2$ $2$ , $Q_2$ $3$ , $Q_2$ $4$ , $Q_2$ $5$ , which is $Q_2$ $6$ .
Calculate IQR: Calculate the interquartile range (IQR). $IQR = Q_3 - Q_1 = 96 - 75 = 21$ .
Determine Bounds: Determine the lower and upper bounds for potential outliers. $\newline$ Lower bound = $Q1 - 1.5 \times IQR = 75 - 1.5 \times 21 = 75 - 31.5 = 43.5$ . $\newline$ Upper bound = $Q3 + 1.5 \times IQR = 96 + 1.5 \times 21 = 96 + 31.5 = 127.5$ .
Identify Outliers: Identify any data points that fall outside the lower and upper bounds. $\newline$ The value $8$ is below the lower bound of $43.5$ , so it is an outlier. $\newline$ No values are above the upper bound of $127.5$ .

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