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Select the outlier in the data set. $\newline$ $36, 46, 54, 60, 62, 74, 88, 94, 371$

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Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

\newline

36, 46, 54, 60, 62, 74, 88, 94, 371

Arrange Data Set: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $36, 46, 54, 60, 62, 74, 88, 94, 371$ .
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. $\newline$ First half (for $Q_1$ ): $36, 46, 54, 60$ $\newline$ Second half (for $Q_3$ ): $62, 74, 88, 94$ $\newline$ Median of first half ( $Q_1$ ): $Q_2$ $0$ $\newline$ Median of second half ( $Q_3$ ): $Q_2$ $2$
Calculate IQR: Calculate the interquartile range (IQR). $IQR = Q3 - Q1 = 81 - 50 = 31$
Determine Bounds: Determine the lower and upper bounds for potential outliers. $\newline$ Lower bound = $Q1 - 1.5 \times IQR = 50 - 1.5 \times 31 = 50 - 46.5 = 3.5$ $\newline$ Upper bound = $Q3 + 1.5 \times IQR = 81 + 1.5 \times 31 = 81 + 46.5 = 127.5$
Identify Outliers: Identify any data points that fall outside the lower and upper bounds. The value $371$ is well above the upper bound of $127.5$ , so it is considered an outlier.

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