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Select the outlier in the data set. $\newline$ $12, 13, 19, 52, 57, 66, 86, 98, 468$

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Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

\newline

12, 13, 19, 52, 57, 66, 86, 98, 468

List Data Set: List the data set in ascending order. $\newline$ Data set: $12, 13, 19, 52, 57, 66, 86, 98, 468$ .
Calculate IQR: Calculate the interquartile range (IQR). $\newline$ First, find the median ( $Q_2$ ) of the data set. The median is $57$ . $\newline$ Lower half (excluding median): $12, 13, 19, 52$ . $\newline$ Upper half (excluding median): $66, 86, 98, 468$ . $\newline$ Median of lower half ( $Q_1$ ): $(19 + 13) / 2 = 16$ . $\newline$ Median of upper half ( $Q_3$ ): $(86 + 98) / 2 = 92$ . $\newline$ $IQR = Q_3 - Q_1 = 92 - 16 = 76$ .
Determine Outlier Threshold: Determine the outlier threshold. $\newline$ Lower bound = $Q1 - 1.5 \times IQR = 16 - 1.5 \times 76 = -98$ . $\newline$ Upper bound = $Q3 + 1.5 \times IQR = 92 + 1.5 \times 76 = 206$ .
Identify Outliers: Identify any outliers beyond these bounds. $\newline$ Only $468$ is beyond the upper bound of $206$ , making it the outlier.

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