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Select the outlier in the data set. $\newline$ $74,84,86,87,89,91,92,98,126$

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Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

\newline

74,84,86,87,89,91,92,98,126

Arrange Data Set: Arrange the data set in ascending order if it is not already. $\newline$ The data set is already in ascending order: $74, 84, 86, 87, 89, 91, 92, 98, 126$ .
Calculate IQR: Calculate the interquartile range (IQR) of the data set. $\newline$ First, find the first quartile ( $Q_1$ ) and the third quartile ( $Q_3$ ). $\newline$ $Q_1$ is the median of the first half of the data set: $(74, 84, 86, 87)$ , which is $(84 + 86) / 2 = 85$ . $\newline$ $Q_3$ is the median of the second half of the data set: $(91, 92, 98, 126)$ , which is $(92 + 98) / 2 = 95$ . $\newline$ $IQR = Q_3 - Q_1 = 95 - 85 = 10$ .
Determine Outlier Boundaries: Determine the outlier boundaries. $\newline$ Lower boundary = $Q1 - 1.5 \times IQR = 85 - 1.5 \times 10 = 85 - 15 = 70$ . $\newline$ Upper boundary = $Q3 + 1.5 \times IQR = 95 + 1.5 \times 10 = 95 + 15 = 110$ .
Identify Outliers: Identify any values outside the outlier boundaries. The value $126$ is above the upper boundary of $110$ , so it is an outlier.

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