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Select the outlier in the data set. $\newline$ $2, 49, 51, 52, 55, 59, 61, 63, 71$

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Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

\newline

2, 49, 51, 52, 55, 59, 61, 63, 71

Arrange Data in Ascending Order: Arrange the data set in ascending order. $\newline$ Data set in order: $2, 49, 51, 52, 55, 59, 61, 63, 71$ .
Calculate Interquartile Range: Calculate the interquartile range (IQR). First, find the medians of the lower and upper halves, excluding the median of the full set. Lower half: $2, 49, 51, 52$ ; Median = $(49 + 51) / 2 = 50$ Upper half: $59, 61, 63, 71$ ; Median = $(61 + 63) / 2 = 62$ IQR = Upper median - Lower median = $62 - 50 = 12$
Determine Outlier Thresholds: Determine the outlier thresholds. $\newline$ Lower bound = $Q1 - 1.5 \times IQR = 50 - 1.5 \times 12 = 32$ $\newline$ Upper bound = $Q3 + 1.5 \times IQR = 62 + 1.5 \times 12 = 80$
Identify Outliers: Identify any numbers outside the outlier thresholds. $\newline$ The number $2$ is below the lower bound of $32$ , making it an outlier.

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