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Select the outlier in the data set. $\newline$ $76, 84, 86, 87, 88, 89, 90, 92, 149$

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Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

\newline

76, 84, 86, 87, 88, 89, 90, 92, 149

Arrange Data in Ascending Order: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $76$ , $84$ , $86$ , $87$ , $88$ , $89$ , $90$ , $92$ , $149$ .
Calculate Interquartile Range: Calculate the interquartile range (IQR). $\newline$ First, find the medians of the lower and upper halves, excluding the median of the full set. $\newline$ Lower half: $76, 84, 86, 87$ ; Median = $(84 + 86) / 2 = 85$ $\newline$ Upper half: $89, 90, 92, 149$ ; Median = $(90 + 92) / 2 = 91$ $\newline$ IQR = Upper median - Lower median = $91 - 85 = 6$
Determine Outlier Threshold: Determine the outlier threshold. $\newline$ Lower bound = $Q1 - 1.5 \times IQR = 85 - 1.5 \times 6 = 76.0$ $\newline$ Upper bound = $Q3 + 1.5 \times IQR = 91 + 1.5 \times 6 = 100.5$
Identify Outliers: Identify any outliers beyond these bounds. $\newline$ The value $149$ is beyond the upper bound of $100.5$ , making it an outlier.

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