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Select the outlier in the data set. $\newline$ $9, 71, 79, 81, 82, 83, 86, 88, 97$

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Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

\newline

9, 71, 79, 81, 82, 83, 86, 88, 97

Arrange Data Set: Arrange the data set in ascending order. $\newline$ Data set in order: $9$ , $71$ , $79$ , $81$ , $82$ , $83$ , $86$ , $88$ , $97$ .
Calculate IQR: Calculate the interquartile range (IQR). $\newline$ First, find the medians of the lower and upper halves. $\newline$ Lower half: $9, 71, 79, 81$ ; Median = $(71 + 79) / 2 = 75$ . $\newline$ Upper half: $83, 86, 88, 97$ ; Median = $(86 + 88) / 2 = 87$ . $\newline$ IQR = Upper median - Lower median = $87 - 75 = 12$ .
Determine Outlier Thresholds: Determine the outlier thresholds. $\newline$ Lower threshold = Lower median - $1.5 \times \text{IQR} = 75 - 1.5 \times 12 = 57$ . $\newline$ Upper threshold = Upper median + $1.5 \times \text{IQR} = 87 + 1.5 \times 12 = 105$ .
Identify Outliers: Identify any values outside these thresholds. $\newline$ Values below $57$ are considered outliers. $\newline$ The value $9$ is below the lower threshold of $57$ , making it an outlier.

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