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Select the outlier in the data set. $\newline$ $10, 11, 21, 27, 31, 32, 35, 51, 520$

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Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

\newline

10, 11, 21, 27, 31, 32, 35, 51, 520

List Data Set: List the data set in ascending order. $\newline$ Data set: $10, 11, 21, 27, 31, 32, 35, 51, 520$ .
Calculate IQR: Calculate the interquartile range (IQR). $\newline$ First, find the median (Q $2$ ) of the data set. The median is $31$ . $\newline$ Lower half (excluding median): $10, 11, 21, 27$ . $\newline$ Upper half (excluding median): $32, 35, 51, 520$ . $\newline$ Median of lower half (Q $1$ ): $(11 + 21) / 2 = 16$ . $\newline$ Median of upper half (Q $3$ ): $(35 + 51) / 2 = 43$ . $\newline$ IQR = $Q3 - Q1 = 43 - 16 = 27$ .
Determine Outlier Threshold: Determine the outlier threshold. $\newline$ Lower bound = $Q1 - 1.5 \times IQR = 16 - 1.5 \times 27 = -24.5$ (not applicable as all data are positive). $\newline$ Upper bound = $Q3 + 1.5 \times IQR = 43 + 1.5 \times 27 = 83.5$ .
Identify Outliers: Identify any outliers beyond these bounds. $520$ is the only number greater than $83.5$ , making it the outlier.

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