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Select the outlier in the data set. $\newline$ $58, 68, 74, 78, 79, 82, 86, 761$

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Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

\newline

58, 68, 74, 78, 79, 82, 86, 761

List Data Set: List the data set in ascending order. $\newline$ Data set: $58, 68, 74, 78, 79, 82, 86, 761$ .
Calculate IQR: Calculate the interquartile range (IQR). $\newline$ First, find the median (Q $2$ ). The median of $58, 68, 74, 78, 79, 82, 86, 761$ is the average of $78$ and $79$ . $\newline$ Median (Q $2$ ) = $(78 + 79) / 2 = 78.5$ $\newline$ Next, find Q $1$ and Q $3$ . $\newline$ Lower half: $58, 68, 74, 78$ $\newline$ Upper half: $79, 82, 86, 761$ $\newline$ Median of lower half (Q $1$ ): $(68 + 74) / 2 = 71$ $\newline$ Median of upper half (Q $3$ ): $(82 + 86) / 2 = 84$ $\newline$ IQR = $Q3 - Q1 = 84 - 71 = 13$
Determine Outlier Threshold: Determine the outlier threshold. $\newline$ Lower bound = $Q1 - 1.5 \times IQR = 71 - 1.5 \times 13 = 51.5$ $\newline$ Upper bound = $Q3 + 1.5 \times IQR = 84 + 1.5 \times 13 = 103.5$ $\newline$ Values outside these bounds are considered outliers.
Identify Outlier: Identify the outlier. $\newline$ The value $761$ is way above the upper bound of $103.5$ , making it the outlier.

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