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Select the outlier in the data set. $\newline$ $6, 56, 62, 66, 67, 68, 69, 79, 89$

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Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

\newline

6, 56, 62, 66, 67, 68, 69, 79, 89

Arrange Data Set: Arrange the data set in ascending order. $\newline$ Data set in order: $6, 56, 62, 66, 67, 68, 69, 79, 89$ .
Calculate IQR: Calculate the interquartile range (IQR). $\newline$ First, find the median ( $Q_2$ ) of the entire data set. The median is $67$ . $\newline$ Lower half (before $67$ ): $6, 56, 62, 66$ . $\newline$ Upper half (after $67$ ): $68, 69, 79, 89$ . $\newline$ Median of lower half ( $Q_1$ ): $(62 + 66) / 2 = 64$ . $\newline$ Median of upper half ( $Q_3$ ): $(69 + 79) / 2 = 74$ . $\newline$ $67$ $0$ .
Determine Outlier Thresholds: Determine the outlier thresholds. $\newline$ Lower bound = $Q1 - 1.5 \times IQR = 64 - 1.5 \times 10 = 49$ . $\newline$ Upper bound = $Q3 + 1.5 \times IQR = 74 + 1.5 \times 10 = 89$ .
Identify Outliers: Identify any numbers outside the outlier thresholds. $\newline$ The number $6$ is below the lower bound of $49$ , making it an outlier.

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