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Select the outlier in the data set. $\newline$ $64, 74, 76, 84, 86, 88, 89, 95, 586$

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Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

\newline

64, 74, 76, 84, 86, 88, 89, 95, 586

Arrange Data Set: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $64, 74, 76, 84, 86, 88, 89, 95, 586$ .
Calculate IQR: Calculate the interquartile range (IQR) of the data set. $\newline$ First, find the median ( $Q_2$ ), which is the middle value of the data set. Since there are $9$ numbers, the median is the $5$ th number: $86$ . $\newline$ Next, find $Q_1$ , the median of the first half of the data set (excluding the median): $(74 + 76) / 2 = 75$ . $\newline$ Then, find $Q_3$ , the median of the second half of the data set (excluding the median): $(89 + 95) / 2 = 92$ . $\newline$ Now, calculate the IQR: $Q_3 - Q_1 = 92 - 75 = 17$ .
Determine Boundaries: Determine the outlier boundaries. $\newline$ The lower boundary is $Q1 - 1.5 \times IQR = 75 - 1.5 \times 17 = 75 - 25.5 = 49.5$ . $\newline$ The upper boundary is $Q3 + 1.5 \times IQR = 92 + 1.5 \times 17 = 92 + 25.5 = 117.5$ .
Identify Outliers: Identify any values outside the outlier boundaries. $\newline$ The value $586$ is well above the upper boundary of $117.5$ , so it is considered an outlier.

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