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Select the outlier in the data set. $\newline$ $18, 28, 40, 57, 59, 83, 88, 90, 647$

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Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

\newline

18, 28, 40, 57, 59, 83, 88, 90, 647

Arrange Data Set: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $18, 28, 40, 57, 59, 83, 88, 90, 647$ .
Calculate IQR: Calculate the interquartile range (IQR) of the data set. $\newline$ First, find the median ( $Q_2$ ), which is the middle value when the data is ordered. For our data set, the median is $59$ . $\newline$ Next, find $Q_1$ , the median of the lower half of the data set (not including the median). The lower half is $18$ , $28$ , $40$ , $57$ . The median of this half is the average of $28$ and $40$ , which is $(28 + 40) / 2 = 34$ . $\newline$ Then, find $59$ $0$ , the median of the upper half of the data set (not including the median). The upper half is $59$ $1$ , $59$ $2$ , $59$ $3$ , $59$ $4$ . The median of this half is the average of $59$ $2$ and $59$ $3$ , which is $59$ $7$ . $\newline$ Now, calculate the IQR: $59$ $8$ .
Outlier Boundaries: Determine the outlier boundaries. $\newline$ The lower boundary for outliers is $Q1 - 1.5 \times IQR = 34 - 1.5 \times 55 = 34 - 82.5 = -48.5$ (since there can't be a negative number of items, we'll consider the lower boundary as the smallest number in the data set, which is $18$ ). $\newline$ The upper boundary for outliers is $Q3 + 1.5 \times IQR = 89 + 1.5 \times 55 = 89 + 82.5 = 171.5$ .
Identify Outliers: Identify any values outside the outlier boundaries. $\newline$ The value $647$ is outside the upper boundary of $171.5$ , so it is considered an outlier.

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