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Select the outlier in the data set. $\newline$ $8, 85, 87, 89, 90, 91, 92, 94, 98$

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Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

\newline

8, 85, 87, 89, 90, 91, 92, 94, 98

Arrange Data Set: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $8, 85, 87, 89, 90, 91, 92, 94, 98$ .
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: $90$ . $\newline$ Next, find $Q_1$ , the median of the lower half. The lower half is $8$ , $85$ , $87$ , $89$ . The median of this half is the average of $85$ and $87$ : $9$ $1$ . $\newline$ Then, find $9$ $2$ , the median of the upper half. The upper half is $9$ $3$ , $9$ $4$ , $9$ $5$ , $9$ $6$ . The median of this half is the average of $9$ $4$ and $9$ $5$ : $9$ $9$ . $\newline$ Now, calculate the IQR: $5$ $0$ .
Determine Boundaries: Determine the outlier boundaries. $\newline$ The lower boundary is $Q1 - 1.5 \times IQR = 86 - 1.5 \times 7 = 86 - 10.5 = 75.5$ . $\newline$ The upper boundary is $Q3 + 1.5 \times IQR = 93 + 1.5 \times 7 = 93 + 10.5 = 103.5$ . $\newline$ Any data point below $75.5$ or above $103.5$ is considered an outlier.
Identify Outliers: Identify any outliers in the data set. The value $8$ is below the lower boundary of $75.5$ , so it is an outlier.

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