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Select the outlier in the data set. $\newline$ $4, 60, 76, 77, 78, 80, 81, 83, 93$

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Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

\newline

4, 60, 76, 77, 78, 80, 81, 83, 93

Arrange Data Set: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $4, 60, 76, 77, 78, 80, 81, 83, 93$ .
Calculate IQR: Calculate the interquartile range (IQR) of the data set. $\newline$ First, find the median ( $Q_2$ ), which is the middle value. For our data set, the median is $78$ . $\newline$ Next, find the first quartile ( $Q_1$ ), which is the median of the lower half of the data set. The lower half is $4$ , $60$ , $76$ , and the median of this is $60$ . $\newline$ Then, find the third quartile ( $Q_3$ ), which is the median of the upper half of the data set. The upper half is $80$ , $81$ , $78$ $0$ , $78$ $1$ , and the median of this is $81$ . $\newline$ Now, calculate the IQR: $78$ $3$ .
Determine Outlier Boundaries: Determine the outlier boundaries. $\newline$ The lower boundary for outliers is $Q1 - 1.5 \times IQR = 60 - 1.5 \times 21 = 60 - 31.5 = 28.5$ . $\newline$ The upper boundary for outliers is $Q3 + 1.5 \times IQR = 81 + 1.5 \times 21 = 81 + 31.5 = 112.5$ .
Identify Outliers: Identify any values outside the outlier boundaries. $\newline$ The value $4$ is below the lower boundary of $28.5$ , so it is an outlier. $\newline$ No values are above the upper boundary of $112.5$ .

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