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Select the outlier in the data set. $\newline$ $11, 17, 21, 26, 34, 35, 37, 425$

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Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

\newline

11, 17, 21, 26, 34, 35, 37, 425

Arrange Data Set: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $11, 17, 21, 26, 34, 35, 37, 425$ .
Calculate IQR: Calculate the interquartile range (IQR) of the data set. $\newline$ First, find the median ( $Q2$ ), which is the middle value of the data set. Since there are $8$ numbers, the median will be the average of the $4$ th and $5$ th values: $(26 + 34) / 2 = 30$ . $\newline$ Next, find $Q1$ , the median of the lower half of the data set (excluding $Q2$ ): $(17 + 21) / 2 = 19$ . $\newline$ Then, find $Q3$ , the median of the upper half of the data set (excluding $Q2$ ): $8$ $0$ . $\newline$ Now, calculate $8$ $1$ .
Determine Outlier Boundaries: Determine the outlier boundaries. $\newline$ The lower boundary for outliers is $Q1 - 1.5 \times IQR = 19 - 1.5 \times 17 = 19 - 25.5 = -6.5$ . $\newline$ The upper boundary for outliers is $Q3 + 1.5 \times IQR = 36 + 1.5 \times 17 = 36 + 25.5 = 61.5$ .
Identify Outliers: Identify any values outside the outlier boundaries. $\newline$ The value $425$ is well above the upper boundary of $61.5$ , so it is considered an outlier.

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