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Select the outlier in the data set. $\newline$ $20, 27, 33, 39, 51, 60, 76, 94, 685$

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Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

\newline

20, 27, 33, 39, 51, 60, 76, 94, 685

Arrange Data Set: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $20, 27, 33, 39, 51, 60, 76, 94, 685$ .
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 $51$ . $\newline$ Next, find $Q_1$ , the median of the lower half of the data set (not including $Q_2$ ). The lower half is $20, 27, 33, 39$ , so $Q_1$ is the average of $27$ and $33$ , which is $\frac{27 + 33}{2} = 30$ . $\newline$ Then, find $Q_3$ , the median of the upper half of the data set (not including $Q_2$ ). The upper half is $51$ $1$ , so $Q_3$ is the average of $51$ $3$ and $51$ $4$ , which is $51$ $5$ . $\newline$ Now, calculate the IQR: $51$ $6$ .
Determine Outlier Boundaries: Determine the outlier boundaries. $\newline$ The lower boundary for outliers is $Q1 - 1.5 \times IQR = 30 - 1.5 \times 55 = 30 - 82.5 = -52.5$ (since there can't be negative values in this context, we'll consider the lower boundary as the smallest value in the data set, which is $20$ ). $\newline$ The upper boundary for outliers is $Q3 + 1.5 \times IQR = 85 + 1.5 \times 55 = 85 + 82.5 = 167.5$ .
Identify Outliers: Identify any values outside the outlier boundaries. $\newline$ Looking at the data set, the value $685$ is clearly above the upper boundary of $167.5$ , so it is an outlier.

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