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Select the outlier in the data set. $\newline$ $57, 67, 69, 73, 75, 78, 80, 84, 864$

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Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

\newline

57, 67, 69, 73, 75, 78, 80, 84, 864

Arrange Data in Ascending Order: Arrange the data set in ascending order. $\newline$ The data set in ascending order is: $57, 67, 69, 73, 75, 78, 80, 84, 864$ .
Calculate Interquartile Range: 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 $75$ . $\newline$ Next, find $Q_1$ , the median of the lower half of the data set (excluding $Q_2$ ). The lower half is $57$ , $67$ , $69$ , $73$ , so $Q_1$ is the average of $67$ and $69$ , which is $75$ $1$ . $\newline$ Then, find $75$ $2$ , the median of the upper half of the data set (excluding $Q_2$ ). The upper half is $75$ $4$ , $75$ $5$ , $75$ $6$ , $75$ $7$ , so $75$ $2$ is the average of $75$ $5$ and $75$ $6$ , which is $Q_1$ $1$ . $\newline$ Now, calculate the IQR: $Q_1$ $2$ .
Determine Outlier Boundaries: Determine the outlier boundaries. $\newline$ The lower boundary for outliers is $Q1 - 1.5 \times IQR = 68 - 1.5 \times 14 = 68 - 21 = 47$ . $\newline$ The upper boundary for outliers is $Q3 + 1.5 \times IQR = 82 + 1.5 \times 14 = 82 + 21 = 103$ .
Identify Outliers: Identify any values outside the outlier boundaries. $\newline$ The value $864$ is well above the upper boundary of $103$ , so it is considered an outlier.

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