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Select the outlier in the data set. $\newline$ $10, 13, 15, 17, 24, 37, 63, 81, 804$

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Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

\newline

10, 13, 15, 17, 24, 37, 63, 81, 804

Arrange Data in Ascending Order: Arrange the data set in ascending order. $\newline$ The data set in ascending order is: $10, 13, 15, 17, 24, 37, 63, 81, 804$ .
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 $24$ . $\newline$ Next, find $Q_1$ , the median of the lower half of the data set (not including the median). The lower half is $10$ , $13$ , $15$ , $17$ , so $Q_1$ is the average of $13$ and $15$ , which is $24$ $0$ . $\newline$ Then, find $24$ $1$ , the median of the upper half of the data set (not including the median). The upper half is $24$ $2$ , $24$ $3$ , $24$ $4$ , $24$ $5$ , so $24$ $1$ is the average of $24$ $3$ and $24$ $4$ , which is $24$ $9$ . $\newline$ Now, calculate the IQR: $Q_1$ $0$ .
Determine Outlier Boundaries: Determine the outlier boundaries. $\newline$ The lower boundary for outliers is $Q1 - 1.5 \times IQR$ , which is $14 - 1.5 \times 58 = 14 - 87 = -73$ . $\newline$ The upper boundary for outliers is $Q3 + 1.5 \times IQR$ , which is $72 + 1.5 \times 58 = 72 + 87 = 159$ . $\newline$ Any data point below $-73$ or above $159$ is considered an outlier.
Identify Outliers: Identify any outliers based on the boundaries. $\newline$ Looking at the data set, the value $804$ is above the upper boundary of $159$ , so it is an outlier.

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