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Select the outlier in the data set. $\newline$ $23, 33, 49, 51, 53, 66, 74, 96, 252$

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Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

\newline

23, 33, 49, 51, 53, 66, 74, 96, 252

Arrange Data Set: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $23, 33, 49, 51, 53, 66, 74, 96, 252$ .
Calculate IQR: Calculate the interquartile range ( $IQR$ ) of the data set. $\newline$ First, find the median ( $Q2$ ), which is the middle value when the data is ordered. For our data set, the median is $53$ . $\newline$ Next, find the first quartile ( $Q1$ ), which is the median of the lower half of the data set. The lower half is $23, 33, 49, 51$ . The median of this half is the average of $33$ and $49$ , which is $(33 + 49) / 2 = 41$ . $\newline$ Then, find the third quartile ( $Q3$ ), which is the median of the upper half of the data set. The upper half is $66, 74, 96, 252$ . The median of this half is the average of $Q2$ $0$ and $Q2$ $1$ , which is $Q2$ $2$ . $\newline$ Now, calculate the IQR: $Q2$ $3$ .
Determine Outlier Boundaries: Determine the outlier boundaries. $\newline$ The lower boundary for outliers is $Q1 - 1.5 \times IQR = 41 - 1.5 \times 44 = 41 - 66 = -25$ . $\newline$ The upper boundary for outliers is $Q3 + 1.5 \times IQR = 85 + 1.5 \times 44 = 85 + 66 = 151$ .
Identify Outliers: Identify any values outside the outlier boundaries. The value $252$ is outside the upper boundary of $151$ , so it is considered an outlier.

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