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Select the outlier in the data set. $\newline$ $45, 53, 59, 60, 61, 63, 64, 70, 965$

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Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

\newline

45, 53, 59, 60, 61, 63, 64, 70, 965

Arrange Data Set: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $45, 53, 59, 60, 61, 63, 64, 70, 965$ .
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 $61$ . $\newline$ Next, find $Q_1$ , the median of the lower half of the data set (not including the median). The lower half is $45$ , $53$ , $59$ , $60$ , so $Q_1$ is the average of $53$ and $59$ , which is $61$ $0$ . $\newline$ Then, find $61$ $1$ , the median of the upper half of the data set (not including the median). The upper half is $61$ $2$ , $61$ $3$ , $61$ $4$ , $61$ $5$ , so $61$ $1$ is the average of $61$ $3$ and $61$ $4$ , which is $61$ $9$ . $\newline$ The IQR is $Q_1$ $0$ , which is $Q_1$ $1$ .
Determine Outlier Threshold: Determine the outlier threshold. $\newline$ The lower bound for outliers is $Q1 - 1.5 \times IQR$ , which is $56 - 1.5 \times 11 = 56 - 16.5 = 39.5$ . $\newline$ The upper bound for outliers is $Q3 + 1.5 \times IQR$ , which is $67 + 1.5 \times 11 = 67 + 16.5 = 83.5$ . $\newline$ Any data point below $39.5$ or above $83.5$ is considered an outlier.
Identify Outliers: Identify the outlier(s) in the data set. Looking at the data set, the value $965$ is above the upper bound of $83.5$ and is therefore an outlier.

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