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Select the outlier in the data set. $\newline$ $5, 47, 51, 55, 56, 57, 59, 64$

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Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

\newline

5, 47, 51, 55, 56, 57, 59, 64

Calculate Range: List the data set and calculate the range. $\newline$ Data set: $5, 47, 51, 55, 56, 57, 59, 64$ . $\newline$ Range $= \text{Maximum value} - \text{Minimum value} = 64 - 5 = 59$ .
Calculate Quartiles: Calculate the first and third quartiles ( $Q1$ and $Q3$ ). $\newline$ To find $Q1$ , the median of the first half ( $5, 47, 51, 55$ ) is $(47 + 51) / 2 = 49$ . $\newline$ To find $Q3$ , the median of the second half ( $56, 57, 59, 64$ ) is $(57 + 59) / 2 = 58$ .
Calculate IQR: Calculate the interquartile range (IQR). $IQR = Q_3 - Q_1 = 58 - 49 = 9$ .
Determine Outlier Threshold: Determine the outlier threshold. $\newline$ Lower bound = $Q1 - 1.5 \times IQR = 49 - 1.5 \times 9 = 35.5$ . $\newline$ Upper bound = $Q3 + 1.5 \times IQR = 58 + 1.5 \times 9 = 71.5$ .
Identify Outliers: Identify any outliers outside the bounds. $\newline$ The value $5$ is below the lower bound of $35.5$ , making it an outlier.

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