Select the outlier in the data set. 8, 71, 79, 80, 85, 89, 94, 98, 99

Arrange Data Set: Arrange the data set in ascending order. The data set is already in ascending order: 8, 71, 79, 80, 85, 89, 94, 98, 99.Calculate Quartiles: Calculate the first quartile (Q1), the median (Q2), and the third quartile (Q3) of the data set. To find Q1, we take the median of the first half of the data set (excluding the median if there is an odd number of data points). For Q3, we take the median of the second half of the data set. Q1 is the median of 8, 71, 79, 80, which is (71 + 79) / 2 = 75. Q3 is the median of 89, 94, 98, 99, which is (94 + 98) / 2 = 96.Calculate IQR: Calculate the interquartile range (IQR). IQR = Q3 - Q1 = 96 - 75 = 21.Determine Bounds: Determine the lower and upper bounds for potential outliers. Lower bound = Q1 - 1.5 * IQR = 75 - 1.5 * 21 = 75 - 31.5 = 43.5. Upper bound = Q3 + 1.5 * IQR = 96 + 1.5 * 21 = 96 + 31.5 = 127.5.Identify Outliers: Identify any data points that fall outside the lower and upper bounds. The value 8 is below the lower bound of 43.5, so it is an outlier. No values are above the upper bound of 127.5.

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Select the outlier in the data set. $\newline$ $8, 71, 79, 80, 85, 89, 94, 98, 99$

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Grade 6

Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

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8, 71, 79, 80, 85, 89, 94, 98, 99

Arrange Data Set: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $8, 71, 79, 80, 85, 89, 94, 98, 99$ .
Calculate Quartiles: Calculate the first quartile ( $Q_1$ ), the median ( $Q_2$ ), and the third quartile ( $Q_3$ ) of the data set. $\newline$ To find $Q_1$ , we take the median of the first half of the data set (excluding the median if there is an odd number of data points). For $Q_3$ , we take the median of the second half of the data set. $\newline$ $Q_1$ is the median of $8$ , $71$ , $79$ , $80$ , which is $Q_2$ $0$ . $\newline$ $Q_3$ is the median of $Q_2$ $2$ , $Q_2$ $3$ , $Q_2$ $4$ , $Q_2$ $5$ , which is $Q_2$ $6$ .
Calculate IQR: Calculate the interquartile range (IQR). $IQR = Q_3 - Q_1 = 96 - 75 = 21$ .
Determine Bounds: Determine the lower and upper bounds for potential outliers. $\newline$ Lower bound = $Q1 - 1.5 \times IQR = 75 - 1.5 \times 21 = 75 - 31.5 = 43.5$ . $\newline$ Upper bound = $Q3 + 1.5 \times IQR = 96 + 1.5 \times 21 = 96 + 31.5 = 127.5$ .
Identify Outliers: Identify any data points that fall outside the lower and upper bounds. $\newline$ The value $8$ is below the lower bound of $43.5$ , so it is an outlier. $\newline$ No values are above the upper bound of $127.5$ .