Select the outlier in the data set. 6, 73, 77, 78, 81, 84, 85, 89, 99

Arrange Data Set: Arrange the data set in ascending order. The data set is already in ascending order: 6, 73, 77, 78, 81, 84, 85, 89, 99.Calculate Quartiles: Calculate the first quartile (Q1), the median (Q2), and the third quartile (Q3) of the data set. To find Q1, we need to find the median of the lower half of the data set. The lower half is 6, 73, 77, 78. The median of this half is the average of 73 and 77. Q1 = (73 + 77) / 2 = 75 To find Q2, which is the median of the data set, we have 81 as the middle value since it is the fifth number in the ordered list. To find Q3, we need to find the median of the upper half of the data set. The upper half is 84, 85, 89, 99. The median of this half is the average of 85 and 89. Q3 = (85 + 89) / 2 = 87Calculate IQR: Calculate the interquartile range (IQR). IQR = Q3 - Q1 = 87 - 75 = 12Determine Bounds: Determine the lower and upper bounds for potential outliers. Lower bound = Q1 - 1.5 * IQR = 75 - 1.5 * 12 = 75 - 18 = 57 Upper bound = Q3 + 1.5 * IQR = 87 + 1.5 * 12 = 87 + 18 = 105Identify Outliers: Identify any values that fall outside the bounds determined in Step 4. The value 6 is below the lower bound of 57, so it is considered an outlier.

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Select the outlier in the data set. $\newline$ $6, 73, 77, 78, 81, 84, 85, 89, 99$

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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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6, 73, 77, 78, 81, 84, 85, 89, 99

Arrange Data Set: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $6, 73, 77, 78, 81, 84, 85, 89, 99$ .
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 need to find the median of the lower half of the data set. The lower half is $6$ , $73$ , $77$ , $78$ . The median of this half is the average of $73$ and $77$ . $\newline$ $Q_2$ $0$ $\newline$ To find $Q_2$ , which is the median of the data set, we have $Q_2$ $2$ as the middle value since it is the fifth number in the ordered list. $\newline$ To find $Q_3$ , we need to find the median of the upper half of the data set. The upper half is $Q_2$ $4$ , $Q_2$ $5$ , $Q_2$ $6$ , $Q_2$ $7$ . The median of this half is the average of $Q_2$ $5$ and $Q_2$ $6$ . $\newline$ $Q_3$ $0$
Calculate IQR: Calculate the interquartile range (IQR). $\newline$ $IQR = Q3 - Q1 = 87 - 75 = 12$
Determine Bounds: Determine the lower and upper bounds for potential outliers. $\newline$ Lower bound = $Q1 - 1.5 \times IQR = 75 - 1.5 \times 12 = 75 - 18 = 57$ $\newline$ Upper bound = $Q3 + 1.5 \times IQR = 87 + 1.5 \times 12 = 87 + 18 = 105$
Identify Outliers: Identify any values that fall outside the bounds determined in Step $4$ . $\newline$ The value $6$ is below the lower bound of $57$ , so it is considered an outlier.