Select the outlier in the data set. 4, 60, 76, 77, 78, 80, 81, 83, 93

Arrange Data Set: Arrange the data set in ascending order. The data set is already in ascending order: 4, 60, 76, 77, 78, 80, 81, 83, 93.Calculate IQR: Calculate the interquartile range (IQR) of the data set. First, find the median (Q2), which is the middle value. For our data set, the median is 78. Next, find the first quartile (Q1), which is the median of the lower half of the data set. The lower half is 4, 60, 76, and the median of this is 60. Then, find the third quartile (Q3), which is the median of the upper half of the data set. The upper half is 80, 81, 83, 93, and the median of this is 81. Now, calculate the IQR: Q3 - Q1 = 81 - 60 = 21.Determine Outlier Boundaries: Determine the outlier boundaries. The lower boundary for outliers is Q1 - 1.5 * IQR = 60 - 1.5 * 21 = 60 - 31.5 = 28.5. The upper boundary for outliers is Q3 + 1.5 * IQR = 81 + 1.5 * 21 = 81 + 31.5 = 112.5.Identify Outliers: Identify any values outside the outlier boundaries. The value 4 is below the lower boundary of 28.5, so it is an outlier. No values are above the upper boundary of 112.5.

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Select the outlier in the data set. $\newline$ $4, 60, 76, 77, 78, 80, 81, 83, 93$

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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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4, 60, 76, 77, 78, 80, 81, 83, 93

Arrange Data Set: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $4, 60, 76, 77, 78, 80, 81, 83, 93$ .
Calculate IQR: Calculate the interquartile range (IQR) of the data set. $\newline$ First, find the median ( $Q_2$ ), which is the middle value. For our data set, the median is $78$ . $\newline$ Next, find the first quartile ( $Q_1$ ), which is the median of the lower half of the data set. The lower half is $4$ , $60$ , $76$ , and the median of this is $60$ . $\newline$ Then, find the third quartile ( $Q_3$ ), which is the median of the upper half of the data set. The upper half is $80$ , $81$ , $78$ $0$ , $78$ $1$ , and the median of this is $81$ . $\newline$ Now, calculate the IQR: $78$ $3$ .
Determine Outlier Boundaries: Determine the outlier boundaries. $\newline$ The lower boundary for outliers is $Q1 - 1.5 \times IQR = 60 - 1.5 \times 21 = 60 - 31.5 = 28.5$ . $\newline$ The upper boundary for outliers is $Q3 + 1.5 \times IQR = 81 + 1.5 \times 21 = 81 + 31.5 = 112.5$ .
Identify Outliers: Identify any values outside the outlier boundaries. $\newline$ The value $4$ is below the lower boundary of $28.5$ , so it is an outlier. $\newline$ No values are above the upper boundary of $112.5$ .