Select the outlier in the data set. 6, 76, 78, 81, 83, 89, 91, 93, 99

Arrange Data Set: Arrange the data set in ascending order. The data set is already in ascending order: 6, 76, 78, 81, 83, 89, 91, 93, 99.Calculate IQR: Calculate the interquartile range (IQR) of the data set. First, find the median (Q2), which is the middle value of the ordered data set. For our data set, the median is 83. Next, find the first quartile (Q1), which is the median of the lower half of the data set. The lower half is 6, 76, 78, 81. The median of this half is the average of 76 and 78, which is (76 + 78) / 2 = 77. Then, find the third quartile (Q3), which is the median of the upper half of the data set. The upper half is 89, 91, 93, 99. The median of this half is the average of 91 and 93, which is (91 + 93) / 2 = 92. The IQR is Q3 - Q1, which is 92 - 77 = 15.Determine Outlier Boundaries: Determine the outlier boundaries. The lower boundary for outliers is Q1 - 1.5 * IQR, which is 77 - 1.5 * 15 = 77 - 22.5 = 54.5. The upper boundary for outliers is Q3 + 1.5 * IQR, which is 92 + 1.5 * 15 = 92 + 22.5 = 114.5.Identify Outliers: Identify any values outside the outlier boundaries. The value 6 is below the lower boundary of 54.5, so it is an outlier. No values are above the upper boundary of 114.5.

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Select the outlier in the data set. $\newline$ $6, 76, 78, 81, 83, 89, 91, 93, 99$

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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, 76, 78, 81, 83, 89, 91, 93, 99

Arrange Data Set: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $6$ , $76$ , $78$ , $81$ , $83$ , $89$ , $91$ , $93$ , $99$ .
Calculate IQR: Calculate the interquartile range (IQR) of the data set. $\newline$ First, find the median ( $Q_2$ ), which is the middle value of the ordered data set. For our data set, the median is $83$ . $\newline$ Next, find the first quartile ( $Q_1$ ), which is the median of the lower half of the data set. The lower half is $6, 76, 78, 81$ . The median of this half is the average of $76$ and $78$ , which is $(76 + 78) / 2 = 77$ . $\newline$ Then, find the third quartile ( $Q_3$ ), which is the median of the upper half of the data set. The upper half is $89, 91, 93, 99$ . The median of this half is the average of $91$ and $83$ $0$ , which is $83$ $1$ . $\newline$ The IQR is $83$ $2$ , which is $83$ $3$ .
Determine Outlier Boundaries: Determine the outlier boundaries. $\newline$ The lower boundary for outliers is $Q1 - 1.5 \times IQR$ , which is $77 - 1.5 \times 15 = 77 - 22.5 = 54.5$ . $\newline$ The upper boundary for outliers is $Q3 + 1.5 \times IQR$ , which is $92 + 1.5 \times 15 = 92 + 22.5 = 114.5$ .
Identify Outliers: Identify any values outside the outlier boundaries. $\newline$ The value $6$ is below the lower boundary of $54.5$ , so it is an outlier. $\newline$ No values are above the upper boundary of $114.5$ .