Select the outlier in the data set. 18, 28, 40, 57, 59, 83, 88, 90, 647

Arrange Data Set: Arrange the data set in ascending order. The data set is already in ascending order: 18, 28, 40, 57, 59, 83, 88, 90, 647.Calculate IQR: Calculate the interquartile range (IQR) of the data set. First, find the median (Q2), which is the middle value when the data is ordered. For our data set, the median is 59. Next, find Q1, the median of the lower half of the data set (not including the median). The lower half is 18, 28, 40, 57. The median of this half is the average of 28 and 40, which is (28 + 40) / 2 = 34. Then, find Q3, the median of the upper half of the data set (not including the median). The upper half is 83, 88, 90, 647. The median of this half is the average of 88 and 90, which is (88 + 90) / 2 = 89. Now, calculate the IQR: Q3 - Q1 = 89 - 34 = 55.Outlier Boundaries: Determine the outlier boundaries. The lower boundary for outliers is Q1 - 1.5 * IQR = 34 - 1.5 * 55 = 34 - 82.5 = -48.5 (since there can't be a negative number of items, we'll consider the lower boundary as the smallest number in the data set, which is 18). The upper boundary for outliers is Q3 + 1.5 * IQR = 89 + 1.5 * 55 = 89 + 82.5 = 171.5.Identify Outliers: Identify any values outside the outlier boundaries. The value 647 is outside the upper boundary of 171.5, so it is considered an outlier.

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Select the outlier in the data set. $\newline$ $18, 28, 40, 57, 59, 83, 88, 90, 647$

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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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18, 28, 40, 57, 59, 83, 88, 90, 647

Arrange Data Set: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $18, 28, 40, 57, 59, 83, 88, 90, 647$ .
Calculate IQR: Calculate the interquartile range (IQR) of the data set. $\newline$ First, find the median ( $Q_2$ ), which is the middle value when the data is ordered. For our data set, the median is $59$ . $\newline$ Next, find $Q_1$ , the median of the lower half of the data set (not including the median). The lower half is $18$ , $28$ , $40$ , $57$ . The median of this half is the average of $28$ and $40$ , which is $(28 + 40) / 2 = 34$ . $\newline$ Then, find $59$ $0$ , the median of the upper half of the data set (not including the median). The upper half is $59$ $1$ , $59$ $2$ , $59$ $3$ , $59$ $4$ . The median of this half is the average of $59$ $2$ and $59$ $3$ , which is $59$ $7$ . $\newline$ Now, calculate the IQR: $59$ $8$ .
Outlier Boundaries: Determine the outlier boundaries. $\newline$ The lower boundary for outliers is $Q1 - 1.5 \times IQR = 34 - 1.5 \times 55 = 34 - 82.5 = -48.5$ (since there can't be a negative number of items, we'll consider the lower boundary as the smallest number in the data set, which is $18$ ). $\newline$ The upper boundary for outliers is $Q3 + 1.5 \times IQR = 89 + 1.5 \times 55 = 89 + 82.5 = 171.5$ .
Identify Outliers: Identify any values outside the outlier boundaries. $\newline$ The value $647$ is outside the upper boundary of $171.5$ , so it is considered an outlier.