Select the outlier in the data set. 23, 33, 49, 51, 53, 66, 74, 96, 252

Arrange Data Set: Arrange the data set in ascending order. The data set is already in ascending order: 23, 33, 49, 51, 53, 66, 74, 96, 252.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 53. Next, find the first quartile (Q1), which is the median of the lower half of the data set. The lower half is 23, 33, 49, 51. The median of this half is the average of 33 and 49, which is (33 + 49) / 2 = 41. Then, find the third quartile (Q3), which is the median of the upper half of the data set. The upper half is 66, 74, 96, 252. The median of this half is the average of 74 and 96, which is (74 + 96) / 2 = 85. Now, calculate the IQR: Q3 - Q1 = 85 - 41 = 44.Determine Outlier Boundaries: Determine the outlier boundaries. The lower boundary for outliers is Q1 - 1.5 * IQR = 41 - 1.5 * 44 = 41 - 66 = -25. The upper boundary for outliers is Q3 + 1.5 * IQR = 85 + 1.5 * 44 = 85 + 66 = 151.Identify Outliers: Identify any values outside the outlier boundaries. The value 252 is outside the upper boundary of 151, so it is considered an outlier.

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Select the outlier in the data set. $\newline$ $23, 33, 49, 51, 53, 66, 74, 96, 252$

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Math Problems

Grade 6

Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

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23, 33, 49, 51, 53, 66, 74, 96, 252

Arrange Data Set: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $23, 33, 49, 51, 53, 66, 74, 96, 252$ .
Calculate IQR: Calculate the interquartile range ( $IQR$ ) of the data set. $\newline$ First, find the median ( $Q2$ ), which is the middle value when the data is ordered. For our data set, the median is $53$ . $\newline$ Next, find the first quartile ( $Q1$ ), which is the median of the lower half of the data set. The lower half is $23, 33, 49, 51$ . The median of this half is the average of $33$ and $49$ , which is $(33 + 49) / 2 = 41$ . $\newline$ Then, find the third quartile ( $Q3$ ), which is the median of the upper half of the data set. The upper half is $66, 74, 96, 252$ . The median of this half is the average of $Q2$ $0$ and $Q2$ $1$ , which is $Q2$ $2$ . $\newline$ Now, calculate the IQR: $Q2$ $3$ .
Determine Outlier Boundaries: Determine the outlier boundaries. $\newline$ The lower boundary for outliers is $Q1 - 1.5 \times IQR = 41 - 1.5 \times 44 = 41 - 66 = -25$ . $\newline$ The upper boundary for outliers is $Q3 + 1.5 \times IQR = 85 + 1.5 \times 44 = 85 + 66 = 151$ .
Identify Outliers: Identify any values outside the outlier boundaries. The value $252$ is outside the upper boundary of $151$ , so it is considered an outlier.