Select the outlier in the data set. 45, 53, 59, 60, 61, 63, 64, 70, 965

Arrange Data Set: Arrange the data set in ascending order. The data set is already in ascending order: 45, 53, 59, 60, 61, 63, 64, 70, 965.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 61. Next, find Q1, the median of the lower half of the data set (not including the median). The lower half is 45, 53, 59, 60, so Q1 is the average of 53 and 59, which is (53 + 59) / 2 = 56. Then, find Q3, the median of the upper half of the data set (not including the median). The upper half is 63, 64, 70, 965, so Q3 is the average of 64 and 70, which is (64 + 70) / 2 = 67. The IQR is Q3 - Q1, which is 67 - 56 = 11.Determine Outlier Threshold: Determine the outlier threshold. The lower bound for outliers is Q1 - 1.5 * IQR, which is 56 - 1.5 * 11 = 56 - 16.5 = 39.5. The upper bound for outliers is Q3 + 1.5 * IQR, which is 67 + 1.5 * 11 = 67 + 16.5 = 83.5. Any data point below 39.5 or above 83.5 is considered an outlier.Identify Outliers: Identify the outlier(s) in the data set. Looking at the data set, the value 965 is above the upper bound of 83.5 and is therefore an outlier.

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Select the outlier in the data set. $\newline$ $45, 53, 59, 60, 61, 63, 64, 70, 965$

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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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45, 53, 59, 60, 61, 63, 64, 70, 965

Arrange Data Set: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $45, 53, 59, 60, 61, 63, 64, 70, 965$ .
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 $61$ . $\newline$ Next, find $Q_1$ , the median of the lower half of the data set (not including the median). The lower half is $45$ , $53$ , $59$ , $60$ , so $Q_1$ is the average of $53$ and $59$ , which is $61$ $0$ . $\newline$ Then, find $61$ $1$ , the median of the upper half of the data set (not including the median). The upper half is $61$ $2$ , $61$ $3$ , $61$ $4$ , $61$ $5$ , so $61$ $1$ is the average of $61$ $3$ and $61$ $4$ , which is $61$ $9$ . $\newline$ The IQR is $Q_1$ $0$ , which is $Q_1$ $1$ .
Determine Outlier Threshold: Determine the outlier threshold. $\newline$ The lower bound for outliers is $Q1 - 1.5 \times IQR$ , which is $56 - 1.5 \times 11 = 56 - 16.5 = 39.5$ . $\newline$ The upper bound for outliers is $Q3 + 1.5 \times IQR$ , which is $67 + 1.5 \times 11 = 67 + 16.5 = 83.5$ . $\newline$ Any data point below $39.5$ or above $83.5$ is considered an outlier.
Identify Outliers: Identify the outlier(s) in the data set. Looking at the data set, the value $965$ is above the upper bound of $83.5$ and is therefore an outlier.