Select the outlier in the data set. 6, 64, 66, 68, 69, 72, 74, 81 If the outlier were removed from the data set, would the mean increase or decrease? Choices: (A)increase (B)decrease

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Select the outlier in the data set. 6, 64, 66, 68, 69, 72, 74, 81  If the outlier were removed from the data set, would the mean increase or decrease?   Choices: (A)increase (B)decrease

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Identify Outlier: Identify the outlier in the given data set: 6, 64, 66, 68, 69, 72, 74, 81. To find the outlier, we can calculate the interquartile range (IQR) and then determine if any values fall more than 1.5 times the IQR above the third quartile or below the first quartile.Arrange Data Set: First, arrange the data set in ascending order, which is already done: 6, 64, 66, 68, 69, 72, 74, 81. Next, find the median (the middle value) of the data set. Since there are 8 numbers, the median will be the average of the 4th and 5th values: (68 + 69) / 2 = 137 / 2 = 68.5.Find Median: Now, find the first quartile (Q1), which is the median of the lower half of the data set (excluding the median of the entire data set if the number of data points is odd). The lower half is 6, 64, 66, 68. The median of this lower half is (64 + 66) / 2 = 130 / 2 = 65.Find Q1: Find the third quartile (Q3), which is the median of the upper half of the data set. The upper half is 69, 72, 74, 81. The median of this upper half is (72 + 74) / 2 = 146 / 2 = 73.Find Q3: Calculate the interquartile range (IQR) by subtracting Q1 from Q3: IQR = Q3 - Q1 = 73 - 65 = 8.Calculate IQR: Determine the lower bound for potential outliers by subtracting 1.5 times the IQR from Q1: Lower Bound = Q1 - 1.5 * IQR = 65 - 1.5 * 8 = 65 - 12 = 53.Lower Bound: Determine the upper bound for potential outliers by adding 1.5 times the IQR to Q3: Upper Bound = Q3 + 1.5 * IQR = 73 + 1.5 * 8 = 73 + 12 = 85.Upper Bound: Any data point below the lower bound or above the upper bound is considered an outlier. In this case, the number 6 is below the lower bound of 53, so it is an outlier.Identify Outlier: Now, to determine if the mean would increase or decrease upon the removal of the outlier, we need to compare the outlier to the current mean of the data set. First, calculate the mean of the original data set: (6 + 64 + 66 + 68 + 69 + 72 + 74 + 81) / 8 = 500 / 8 = 62.5.Calculate Mean: Since the outlier 6 is much lower than the current mean 62.5, removing it will result in a higher mean because the remaining numbers are all higher than the original mean.

Select the outlier in the data set. $\newline$ $6, 64, 66, 68, 69, 72, 74, 81$ $\newline$ If the outlier were removed from the data set, would the mean increase or decrease? $\newline$ Choices: $\newline$ (A)increase $\newline$ (B)decrease

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Select the outlier in the data set.\newline6,64,66,68,69,72,74,816, 64, 66, 68, 69, 72, 74, 816,64,66,68,69,72,74,81\newlineIf the outlier were removed from the data set, would the mean increase or decrease?\newlineChoices:\newline(A)increase\newline(B)decrease

Select the outlier in the data set. $\newline$ $6, 64, 66, 68, 69, 72, 74, 81$ $\newline$ If the outlier were removed from the data set, would the mean increase or decrease? $\newline$ Choices: $\newline$ (A)increase $\newline$ (B)decrease