Select the outlier in the data set. 1, 51, 53, 55, 58, 59, 63, 65, 75 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. 1, 51, 53, 55, 58, 59, 63, 65, 75  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: 1, 51, 53, 55, 58, 59, 63, 65, 75. An outlier is a data point that is significantly different from the rest of the data. We can use the interquartile range (IQR) method to identify outliers.Calculate Quartiles: Calculate the first quartile (Q1) and the third quartile (Q3) of the data set. To do this, we need to arrange the data in ascending order and find the median of the lower and upper halves of the data set. The data is already in ascending order: 1, 51, 53, 55, 58, 59, 63, 65, 75. The median (second quartile, Q2) is 58, which splits the data into two halves: 1, 51, 53, 55 and 59, 63, 65, 75. The median of the lower half is Q1 = (51 + 53) / 2 = 52. The median of the upper half is Q3 = (63 + 65) / 2 = 64.Calculate IQR: Calculate the interquartile range (IQR) by subtracting Q1 from Q3. IQR = Q3 - Q1 = 64 - 52 = 12.Determine Bounds: Determine the lower and upper bounds for outliers. The lower bound is Q1 - 1.5 * IQR = 52 - 1.5 * 12 = 52 - 18 = 34. The upper bound is Q3 + 1.5 * IQR = 64 + 1.5 * 12 = 64 + 18 = 82. Any data point below 34 or above 82 is considered an outlier.Identify Outliers: Identify the outlier(s) in the data set. Looking at the data set 1, 51, 53, 55, 58, 59, 63, 65, 75, the number 1 is below the lower bound of 34, so it is an outlier.Effect on Mean: Determine the effect on the mean if the outlier is removed. Removing an outlier that is lower than the mean will increase the overall mean of the data set.Calculate Means: Calculate the mean of the original data set and the mean of the data set without the outlier to confirm the effect on the mean. Original mean = (1 + 51 + 53 + 55 + 58 + 59 + 63 + 65 + 75) / 9 = 480 / 9 ≈ 53.33. Mean without the outlier = (51 + 53 + 55 + 58 + 59 + 63 + 65 + 75) / 8 = 479 / 8 ≈ 59.88. The mean without the outlier is higher than the original mean.

Select the outlier in the data set. $\newline$ $1, 51, 53, 55, 58, 59, 63, 65, 75$ $\newline$ 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.\newline1,51,53,55,58,59,63,65,751, 51, 53, 55, 58, 59, 63, 65, 751,51,53,55,58,59,63,65,75\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. $\newline$ $1, 51, 53, 55, 58, 59, 63, 65, 75$ $\newline$ If the outlier were removed from the data set, would the mean increase or decrease? $\newline$ Choices: $\newline$ (A)increase $\newline$ (B)decrease