Select the outlier in the data set. 6, 51, 57, 59, 60, 66, 70, 76 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, 51, 57, 59, 60, 66, 70, 76  If the outlier were removed from the data set, would the mean increase or decrease?   Choices: (A)increase (B)decrease

Bytelearn · Accepted Answer

Identify Outlier: Identify the outlier in the given data set. The data set is: 6, 51, 57, 59, 60, 66, 70, 76. 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 quartiles (Q1, Q2, Q3) of the data set. First, we need to find the median (Q2), which is the middle number when the data is in order. For our data set, the median is between 59 and 60, so Q2 = (59 + 60) / 2 = 59.5. Next, we find Q1, which is the median of the lower half of the data (not including Q2). The lower half is 6, 51, 57, 59. The median of this half is between 51 and 57, so Q1 = (51 + 57) / 2 = 54. Finally, we find Q3, which is the median of the upper half of the data (not including Q2). The upper half is 60, 66, 70, 76. The median of this half is between 66 and 70, so Q3 = (66 + 70) / 2 = 68.Calculate IQR: Calculate the interquartile range (IQR). IQR = Q3 - Q1 = 68 - 54 = 14.Determine Boundaries: Determine the outlier boundaries. The lower boundary for outliers is Q1 - 1.5 * IQR = 54 - 1.5 * 14 = 54 - 21 = 33. The upper boundary for outliers is Q3 + 1.5 * IQR = 68 + 1.5 * 14 = 68 + 21 = 89. Any data point below 33 or above 89 is considered an outlier.Identify Outlier: Identify the outlier in the data set. Looking at the data set, the number 6 is below the lower boundary of 33, so it is an outlier.Calculate Mean: Calculate the mean of the data set with and without the outlier. First, calculate the mean with the outlier: Mean with outlier = (6 + 51 + 57 + 59 + 60 + 66 + 70 + 76) / 8 = 445 / 8 = 55.625. Next, calculate the mean without the outlier: Mean without outlier = (51 + 57 + 59 + 60 + 66 + 70 + 76) / 7 = 439 / 7 = 62.714.Determine Increase/Decrease: Determine if the mean would increase or decrease upon removal of the outlier. Since the mean without the outlier (62.714) is greater than the mean with the outlier (55.625), the mean would increase if the outlier were removed.

Select the outlier in the data set. $\newline$ $6, 51, 57, 59, 60, 66, 70, 76$ $\newline$ 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.\newline6,51,57,59,60,66,70,766, 51, 57, 59, 60, 66, 70, 766,51,57,59,60,66,70,76\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. $\newline$ $6, 51, 57, 59, 60, 66, 70, 76$ $\newline$ If the outlier were removed from the data set, would the mean increase or decrease? $\newline$ Choices: $\newline$ (A)increase $\newline$ (B)decrease