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Select the outlier in the data set.\newline68,78,80,83,85,89,91,95,13868, 78, 80, 83, 85, 89, 91, 95, 138\newlineIf the outlier were removed from the data set, would the mean increase or decrease?\newlineChoices:\newline(A)increase\newline(B)decrease

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Q. Select the outlier in the data set.\newline68,78,80,83,85,89,91,95,13868, 78, 80, 83, 85, 89, 91, 95, 138\newlineIf the outlier were removed from the data set, would the mean increase or decrease?\newlineChoices:\newline(A)increase\newline(B)decrease
  1. Identify Outlier: Identify the outlier in the data set.\newlineTo find the outlier, we can look for a number that is significantly different from the rest of the numbers in the set. In this case, 138138 stands out as it is much higher than the other values.
  2. Calculate Mean with Outlier: Calculate the mean of the data set including the outlier.\newlineTo find the mean, add all the numbers together and then divide by the number of values.\newlineMean = (68+78+80+83+85+89+91+95+138)/9(68 + 78 + 80 + 83 + 85 + 89 + 91 + 95 + 138) / 9\newlineMean = 807/9807 / 9\newlineMean 89.67\approx 89.67
  3. Calculate Mean without Outlier: Calculate the mean of the data set without the outlier. Remove the outlier 138138 and then calculate the new mean. New Mean = (68+78+80+83+85+89+91+95)/8(68 + 78 + 80 + 83 + 85 + 89 + 91 + 95) / 8 New Mean = 669/8669 / 8 New Mean 83.625\approx 83.625
  4. Compare Means: Compare the two means to determine if the mean would increase or decrease upon removal of the outlier. The original mean with the outlier was approximately 89.6789.67, and the new mean without the outlier is approximately 83.62583.625. Since the new mean is lower, the mean would decrease if the outlier were removed.

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