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Select the outlier in the data set.\newline2,70,78,88,89,90,91,97,992, 70, 78, 88, 89, 90, 91, 97, 99\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.\newline2,70,78,88,89,90,91,97,992, 70, 78, 88, 89, 90, 91, 97, 99\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 given data set: 2,70,78,88,89,90,91,97,992, 70, 78, 88, 89, 90, 91, 97, 99. To find the outlier, we can look for a number that is significantly different from the rest of the data. In this case, 22 stands out as it is much lower than all other numbers.
  2. Calculate Mean with Outlier: Calculate the mean of the data set with the outlier included.\newlineMean = (2+70+78+88+89+90+91+97+99)/9(2 + 70 + 78 + 88 + 89 + 90 + 91 + 97 + 99) / 9\newlineMean = (704)/9(704) / 9\newlineMean ≈78.22\approx 78.22 (rounded to two decimal places)
  3. Calculate Mean without Outlier: Calculate the mean of the data set without the outlier.\newlineMean without outlier = (70+78+88+89+90+91+97+99)/8(70 + 78 + 88 + 89 + 90 + 91 + 97 + 99) / 8\newlineMean without outlier = (702)/8(702) / 8\newlineMean without outlier ≈87.75\approx 87.75 (rounded to two decimal places)
  4. Compare Mean Changes: Compare the two means to determine if the mean would increase or decrease upon the removal of the outlier. The mean without the outlier (87.7587.75) is greater than the mean with the outlier (78.2278.22). Therefore, removing the outlier would increase the mean.

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