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Select the outlier in the data set.\newline14,19,27,30,33,45,48,58,72214, 19, 27, 30, 33, 45, 48, 58, 722\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.\newline14,19,27,30,33,45,48,58,72214, 19, 27, 30, 33, 45, 48, 58, 722\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 look for a number that is significantly different from the rest of the numbers in the set. In this case, 722722 stands out as it is much larger than the other numbers.
  2. Calculate Mean with Outlier: Calculate the mean of the data set including the outlier.\newlineTo calculate the mean, add all the numbers together and divide by the number of values in the set.\newlineMean = (14+19+27+30+33+45+48+58+722)/9(14 + 19 + 27 + 30 + 33 + 45 + 48 + 58 + 722) / 9\newlineMean = (996)/9(996) / 9\newlineMean ≈110.67\approx 110.67
  3. Calculate Mean without Outlier: Calculate the mean of the data set without the outlier. Remove the outlier 722722 and calculate the new mean. New Mean = (14+19+27+30+33+45+48+58)/8(14 + 19 + 27 + 30 + 33 + 45 + 48 + 58) / 8 New Mean = (274)/8(274) / 8 New Mean ≈34.25\approx 34.25
  4. Compare Means: Compare the two means to determine if the mean would increase or decrease.\newlineThe original mean with the outlier is approximately 110.67110.67, and the new mean without the outlier is approximately 34.2534.25. Since the new mean is lower, removing the outlier would decrease the mean.

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