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Select the outlier in the data set.\newline3,70,74,77,78,79,81,85,953, 70, 74, 77, 78, 79, 81, 85, 95\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.\newline3,70,74,77,78,79,81,85,953, 70, 74, 77, 78, 79, 81, 85, 95\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.\newlineThe data set is: 3,70,74,77,78,79,81,85,953, 70, 74, 77, 78, 79, 81, 85, 95\newlineAn outlier is a data point that is significantly different from the rest of the data. We can often spot an outlier by looking for a number that is much smaller or larger than the rest.\newlineIn this case, the number 33 is much smaller than all other numbers in the set, so it is the outlier.
  2. Calculate Mean with Outlier: Calculate the mean of the data set with the outlier included.\newlineTo find the mean, add all the numbers together and divide by the number of data points.\newlineMean = (3+70+74+77+78+79+81+85+95)/9(3 + 70 + 74 + 77 + 78 + 79 + 81 + 85 + 95) / 9\newlineMean = 632/9632 / 9\newlineMean ≈70.22\approx 70.22
  3. Calculate Mean without Outlier: Calculate the mean of the data set without the outlier.\newlineRemove the outlier 33 and calculate the new mean.\newlineNew Mean = (70+74+77+78+79+81+85+95)/8(70 + 74 + 77 + 78 + 79 + 81 + 85 + 95) / 8\newlineNew Mean = 629/8629 / 8\newlineNew Mean ≈78.625\approx 78.625
  4. Compare Mean Changes: Compare the two means to determine if the mean would increase or decrease upon the removal of the outlier. The original mean with the outlier was approximately 70.2270.22, and the new mean without the outlier is approximately 78.62578.625. Since the new mean is higher than the original mean, the mean would increase if the outlier were removed.

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