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Select the outlier in the data set.\newline72,82,88,89,92,93,95,97,55472, 82, 88, 89, 92, 93, 95, 97, 554\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.\newline72,82,88,89,92,93,95,97,55472, 82, 88, 89, 92, 93, 95, 97, 554\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: 72,82,88,89,92,93,95,97,55472, 82, 88, 89, 92, 93, 95, 97, 554\newlineAn outlier is a data point that is significantly different from the rest of the data. In this case, 554554 stands out as it is much larger than the other numbers.
  2. Remove Outlier, Calculate Mean: Remove the outlier and calculate the mean of the remaining data points.\newlineFirst, we add up all the data points except the outlier: 72+82+88+89+92+93+95+97=70872 + 82 + 88 + 89 + 92 + 93 + 95 + 97 = 708\newlineNext, we count the number of data points without the outlier: 88\newlineNow, we calculate the mean: 708/8=88.5708 / 8 = 88.5
  3. Calculate Mean with Outlier: Calculate the mean of the entire data set including the outlier.\newlineFirst, we add the outlier to the previous total: 708+554=1262708 + 554 = 1262\newlineNext, we count the total number of data points including the outlier: 99\newlineNow, we calculate the mean: 12629≈140.22\frac{1262}{9} \approx 140.22
  4. Compare Means: Compare the means to determine if the mean would increase or decrease upon the removal of the outlier. The mean without the outlier is 88.588.5, and the mean with the outlier is approximately 140.22140.22. Removing the outlier would decrease the mean.

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