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Select the outlier in the data set.\newline74,82,84,85,88,89,95,85374, 82, 84, 85, 88, 89, 95, 853\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.\newline74,82,84,85,88,89,95,85374, 82, 84, 85, 88, 89, 95, 853\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: 74,82,84,85,88,89,95,85374, 82, 84, 85, 88, 89, 95, 853.\newlineAn outlier is a data point that is significantly different from the other data points in a set. In this case, 853853 is much larger than all the other numbers, which are relatively close to each other.
  2. Remove Outlier and Calculate Mean: Remove the outlier and calculate the mean of the remaining data set.\newlineFirst, we calculate the mean with the outlier included:\newlineMean with outlier = (74+82+84+85+88+89+95+853)/8(74 + 82 + 84 + 85 + 88 + 89 + 95 + 853) / 8\newlineMean with outlier = 1350/81350 / 8\newlineMean with outlier = 168.75168.75
  3. Calculate Mean Without Outlier: Now, calculate the mean without the outlier:\newlineMean without outlier = (74+82+84+85+88+89+95)/7(74 + 82 + 84 + 85 + 88 + 89 + 95) / 7\newlineMean without outlier = 597/7597 / 7\newlineMean without outlier = 85.2857…85.2857\ldots
  4. Compare Means: Compare the two means to determine if the mean would increase or decrease with the removal of the outlier. The mean with the outlier is 168.75168.75, and the mean without the outlier is approximately 85.2985.29. Since the mean without the outlier is lower, removing the outlier would decrease the mean.

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