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Select the outlier in the data set.\newline3,81,87,89,90,92,94,963, 81, 87, 89, 90, 92, 94, 96\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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Identify an outlier and describe the effect of removing itright chevron icon

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Q. Select the outlier in the data set.\newline3,81,87,89,90,92,94,963, 81, 87, 89, 90, 92, 94, 96\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: 3,81,87,89,90,92,94,963, 81, 87, 89, 90, 92, 94, 96. An outlier is a data point that is significantly different from the rest of the data. We can visually inspect the data set and see that 33 is much lower than all other numbers, which are all above 8080.
  2. Confirm Outlier: To confirm that 33 is an outlier, we can calculate the mean and standard deviation of the data set and see if 33 falls far from the mean compared to the standard deviation. However, since the question does not require this and the difference is quite apparent, we can proceed with the understanding that 33 is the outlier.
  3. Remove Outlier: Remove the outlier 33 from the data set and observe the remaining numbers: 8181, 8787, 8989, 9090, 9292, 9494, 9696.
  4. Calculate Mean with Outlier: Calculate the mean of the original data set including the outlier:\newlineMean = (3+81+87+89+90+92+94+96)/8(3 + 81 + 87 + 89 + 90 + 92 + 94 + 96) / 8\newlineMean = (632)/8(632) / 8\newlineMean = 7979
  5. Calculate Mean without Outlier: Calculate the mean of the data set without the outlier:\newlineMean = (81+87+89+90+92+94+96)/7(81 + 87 + 89 + 90 + 92 + 94 + 96) / 7\newlineMean = (629)/7(629) / 7\newlineMean = 89.85789.857 (approximately)
  6. Compare Means: Compare the two means:\newlineThe original mean with the outlier is 7979.\newlineThe new mean without the outlier is approximately 89.85789.857.\newlineSince the new mean without the outlier is higher than the original mean, removing the outlier would cause the mean to increase.

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