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Select the outlier in the data set.\newline37,47,49,62,70,71,79,91,41037, 47, 49, 62, 70, 71, 79, 91, 410\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.\newline37,47,49,62,70,71,79,91,41037, 47, 49, 62, 70, 71, 79, 91, 410\newlineIf the outlier were removed from the data set, would the mean increase or decrease?\newlineChoices:\newline(A)increase\newline(B)decrease
  1. Identify the Outlier: Identify the outlier in the given data set.\newlineThe data set is: 37,47,49,62,70,71,79,91,41037, 47, 49, 62, 70, 71, 79, 91, 410\newlineAn outlier is a value that is significantly higher or lower than the rest of the data. In this case, 410410 is much higher than all other values, 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 values.\newlineMean = (37+47+49+62+70+71+79+91+410)/9(37 + 47 + 49 + 62 + 70 + 71 + 79 + 91 + 410) / 9\newlineMean = (916)/9(916) / 9\newlineMean ≈101.78\approx 101.78
  3. Calculate Mean without Outlier: Calculate the mean of the data set without the outlier.\newlineRemove the outlier 410410 and calculate the new mean.\newlineNew Mean = (37+47+49+62+70+71+79+91)/8(37 + 47 + 49 + 62 + 70 + 71 + 79 + 91) / 8\newlineNew Mean = (506)/8(506) / 8\newlineNew Mean ≈63.25\approx 63.25
  4. Compare Means: Compare the means to determine if the mean would increase or decrease with the removal of the outlier. The original mean with the outlier was approximately 101.78101.78, and the new mean without the outlier is approximately 63.2563.25. Since the new mean is lower, the mean would decrease if the outlier were removed.

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