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Select the outlier in the data set.\newline78,83,85,87,88,90,91,95,90078, 83, 85, 87, 88, 90, 91, 95, 900\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.\newline78,83,85,87,88,90,91,95,90078, 83, 85, 87, 88, 90, 91, 95, 900\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 data set.\newlineTo find the outlier, we look for a number that is significantly different from the rest of the numbers in the set. In this case, 900900 is much larger than all other values, which are all below 100100.
  2. Calculate Mean: Calculate the mean of the original data set.\newlineTo calculate the mean, add all the numbers together and divide by the count of numbers.\newlineMean = (78+83+85+87+88+90+91+95+900)/9(78 + 83 + 85 + 87 + 88 + 90 + 91 + 95 + 900) / 9\newlineMean = (1597)/9(1597) / 9\newlineMean ≈177.44\approx 177.44
  3. Remove Outlier: Remove the outlier and calculate the new mean.\newlineWithout the outlier (900900), the new sum of the data set is 1597−900=6971597 - 900 = 697.\newlineThe new mean is 697/8697 / 8 (since there are now 88 numbers).\newlineNew Mean = 697/8697 / 8\newlineNew Mean ≈87.125\approx 87.125
  4. Compare Means: Compare the original mean to the new mean to determine if it would increase or decrease.\newlineThe original mean was approximately 177.44177.44, and the new mean is approximately 87.12587.125. Removing the outlier significantly decreased the mean.

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