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Select the outlier in the data set.\newline78,86,88,89,90,91,92,94,85978, 86, 88, 89, 90, 91, 92, 94, 859\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.\newline78,86,88,89,90,91,92,94,85978, 86, 88, 89, 90, 91, 92, 94, 859\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: 78,86,88,89,90,91,92,94,85978, 86, 88, 89, 90, 91, 92, 94, 859. An outlier is a data point that is significantly different from the rest of the data. In this case, 859859 is much larger than all other numbers, which are all below 100100.
  2. Remove Outlier: Remove the outlier 859859 from the data set and observe the remaining data: 7878, 8686, 8888, 8989, 9090, 9191, 9292, 9494.
  3. Calculate Mean Original: Calculate the mean of the original data set including the outlier:\newlineMean = (78+86+88+89+90+91+92+94+859)/9(78 + 86 + 88 + 89 + 90 + 91 + 92 + 94 + 859) / 9\newlineMean = (1567+859)/9(1567 + 859) / 9\newlineMean = 2426/92426 / 9\newlineMean ≈269.56\approx 269.56
  4. Calculate Mean Without Outlier: Calculate the mean of the data set without the outlier:\newlineMean = 78+86+88+89+90+91+92+948\frac{78 + 86 + 88 + 89 + 90 + 91 + 92 + 94}{8}\newlineMean = 7088\frac{708}{8}\newlineMean = 88.588.5
  5. Compare Means: Compare the two means to determine if the mean would increase or decrease upon removal of the outlier:\newlineThe original mean with the outlier is approximately 269.56269.56.\newlineThe mean without the outlier is 88.588.5.\newlineRemoving the outlier significantly decreases the mean.

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