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Select the outlier in the data set.\newline1,70,80,87,89,94,95,97,991, 70, 80, 87, 89, 94, 95, 97, 99\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.\newline1,70,80,87,89,94,95,97,991, 70, 80, 87, 89, 94, 95, 97, 99\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: 1,70,80,87,89,94,95,97,991, 70, 80, 87, 89, 94, 95, 97, 99. An outlier is a data point that is significantly different from the rest of the data. We can often spot an outlier by looking for a number that is much smaller or larger than the rest.
  2. Spot Outlier: Looking at the data set, 11 is much smaller than all other numbers, which are all between 7070 and 9999. Therefore, 11 is the outlier in this data set.
  3. Calculate Mean with Outlier: Calculate the mean of the data set with the outlier included:\newlineMean = (1+70+80+87+89+94+95+97+99)/9(1 + 70 + 80 + 87 + 89 + 94 + 95 + 97 + 99) / 9\newlineMean = 712/9712 / 9\newlineMean ≈79.11\approx 79.11
  4. Calculate Mean without Outlier: Calculate the mean of the data set without the outlier:\newlineMean = 70+80+87+89+94+95+97+998\frac{70 + 80 + 87 + 89 + 94 + 95 + 97 + 99}{8}\newlineMean = 7118\frac{711}{8}\newlineMean ≈88.88\approx 88.88
  5. Compare Mean: Compare the two means to determine if the mean would increase or decrease upon the removal of the outlier: With the outlier, the mean is approximately 79.1179.11. Without the outlier, the mean is approximately 88.8888.88. Removing the outlier increases the mean.

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