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Select the outlier in the data set.\newline78,84,86,87,88,89,93,21878, 84, 86, 87, 88, 89, 93, 218\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.\newline78,84,86,87,88,89,93,21878, 84, 86, 87, 88, 89, 93, 218\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: 78,84,86,87,88,89,93,21878, 84, 86, 87, 88, 89, 93, 218. To find the outlier, we can look for a number that is significantly different from the rest of the data.
  2. Find Outlier: Looking at the data set, we can see that 218218 is much larger than all the other numbers, which are all below 100100. Therefore, 218218 is the outlier.
  3. Calculate Mean with Outlier: Now, let's calculate the mean of the data set with the outlier included.\newlineMean with outlier = 78+84+86+87+88+89+93+2188\frac{78 + 84 + 86 + 87 + 88 + 89 + 93 + 218}{8}\newlineMean with outlier = 8238\frac{823}{8}\newlineMean with outlier = 102.875102.875
  4. Calculate Mean without Outlier: Next, calculate the mean of the data set without the outlier.\newlineMean without outlier = (78+84+86+87+88+89+93)/7(78 + 84 + 86 + 87 + 88 + 89 + 93) / 7\newlineMean without outlier = 605/7605 / 7\newlineMean without outlier = 86.428686.4286
  5. Compare Means: Compare the two means to determine if the mean would increase or decrease with the removal of the outlier. Since 102.875102.875 (with outlier) is greater than 86.428686.4286 (without outlier), removing the outlier will decrease the mean.

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