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Select the outlier in the data set.\newline83,89,91,92,93,94,95,97,84883, 89, 91, 92, 93, 94, 95, 97, 848\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.\newline83,89,91,92,93,94,95,97,84883, 89, 91, 92, 93, 94, 95, 97, 848\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.\newlineThe data set is: 83,89,91,92,93,94,95,97,84883, 89, 91, 92, 93, 94, 95, 97, 848.\newlineAn outlier is a value that is significantly higher or lower than the other values in a data set. In this case, 848848 is much higher than all the other values, which are all below 100100.
  2. Remove Outlier, Calculate Mean: Remove the outlier and calculate the mean of the remaining data set.\newlineFirst, we add up all the values except the outlier: 83+89+91+92+93+94+95+97=73483 + 89 + 91 + 92 + 93 + 94 + 95 + 97 = 734.\newlineNext, we count the number of values in the data set without the outlier, which is 88.\newlineNow, we calculate the mean by dividing the sum by the number of values: 734/8=91.75734 / 8 = 91.75.
  3. Calculate Mean with Outlier: Calculate the mean of the original data set including the outlier.\newlineFirst, we add the outlier to the previous sum: 734+848=1582734 + 848 = 1582.\newlineNext, we count the number of values in the original data set, which is 99.\newlineNow, we calculate the mean by dividing the sum by the number of values: 15829175.78\frac{1582}{9} \approx 175.78.
  4. Compare Means: Compare the two means to determine if the mean would increase or decrease upon the removal of the outlier. The mean of the original data set with the outlier is approximately 175.78175.78. The mean of the data set without the outlier is 91.7591.75. Since 91.7591.75 is less than 175.78175.78, removing the outlier will decrease the mean.

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