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Select the outlier in the data set.\newline21,31,49,54,66,70,71,81,90321, 31, 49, 54, 66, 70, 71, 81, 903\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.\newline21,31,49,54,66,70,71,81,90321, 31, 49, 54, 66, 70, 71, 81, 903\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: 21,31,49,54,66,70,71,81,90321, 31, 49, 54, 66, 70, 71, 81, 903. To find the outlier, we look for a number that is significantly different from the rest of the numbers in the set.
  2. Find Outlier: By inspection, 903903 is significantly higher than all other numbers in the data set, which range from 2121 to 8181. Therefore, 903903 is the outlier.
  3. Calculate Mean with Outlier: Calculate the mean of the data set with the outlier included:\newlineMean = (21+31+49+54+66+70+71+81+903)/9(21 + 31 + 49 + 54 + 66 + 70 + 71 + 81 + 903) / 9\newlineMean = (1346)/9(1346) / 9\newlineMean ≈149.56\approx 149.56
  4. Calculate Mean without Outlier: Calculate the mean of the data set without the outlier:\newlineMean without outlier = (21+31+49+54+66+70+71+81)/8(21 + 31 + 49 + 54 + 66 + 70 + 71 + 81) / 8\newlineMean without outlier = (443)/8(443) / 8\newlineMean without outlier ≈55.375\approx 55.375
  5. Compare Means: Compare the two means to determine if the mean would increase or decrease upon the removal of the outlier:\newlineThe mean without the outlier (55.37555.375) is less than the mean with the outlier (149.56149.56).\newlineTherefore, the mean would decrease if the outlier were removed.

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