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Select the outlier in the data set.\newline41,51,53,54,56,57,58,60,94541, 51, 53, 54, 56, 57, 58, 60, 945\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.\newline41,51,53,54,56,57,58,60,94541, 51, 53, 54, 56, 57, 58, 60, 945\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: 41,51,53,54,56,57,58,60,94541, 51, 53, 54, 56, 57, 58, 60, 945.\newlineAn outlier is a value that is significantly higher or lower than the rest of the data. By inspection, 945945 is much higher than all other values in the data set.
  2. Calculate Mean with Outlier: Calculate the mean of the data set including the outlier.\newlineTo find the mean, sum all the values and divide by the number of values.\newlineMean = (41+51+53+54+56+57+58+60+945)/9(41 + 51 + 53 + 54 + 56 + 57 + 58 + 60 + 945) / 9\newlineMean = (1425)/9(1425) / 9\newlineMean = 158.33158.33 (rounded to two decimal places)
  3. Calculate Mean without Outlier: Calculate the mean of the data set without the outlier.\newlineRemove the outlier 945945 and calculate the new mean.\newlineNew Mean = (41+51+53+54+56+57+58+60)/8(41 + 51 + 53 + 54 + 56 + 57 + 58 + 60) / 8\newlineNew Mean = (430)/8(430) / 8\newlineNew Mean = 53.7553.75
  4. Compare Means: Compare the means to determine if the mean would increase or decrease upon removal of the outlier. The original mean with the outlier was 158.33158.33, and the new mean without the outlier is 53.7553.75. Since the new mean is lower than the original mean, removing the outlier would decrease the mean.

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