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Select the outlier in the data set.\newline11,16,26,31,32,36,46,58111, 16, 26, 31, 32, 36, 46, 581\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.\newline11,16,26,31,32,36,46,58111, 16, 26, 31, 32, 36, 46, 581\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: 11,16,26,31,32,36,46,58111, 16, 26, 31, 32, 36, 46, 581.\newlineAn outlier is a data point that is significantly different from the rest of the data. We can visually inspect the data set and see that 581581 is much larger than all other numbers, which are relatively close to each other.
  2. Calculate Mean with Outlier: Calculate the mean of the data set with the outlier.\newlineMean = (11+16+26+31+32+36+46+581)/8(11 + 16 + 26 + 31 + 32 + 36 + 46 + 581) / 8\newlineMean = (779)/8(779) / 8\newlineMean = 97.37597.375
  3. Calculate Mean without Outlier: Calculate the mean of the data set without the outlier.\newlineMean without outlier = (11+16+26+31+32+36+46)/7(11 + 16 + 26 + 31 + 32 + 36 + 46) / 7\newlineMean without outlier = (198)/7(198) / 7\newlineMean without outlier = 28.285728.2857...
  4. Compare Means: Compare the means to determine if the mean would increase or decrease upon removal of the outlier. The mean with the outlier is 97.37597.375, and the mean without the outlier is approximately 28.2928.29. Removing the outlier significantly decreases the mean.

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