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Select the outlier in the data set.\newline42,52,60,64,65,68,72,78,67842, 52, 60, 64, 65, 68, 72, 78, 678\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.\newline42,52,60,64,65,68,72,78,67842, 52, 60, 64, 65, 68, 72, 78, 678\newlineIf the outlier were removed from the data set, would the mean increase or decrease?\newlineChoices:\newline(A)increase\newline(B)decrease
  1. Identify the outlier: Step 11: Identify the outlier in the data set.\newlineData set: 42,52,60,64,65,68,72,78,67842, 52, 60, 64, 65, 68, 72, 78, 678\newlineTo find the outlier, look for a number that is significantly different from the rest. Here, 678678 stands out as it is much higher than the other numbers.
  2. Calculate mean with outlier: Step 22: Calculate the mean of the data set including the outlier.\newlineMean = 42+52+60+64+65+68+72+78+6789\frac{42 + 52 + 60 + 64 + 65 + 68 + 72 + 78 + 678}{9}\newlineMean = 12299\frac{1229}{9}\newlineMean = 136136.5656
  3. Calculate mean without outlier: Step 33: Calculate the mean of the data set without the outlier.\newlineMean without outlier = (42+52+60+64+65+68+72+78)/8(42 + 52 + 60 + 64 + 65 + 68 + 72 + 78) / 8\newlineMean without outlier = 501/8501 / 8\newlineMean without outlier = 62.62562.625
  4. Compare mean with and without outlier: Step 44: Compare the two means to determine if the mean increases or decreases when the outlier is removed.\newlineMean with outlier = 136.56136.56\newlineMean without outlier = 62.62562.625\newlineSince the mean without the outlier is less than the mean with the outlier, removing the outlier decreases the mean.

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