SOLUTION: If I have a data set and calculate the mean, then I have the same data set that has an outlier that is much greater than the rest of the data, is the mean with the outlier greater

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Question 256668: If I have a data set and calculate the mean, then I have the same data set that has an outlier that is much greater than the rest of the data, is the mean with the outlier greater or less than the mean without the outlier? Explain.
Answer by stanbon(75887) About Me  (Show Source):
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If I have a data set and calculate the mean, then I have the same data set that has an outlier that is much greater than the rest of the data, is the mean with the outlier greater or less than the mean without the outlier? Explain.
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The mean with the outlier is greater because the sum of the numbers
that include the outlier will be greater than the sum of the numbers
without the outlier. In each case you will divide by the number which
is the number of elements in the set to obtain the mean value. Since
the sum is greater with the outlier the quotient will be larger.
That quotient is the mean of the set.
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Cheers,
Stan H.