A sample of 13 college professors has a mean age of 30 years and a standard deviation of 5 years. Suppose that the sample is enlarged to 15 college professors, by including two additional professors that are each 30 years old. Will the standard deviation increase, decrease, or stay the same, and why?
The new standard deviation will be smaller than the original one because the two new professors' ages don't deviate from the mean, but they add two more observations to the data set, bringing down the average deviation from the mean. The new standard deviation actually is s = 4.643.
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