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You work in a department with 24 other persons (25 persons total). If each of you...

You work in a department with 24 other persons (25 persons total). If each of you just received a 6% cost-of-living pay raise, what has happened to (please provide specific/precise responses to the Parts below; for example, if a summary statistic changes, note by how much as a %) a. the mean salary for the department? b. the standard deviation of salaries for the department? c. the range of salaries for the department? d. the coefficient of variation of salaries for the department?

Math   Statistics-And-Probability   
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Answer #1

(A) mean salary for the department will increase by exactly 6% because each data vaue is increased by 6%. So, the sum of all values gets increased by 150%. Therefore, the mean salary goes up by 6%

(B) Standard deviation will remain same because the difference between the mean and data values will remain the same. So, there will be no change in standard deviation.

(C) Range will remain same because the difference between the minimum and maximum values will remain the same. So, there will be no change in Range.

(D) coefficient of variation will decrease due to increase in mean value, but no change in standard deviation. To find the exact change in coefficient of variation, we need original mean and standard deviation value.

So, coefficient of variation will decrease.

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