Standard deviation ?

Question

Determine the standard deviation, if the mean is 3.0 and the coefficient of variation is 2.0%. (Enter your answer to 4 decimal places.)

Answer 1

The coefficient of variation (CV) is the ratio of the standard deviation (SD) over the mean.

CV=SD/mean.

You're given that the coefficient of variation which is 2.0%, converting to decimal gives a CV=0.020.

Then you're given that the mean is 3.0.

Plugging the values for CV=0.020 and the mean=3.0 into the CV equation gives:

CV=SD/mean

0.020=SD/3.0

Multiplying both sides of the equation by 3 to clear fractions gives:

SD=0.020(3)=0.06.

Thus, the standard deviation is 0.06.