Question

A population has a mean of 50 and a standard deviation of 4. How many standard deviations above the mean is a data value of 60?

Answer 1

One way of approaching the solution of this problem is to use the "z-score" formula.  The z-score tells us how many s. d. a given point is above or below the given mean.

The formula for z score is as follows:

        x-mean
z = --------------
           s. d.

Thus, with mean =50 and std. dev. = 4, we get 


        x-mean                    60-50
z = --------------        z = -------------- = 10/4 = 2.5
           s. d.                          4
   
         Thus, 60 is 2.5 std. dev. above the mean, 50.