In a certain set of numbers, 12.5 is 1.5 units of standard deviation above the mean, and 8.9 is 0.5 units of standard deviation below the mean. what is the mean of the set?

Standard deviation is a statistical tool that is used to measure the spread or variation of a certain set of data. It is the square root is the variance. It determines the difference of each data relative to the mean. To calculate the mean, we do as follows:

12.5 is 1.5 units of standard deviation
So the value for the upper standard deviation would be:
12.5 - 1.5 = 11

8.9 is 0.5 units of standard deviation
So the value for the lower standard deviation would be:
8.9 + 0.5 =  9.4

So, the range of the standard deviation would be about 11 - 9.4 = 1.6 units. The mean would be located at the center of this range which is 0.8 from each of the values. Therefore, the mean would be 11-0.8 = 10.2.