Question

Solve the following problems.a. After 6 points have been added to every score ina sample, the mean is found to be M=70 and thestandard deviation is s= 13. What were the valuesfor the mean and standard deviation for the originalsample?b. After every score in a sample is multiplied by 3, themean is found to be M=48 and the standard devia-tion is s=18. What were the values for the meanand standard deviation for the original sample?

Answer 1

Original mean = 64

standand deviation = 13

Explanations:

Let the value of of the originalmean be X. If after 6 points have been added to every score in a sample, the mean is found to be M = 70, then;

X + 6 = 70

Subtract 6 from both sides

X + 6 - 6 = 70 - 6

X = 70 - 6

X = 64

Hence the mean of the original sample will be 64.

The standard deviation of the data will remain unchanged since the distance from the mean will remain the same no matter the change in mean. Therefore the standard deviation of the sample will be 13.