Question

After 6 points have been added to every score in a sample, the mean is found to be M = 70 and the standard deviation is s = 13. What were the values for the mean and standard deviation for the original sample?

Answer 1

mean of original sample=64

S.D of original sample=13

Explanation:

The given information indicates that after 6 units added the mean and standard deviation are 70 and 13. So,

mean=E(X+6)=70

E(X+6)=70

E(x)+6=70

E(x)=70-6

E(x)=64

Standard deviation can be computed by taking square root of variance.

Variance=V(X+6)=13²

V(X+6)=169

V(x)=169

S.D(x)=13.

Answer 2

Answer: original mean = 64

Original standard deviation = 13

Explanation:

M = 70

X = original mean

After adding 6 to each score;

X + 6 = 70

X = 70 - 6

X = 64

Standard deviation will remain unchanged because, standard deviation refers to the distance from the mean of a distribution.

However, since the 6 point was added to every score in the sample, the distance from the mean will remain the same even though the mean value has changed.

Therefore, original standard deviation is 13.