std deviation/variance?

Question

if i know that the variance of a certain amount of numbers is X.
I also know that these numbers have a mean of X
1)What would be the variance if i divide all these numbers by 5?
2)What would be the variance if i divided all these numbers by 5 and then added an extra number (say the number is 5).

Answer 1

1) X/25
2) X/25

Explanation:
1) If you divide a set of values by a constant, then both the mean and the standard deviation are divided by that constant.
Since your question is about the variance, which is the SQUARE of the standard deviation, the variance is divided by the SQUARE of the constant (5, in this case).

2) When you add a constant to a set of values, the mean is increased by the amount of that constant, but the standard deviation is unchanged. This is true because the group of values has all moved up by a constant amount, but their relation to each other is unchanged, and their variation from each other is unchanged. Since the standard deviation is unchanged, the variance (the square of the standard deviation) is also unchanged.