Question

If you have a set of scores and add 2 to every score, how will the standard deviation
change?
a. The new standard deviation and the old standard deviation will be the same
b. The new standard deviation will be twice as large as the old standard
deviation
c. The new standard deviation will be half the size (twice as small) as the old
standard deviation
d. Not enough information to answer this question

Answer 1

The correct option is,

a. The new standard deviation and the old standard deviation will be the same.

Explanation : supposed if we have 10 observations in our data set and we found that the Standerd deviation is 4. First of all we need to understand what is Standerd deviation.

The Standerd deviation is tells us how much our data is spread around the mean. Suppose if our mean is 12 then around the mean +-4 our most of the data lie.

If we add 2 to every score then we have new mean i.e 14 and our rest of the new score will be same around the mean. So again around mean +- 4 our most of the data lie.

So there is no effect on Standerd deviation.

Hope you understood.

Thank you.