Question

Suppose that the distribution of a set of scores has a mean of 47 and a standard deviation of 14. If 4 is added to each score, what will be the mean and the standard deviation of the distribution of new scores?

Answer 1

Mean of new data = 51

Standard deviation of new data = 14

Explanation:

We are given the following in the question:

Mean of data = 47

Standard deviation = 14.

Then, 4 is added to every observation of the data.

a) Mean of new data

When a constant value is added to every observation, the mean of the data increases by the same amount

Mean of new score =

`\mu' = \mu+4 = 47+4=51`

b) Standard deviation of new data

When a constant value is added to every observation, the standard deviation remains the same.

Standard deviation of new score =

`\sigma' = \sigma = 14`