Question

A random variable X has a mean of 10 and a standard deviation of 3. If 2 is added to each value of X, what will the new mean and standard deviation be?

Answer 1

New mean will be 12

And no change in standard deviation

Explanation:

We know the relationship between the two mean and standard deviation

`\sigma=\frac{√(x-x_i)}^2{n}`

`\sigma=\text{standard deviation},x=mean,n=\text{number of observations}`

If we add 2 to each value of x that means the mean will become n will become 2n and since we are adding 2 to each value

The new mean will become 12

And there will be no change in the standard deviation because of equal change in the each data.