When you add or subtract a constant from the outcomes of a random variable, the mean will increase or decrease by that amount, and the standard deviation will stay the same.
Example: This distribution is called X.
If we add 2 to the distribution, it becomes X + 2. Now the distribution has a mean of 5, but the standard deviation is still 1:
When you multiply or divide the outcomes of a random variable by a constant, the mean and the standard deviation will also be multiplied or divided by that constant.
Let’s see what happens if we multiply each outcome by 3, and find and :