If the mean observations x₁, x₂, ..., x_n is , then the means of x₁ + a, x₂ + a, ..., x_n + a is

Given, mean is ,

and x₁, x₂, …, x_n are n observations.

And we know

The mean or average of observations, is the sum of the values of all the observations divided by the total number of observations.

i.e.

…[1]

And we have another series

x₁ + a, x₂ + a, …,x_n + a

Let the new mean be x

Now, From [1] we have