To increase the mean of 4 numbers by 2. by how much would the sum of the 4 numbers have to increase?

So mean also translates to average so

the mean of 4 numbers is aprox

x=average

(x+x+x+x) / 4=average

to increase x by 2 you add 2

x+2=average

(x+2+x+2+x+2+x+2) = 4 = (4x+8) / 4=x+2

you would have to increase the sum/total by 8 to make the numbers' averages' go up by 2