Question

The mean of 16 numbers is 8. If 4 is added to each number, what will be the new mean​

Answer 1

Let the numbers be x1, x2, x3, ...., x16

Mean = (x1 + x2 + x3 + ....+ x16)/16

8*16 = x1 + x2 + x3 + ....+ x16

x1 + x2 + x3 + ....+ x16 = 144 ——> 1

If 4 is added to each number, then sum of all 16 numbers can be written as:

(x1 + 4) + (x2 + 4) + (x3 + 4) + ....+ (x16 + 4)

= (x1 + x2 + x3 + ....+ x16) + (4 + 4 + ....16 times)

= (x1 + x2 + x3 + ....+ x16) + 16*4

= (x1 + x2 + x3 + ....+ x16) + 64

= 144 + 64 [From equation 1]

= 208

Mean = 208/16 = 13 ——> Answer