Question

The mean of 30 numbers is 18, what will be the new mean if each observation is increased by 2?

Answer 1

Let the 30 observations be x 1, x 2, x 3,.......,x 8, x 9, x 10, x 11, x 12,..........,x 30.

As, we know that,

Sum of n observations = Mean × Number of observation, n

∴ Sum of 30 observations = 18 × 30

⇒ x 1+ x 2 + x 3 +.......x 8 + x 9 + x 10 + x 11 + x 12 +..........+x 30 = 540 ...(i)

when each number is increased by 2, then

Sum of new observations

= (x 1 + 2) + (x 2 + 2) + (x 3 + 2) +......+ (x 8 + 2) + (x 9 + 2) + (x 10 + 2) +...........+ (x 30 + 2)

= (x 1 + x 2 + ...... + x 30) + 2 × 30

= 540+60 [Using (i)]

= 600

Therefore the mean =sum of new observations/no of observations=600/30=20