The mean of 20 numbers is 18. If 3 is added to each of the first ten numbers, find the mean of the new set of 20 numbers.

@kmr.rv: Good answer!Keep posting!

Let the 20 observations be x₁, x₂, x₃,.......,x₈, x₉, x₁₀, x₁₁, x₁₂,..........,x₂₀.

We know that,

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

∴ Sum of 20 observation = 18 × 20 

⇒  x₁+ x₂ + x₃ +.......x₈ + x₉ + x₁₀ + x₁₁ + x₁₂ +..........+x₂₀ = 360   ...(1)

when 3 is added to first 10 observation, then

Sum of new observations

= (x₁ + 3) + (x₂ + 3) + (x₃ + 3) +......+ (x₈ + 3) + (x₉ + 3) + (x₁₀ + 3) + x₁₁ + x₁₂ +..........+ x₂₀.

= (x₁ + x₂ + ...... + x₂₀) + 3 × 10

= 360 + 30         (Using (1))

= 390

Thus, the mean of new observations is 19.5.