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

Mean = $\dfrac{\text{Sum of observations}}{\text{No. of observations}}$

∴ Sum of observations = Mean × No. of observations
⇒ Sum of observations = 18 × 20 = 360.

Since 3 is added to first ten numbers then total sum increases by 10 × 3 = 30.

New sum = 360 + 30 = 390.

Mean = $\dfrac{\text{Sum of observations}}{\text{No. of observations}} = \dfrac{390}{20}$ = 19.5

Hence, the mean of new set of 20 numbers is 19.5