The average of 19 numbers is 22.8. The average of the first ten numbers is 18.4 and that of the last ten numbers is 28.6. If the $$10^{th}$$ number is excluded from the given numbers, then what is the average of the remaining numbers? (Your answer should be nearest to an integer.)

The Average of 19 numbers = 22.8

so sum of 19 numbers = $$22.8 \times 13$$ = 433.2

The average of first 10 number = 18.4 

so , sum of first 10 number = $$18.4 \times 10 $$ = 184

The Average of last 10 number = 28.6 

the sum of last 10 number = $$28.6\times 10 $$ = 286 

sum of  all number + 10th number (except 10th number) + 2time 10th number = 184 + 286 = 470

sum of all number + 10th number = 470 

$$\Rightarrow  433.2$$ + 10th number = 470 

$$10th  number = 470-433.2 = 36.8$$

sum of 18th number including 10th number = 433.2-36.8 = 396.4

the Average = $$\dfrac {396.4}{18} = 22.02222 = 22$$ Ans