Question : 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 $10^{\text {th}}$ number is excluded from the given numbers, then what is the average of the remaining numbers? (Your answer should be nearest to an integer.)
Option 1: 21
Option 2: 23
Option 3: 22
Option 4: 20
Correct Answer: 22
Solution : An average of 19 numbers = 22.8 The sum of the 19 numbers = 22.8 × 19 = 433.2 Average of first 10 numbers = 18.4 Sum of first 10 numbers = 18.4 × 10 = 184 Average of last 10 numbers = 28.6 Sum of last 10 numbers = 28.6 × 10 = 286 10th number = 286 + 184 – 433.2 = 36.8 Sum of 18 numbers = 433.2 – 36.8 = 396.4 An average of 18 number = $\frac{\text{sum of 18 numbers}}{18}$ = $\frac{396.4}{18}$ = 22 Hence, the correct answer is 22.
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