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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