Question : The average of 25 results is 20. The average of the first 12 results is 15 and that of the last 12 results is 18. Then the 13th result is:
Option 1: 100
Option 2: 101
Option 3: 104
Option 4: 103
Correct Answer: 104
Solution :
Use: Average = $\frac{\text{Sum of observations}}{\text{Number of observations}}$
An average of 25 results = 20
⇒ Sum of 25 results = 20 × 25 = 500
Average of first 12 results = 15
⇒ Sum of first 12 results = 15 × 12 = 180
The average of the last 12 results = 18
⇒ Sum of last 12 results = 18 × 12 = 216
13th result = sum of 25 results – (sum of first 12 results + sum of last 12 results)
= 500 – (180 + 216)
= 104
Hence, the correct answer is 104.
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