Question : The average of 15 numbers is 7. If the average of the first 8 numbers is 6.5 and the average of the last 8 numbers is 8.5, then the middle number is:
Option 1: 10
Option 2: 23
Option 3: 13
Option 4: 15
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Correct Answer: 15
Solution :
Given:
Average of 15 results = 7
Average of first seven = 6.5
Average of last seven = 7.5
According to the question,
Sum of all results = 15 × 7 = 105
Sum of first seven results = 8 × 6.5 = 52
Sum of last eight results = 8 × 8.5 = 68
Eighth result = Sum of first eight results + Sum of last eight results – Sum of all results
⇒ Eighth result = 52 + 68 – 105 = 15
Hence, the correct answer is 15.
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