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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Question : The average of twenty-five numbers is 54. The average of the first 13 numbers and that of the last 13 numbers is 52.8 and 62.2, respectively. If the 13th number is excluded, then what is the average of the remaining numbers (corrected to one decimal place)?
Question : The average of 8 numbers is 18. If one of the numbers is excluded, the average becomes 20. Find the excluded number.
Question : The average of 25 numbers is 64. The averages of the first 13 numbers and that of the last 13 numbers are 62.8 and 72.2, respectively. If the $12^{\text {th }}$ number is 61, and if the $12^{\text {th }}$ and $13^{\text {th }}$ numbers are excluded, then what is the average of
Question : The average of five positive numbers is 56. If the first number is three-fourths of the sum of the last four numbers, then the average of the last four numbers is:
Question : The average of the first three numbers is double the fourth number. If the average of all the four numbers is 12. Find the 4th number.
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