Question
Download Solution PDFThe average of 28 numbers is 77. The average of first 14 numbers is 74 and the average of last 15 numbers is 84. If the 14th number is excluded, then what is the average of remaining numbers? (correct to one decimal places)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Average of 28 numbers = 77
Average of first 14 numbers = 74
Average of last 15 numbers = 84
Formula used:
Average = Sum of observations ÷ No of observations
Calculation:
Value of 14th number = (Sum of first 14 numbers + Sum of last 15 numbers) - Sum of 28 numbers
⇒ 14th Number = (14 × 74 + 15 × 84 - 28 × 77)
⇒ 1036 + 1260 - 2156 = 140
Average of remaining 27 numbers = (Sum of 28 numbers - 14th number) ÷ 27
⇒ (2156 - 140) ÷ 27 = 2016 ÷ 27
⇒ 74.66 or 74.7
∴ The required result = 74.7
Alternate Method
Average of 28 numbers = 77
Average of first 14 numbers = 74
Average of last 15 numbers = 84
Deviation on first 14 numbers = 74 - 77 = - 3 × 14 = - 42
Deviation on last 15 numbers = 84 - 77 = 7 × 15 = 105
14th number = 77 - 42 + 105 = 140
∴ Average of remaining 27 numbers = (28 × 77 - 140) ÷ 27 = 74.7
Last updated on Jul 19, 2025
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