The average of the remaining three numbers is 81.
What is the average of n numbers a₁, a₂, ..., aₙ?
The average of the numbers a₁, a₂, ..., aₙ is calculated as
Average = (a₁ + a₂ + ··· + aₙ) / n.
Given
Average of the four numbers = 85,
The largest of the four numbers is 97.
Find the sum of all the four numbers
Let the four numbers be a, b, c, and d. Then, using their given average,
(a + b + c + d) / 4 = 85
⇒ a + b + c + d = 85 × 4 = 340.
Find the sum of the numbers excluding the largest one
Let the largest number be d. So, d = 97. Then, the sum of the remaining three is
a + b + c = 340 - d = 340 - 97 = 243.
Find the average of the three numbers
Using the above definition average of the remaining three numbers is calculated as
Av(a,b,c) = (a + b + c)/3 = 243 / 3 = 81.
The required average of the remaining three numbers is 81.
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