Average Interview Questions & Answers

Average

30 Questions

Practice Problems

30 Questions

Average = Sum of quantities / Number of quantities
Sum of quantities = Average × Number of quantities
Number of quantities = Sum of quantities / Average
Combined average of two groups = (n1x + n2y) / (n1 + n2)
Average of remaining group (after removing n2 quantities) = (n1x − n2y) / (n1 − n2)
If average of x1, x2,...,xn is x: average of (x1+a,...,xn+a) = x + a
Average of (x1−a,...,xn−a) = x − a
Average of (a·x1,...,a·xn) = a·x (a ≠ 0)
Average of (x1/a,...,xn/a) = x̄/a (a ≠ 0)
If a quantity p is replaced by q, average changes x → y: q = p + n(y − x)
Value of removed quantity (average x → y, n quantities originally) = n(x − y) + y
Value of added quantity (average x → y, n quantities finally) = n(y − x) + y

Average of first n natural numbers = (n + 1) / 2
Average of squares of natural numbers till n = (n + 1)(2n + 1) / 6
Average of cubes of natural numbers till n = n(n + 1)² / 4
Average of odd numbers from 1 to n = (last odd number + 1) / 2
Average of even numbers from 1 to n = (last even number + 2) / 2
If n is odd: average of n consecutive/even/odd numbers = middle number
If n is even: average of n consecutive/even/odd numbers = average of middle two numbers
Average of first n consecutive even numbers = (n + 1)
Average of first n consecutive odd numbers = n
Average of squares of first n consecutive even numbers = 2(n + 1)(2n + 1) / 3
Average of squares of consecutive even numbers till n = (n + 1)(n + 2) / 3
Average of squares of consecutive odd numbers till n = n(n + 2) / 3
If average of n consecutive numbers is m, difference between smallest and largest number = 2(n − 1)

G.M. of x1, x2,...,xn = (x1 × x2 × ... × xn)^(1/n)
H.M. of x1, x2,...,xn = 1 / [(1/n)(1/x1 + 1/x2 + ... + 1/xn)]
H.M. of two numbers x, y = 2xy / (x + y)
Equal distance at speeds x and y: Average speed = 2xy / (x + y)
Equal distances at speeds x, y, z: Average speed = 3xyz / (xy + yz + zx)
Distances A, B, C at speeds x, y, z: Average speed = (A + B + C) / (A/x + B/y + C/z)
Parts A, B, C of distance at speeds x, y, z: Average speed = 1 / (A/x + B/y + C/z)