1. Average → The average of N numbers is their sum divided by N, that is
2. Weighted average → The concept of weighted average is used mostly when different sets of numbers is given.
As 3 section of a class, having strength of a, b and c have their average marks x, y and z.
So average marks of whole class =
The coined term is called weighted average.
Note → The average of two sets of numbers is closer to the set with more number.
3. Average speed → Suppose a man covers a distance with x km/hr and equal distance with y km/hr, then average speed during the whole journey is =
And if his total distance is divided in 3 parts each covering with x, y and z km/hr then average speed =
Some tricks for average →
1) If some given number have their average and.
(a) If each number is increased by a, then new average = old average + a
(b) If each number is decreased by a, then new average = old average – a
(c) If each number is multiplied by a, then new average = a × old average
(d) If each number is divided by a, then new average = old average / a
2) If average of n1 numbers is x1, and of n2 numbers is x2 then average of all numbers =
3) If average of 'm' numbers is 'x' and out of 'n' numbers have their average 'y', then average of remaining numbers =
4. Some tricks for natural numbers →
(a) average of first 'n' natural numbers =
(b) average of first 'n' even numbers which are natural = n + 1
(c) average of first 'n' natural odd numbers = n
(d) average of 'n' consecutive numbers =
(e) average of square of first 'n' natural numbers =
(f) average of cubes of first 'n' natural numbers =