### Average

Coming Soon

1. Average → The average of N numbers is their sum divided by N, that is

Average =

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 =

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