**Average**is just a

**mean value**of all the given observation or i can say it is an arithmetic mean of observations.

Average = (Sum of all observations)/ (Number of observations)

**Example1:**Find an average of following observations:

`3, 4, 8, 12, 2, 5, 1`

**Solution:**Average = (Sum of all observations)/ (Number of observations)

Average = `(3+ 4+ 8+ 12 +2+ 5+ 1)/7` = `35/7` = `5`

So, Average = `5`

***But, remember that this formula does not directly applies on average speed. Discussed in special cases***

## Properties of Average

**i)**Average lies between maximum and minimum observation.

**ii)**If value of each observation is multiplied by some value 'N', then average will also be multiplied by the same value i.e.N.

**For example:**Assume the previous set of observations. If `2` is multiplied with all observations, then new observations will be as follows:

**iii)**If value of each observation is increased or decreased by some number, then average will also be increased or decreased by the same number.

**For example:**Continuing with the same example. If `2` is added to all observations, then new observations will be as follows:

**iv)**Similarly, if each observation is divided by some number, then average will also be divided by same number.

**For example:**If `2` is divided from all observations, then new observations will be as follows:

**Example2:**Find an average of first 20 natural numbers.

**Solution:**Average =`(Sum of first 20 natural numbers)/ (20)`

**Example3:**Out of three numbers, second number is twice the first and is also thrice the third. If average of these numbers if `44`, then find the largest number.

**Solution:**Let `x` be the third number

**Example4:**Average of four consecutive even numbers is `27`. Find the numbers.

**Solution:**Let `x`, `x+2`, `x+4` and `x+6` be the four consecutive even numbers.

## Special Case

### To find average speed

**average speed**during the whole distance covered will be

**`(2xy)/ (x+y)`**

**Example5**: A bike covers certain distance from A to B at `50` km/hr speed and returns back to A at `56` km/hr. Find the average speed of the bike during the whole journey.

**Solution:**Average speed = `((2xy)/(x+y))` = `(2 times (50) times (56))/ (50 + 56)`

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