### Average

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__Average__

Average

An average also known as the arithmetic mean is the sum of the given observations divided by the number of observations.

Number of observations

Sum of given observations

* If the average of 'm' quantities is 'x' and the average age of 'n' other quantities is 'y' then the average of all of them put together is =

m + n

mx + ny

* If the average age of 'm' quantities is 'x' and the average age of 'n' quantities out of them (m quantities) is 'y' then the average of the rest of the quantities is =

m - n

mx - ny

Average Speed

* If a car or a train travels D distance in T time then the average speed of the car or the train is S.

Average Speed =

Time T

Distance D

* If a car travels from point A to point B at a speed of X kph (kilometer per hour) and travels from point B to point A at a speed of Y kph. Then average speed of the car during the whole journey is

Average Speed =

(X+Y)

2XY

Important Points

* Average of given observations is always greater than the least number and smaller than the greatest number.

For example, if the numbers are 10, 20 and 30 then the average is 20 which are greater than 10 and smaller than 30.

* If all the observations are equal then the average is equal.

* While calculating the average we take into consideration all the observations even if it is zero.

For example, if the observations are 10, 20 and 0 the average of the 3 numbers is 10.

* If all the observations are increased by X then the average is also increased by X.

* If all the observations are decreased by X then the average is also decreased by X.

* If all the observations are divided by X then the average is also divided by X.

* If all the observations are multiplied by X then the average is also divided by X.

For example, if the numbers are 10, 20 and 30 then the average is 20 which are greater than 10 and smaller than 30.

* If all the observations are equal then the average is equal.

* While calculating the average we take into consideration all the observations even if it is zero.

For example, if the observations are 10, 20 and 0 the average of the 3 numbers is 10.

* If all the observations are increased by X then the average is also increased by X.

* If all the observations are decreased by X then the average is also decreased by X.

* If all the observations are divided by X then the average is also divided by X.

* If all the observations are multiplied by X then the average is also divided by X.