**Assignment On Average**

**AVERAGE**

**Rule 1**

To find the average, when the number of quantities and their sum is given. We have the following formula

Sum of the quantities

Average = ————————————————————————

Number of quantities

**Rule 2**

Theorem: If the average of ‘m’ boys is ‘x’ and the average of ‘n’ boys is ‘b’ then the average of all of them put together

mx + ny

(= total average) is = ——————————————————

m + n

**Rule 3**

Theorem: If the average of ‘m’ boys is ‘x’ and the average of ‘n’ boys out of them (m boys) is ‘y’ then the average age of rest of the boys is

mx - ny

————————————

m - n

**Rule 4**

Theorem: If the average of ‘n’ quantities is equal to ‘x’. When a quantity is removed the average becomes ‘y’. Then the value of the removed quantity is [n (x – y) + y].

**Rule 5**

Theorem: If the average of ‘n’ number is ‘m’ and if ‘x’ is added to or subtracted from each given number, the average of ‘n’ numbers becomes (m + x) or (m – x) respectively. In the other words average value will be increased or decreased by ‘x’.

SOME PROBLEMS

Find the average of first 5 prime number.

Find the average of first 18 multiples of 6.

The average marks obtained by 144 candidates in a certain examination is 55. Find the total marks.

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