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**Average:**An average or can say arithmetic mean of n number observations is, total sum of n observations divided by n.

Average = Sum of observations/Number of observations | |||

**Average Speed:**

v If a person covers the same
distance at two different speeds i.e x km/h and y km/h
respectively, Then his total Average Speed

**= (2xy)/(x+y)**
v If a person covers the same
distance at different speeds x km/h, y km/h and z km/h respectively, Then his total Average Speed

**=(3xyz)/(xy+yz+zx)**
·
If the
average of n1 observations is x1 and average of n2 observations is x2, then
the Average of total observations(n1+n2)

**=(n1x1+n2x2)/(n1+n2)**
·
Suppose if the
total average age of x members of a family is y years and Now if a new
member joins the family and the new average age the family is n, then the age
of new member will be

**=[n-x(n-y)] years**
·
Total average
age of x members of a family is y years Now if a member leaves the family,
and the new average age of the family is n, then the age of that member will be
=[n+x(y-n)] years

·
Average of
first n consecutive natural numbers =(n+1)/2

·
Average of first
n natural Even numbers =(n+1)

·
Average of
natural even numbers up to n =(n/2)+1

·
Average of
first n natural odd numbers=n

·
Average of
natural odd numbers up to n =(n+1)/2

**Some Important Points to be remember:**

ü If the value of each observation
is increased by the same value n, then their total average will also be
increase by n.

ü If the value of each observation
is decreased by the same value n, then their total average will also be
decrease by n.

ü If the value of each observations
is multiplied by the same value n, then their total average will also be
get multiplied by n.

ü If the value of each observation
is divided by the same value n, then their total average will also be
get divided by n.

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