The average of 'n' numbers is sum of the numbers divided by n.
So to find the sum of 'n' values we multiply their average
with total number of values.
An = ( x1 + x2 + x3
...) / n AND An * n =
Calculation of weighted average:
If we want to calculate the weighted average or
combined average of two groups whose individual averages are
A1 and A2 and strengths are n1 and n2.
Then Wavg = ( n1 * A1 + n2
* A2 ) / ( n1 + n2 )
Suppose we are given 4 numbers 10, 11, 12, 13
and told to calculate the average which is 11.5. This also
means that we can replace all numbers with the average and not
affect the total viz. 11.5, 11.5, 11.5, 11.5 shall become the
new series that shall be same as old one.
This can be used to solve sums. Suppose you have to find a
fifth number that increases their average by 0.5.
So new series is 11.5+0.5, 11.5+0.5, 11.5+0.5, 11.5+0.5,
11.5+0.5. So X has to be such that it is 11.5 + 5 * 0.5
Assume two groups with Averages A1, A2
and number of members n1 and n2. Then
the weighted average of the groups Aw is:
Aw = ( n1 * A1 + n2
* A2 ) / ( n1 + n2 )
n1 * Aw + n2 * Aw
= n1 * A1 + n2 * A2
n1 ( Aw - A1 ) = n2
( A2 - Aw)
n1 / n2 = ( A2 - Aw)
/ ( Aw - A1 )
Note: For convenience when two averages
are given we taken smaller value as A1 and other
value as A2.
Calculate Absolute value change or percentage change:
If sales of a year is Rs. 1000 and next year is Rs. 2000
then the absolute value change is Rs. 1000 and the
percentage change is:
%change = (Absolute value change) * 100 / Original quantity
Calculate percentage change and percentage point
If earlier Yes bank offered 6% interest rate on savings and
now offers 4% interest. Then calculate percentage change and
percentage point change.
%point change = 6 - 4 = 2%
%change in savings rate = (6 - 4) / 2 * 100 = 100%
Effect of percentage change on a ratio:
The ratio has a relation with the numerator, when numerator
increases the ratio increases. Thus increase in the
numerator only keeping the denominator constant will
increase the ratio.
11 / 17 is 10% more than 10 / 17.
Calculation of successive percentage changes:
A's salary increases by 20% and then decreases by 20%. What
is the net percentage change in salary of A.
To calculate this we assume A's initial salary is 100 which
increases by 20% so ( + 20 ) and then becomes 120. Then it
decreases by 20% so becomes 96 (-24). Hence net change is
+20 - 24 = -4% change or 4% decrease.
A trader gives successive discounts of 10, 20, 10% find the
net percentage change.
To calculate this we should assume original price as 100.
Then 10% discount makes it 90 (-10), 20% discount on 90 is
72 (-18) and then 10% discount on 72 is 64.8 (-7.2) so net
change is = -10-18-7.2 = -35.2 or 35.2% reduction.