Arithmetic mean
The most popular and widely used
measure of representing the entire data by one value is what a layman call an
‘average’ and what the statisticians called is
‘arithmetic mean’. Arithmetic
mean may be
1)
Simple arithmetic mean
2)
Weighted arithmetic mean.
1) Simple arithmetic mean:
Case-(i) Calculation of simple
arithmetic mean -Individual series:
The
process of computing mean in case of individual series (i.e. where frequencies
are not given) is very simple. Add together the various values of the variable
and divide the total by the no of items.
Direct method:
If 
are ‘n’ individual observed values of a variable X,
are ‘n’ individual observed values of a variable X,
then the A.M is denoted by 
and is defined as
and is defined as = 
= 
Short cut method:
Under this
method the formula for calculating mean is = 
=
Where A=assumed
mean 
= deviations of items taken from the assumed mean.
= deviations of items taken from the assumed mean.
n = Number of observations
Note: Any value whether
existing in the data or not can be taken as the assumed mean and the final
answer would be the same. However it’s better to take assumed mean nearer to
the actual mean for lesser calculations.
Example: The following
table gives the monthly income of 10 employees in an office. Income (in Rs): 1780, 1760, 1690, 1750, 1840, 1920, 1100,
1810, 1050, 1950.
Calculate the A.M.
Sol.
Calculation of arithmetic mean
|
Employee
|
Income(in Rs) x
|
d=(x-1800)
|
|
1
2
3
4
5
6
7
8
9
10
|
1780
1760
1690
1750
1840
1920
1100
1810
1050
1950
|
-20
-40
-110
-50
+40
+120
-700
+10
-750
+150
|
|
n=10
|
 16,650 |
 -1350 |
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