Arithmetic Mean
The process of computing Arithmetic Mean in the case of individual observations is to take the sum of the values of the variable and then divide by the number of such values. It is denoted by and the formula is
where n is the number of observations and the variable X takes the values X_{1}, X_{2}, ... Xn.
In statistics the collection of all the elements under study is called a POPULATION whereas a collection of some (but not all) of the elements under study is called a sample. It is necessary to distinguish whether we are considering a population or a sample because certain formulas, like those for computing standard deviation (explained later) of a population are different from those for computing the standard deviation of a sample. Hence population mean is denoted by
and sample mean is denoted by
Example 1
The following table gives the annual profits of 10 financial services companies for the year 20x1-x2.
Companies
Net Profit (Rs. crore)
Ashok Leyland Finance
9.19
Classic Finance
4.27
Empire Finance
1.74
First Leasing Company
5.71
Lloyds Finance
4.80
Nagarjuna Finance
4.01
Reliance Finance
9.22
Sakti Finance
3.00
Sundaram Finance
15.16
Tata Finance
3.93
Now, the arithmetic mean of profits of the financial services industry as represented by the above companies for the year 20x1-x2 can be calculated as follows:
This single figure of mean profit represents the profits of the group of financial services companies under the industry.