The Variance
Variance is another absolute measure of dispersion. It is defined as the average of the squared difference between each of the observations in a set of data and the mean. For a sample data the variance is denoted is denoted by and the population variance is denoted by (sigma square).
The sample variance has the formula:
Where sample is mean and is the number of observations in the sample.
The population variance is defined as:
Where is the mean of the population and is the number of observations in the data. It may be remembered that the population variance is usually not calculated. The sample varianceis calculated and if need be, this is used to make inference about the population variance.
The term is positive, therefore is always positive. If the original observations are in centimeter, the value of the variance will be (centimeter)2. Thus the unit of is the square of the units of the original measurement.
For a frequency distribution the sample variance is defined as:
For a frequency distribution the population variance is defined as:
In simple words we can say that variance is the square of standard deviation.
Example:
Calculate the variance for the following sample data: 2, 4, 8, 6, 10, and 12.
Solution:
















Example:
Calculate variance from the following distribution of marks:
Marks

No. of Students









Solution:
Marks






























Total





