Finding variance and variance analysis

We know that the mean is a measure of central tendency. However, what we don’t know is that the mean is many a times not very useful in making informed decisions. Let us consider the following example to drive the point.Suppose one cricketer is to be selected from two on the basis of his batting performance.

The scores of the cricketers A and B in the last 5 innings which they played together are as follows:
Cricketer A: 51, 53, 52, 55, 59
Cricketer B: 85, 23, 69, 07, 96

If we compare the scores based on the mean, then mean of cricketer A is (51 + 53 + 52 + 55 + 59)/5
= 54 runs
And the mean of cricketer B = (85 + 23 + 69 + 07 + 96)/5 = 56 runs.

Thus if the decision is to be taken on the basis of comparison of the means only, then cricketer B would be selected since he has a higher mean runs. But if we take into consideration the reliability of A and B we can obviously notice that B is not reliable, because he is not consistent. B scores 96 runs in one inning but at the same time scores only 7 runs in another inning also. A is consistent in his score and so is more reliable. In other words the difference between two scores of B is very large where as in case of A it is very small. It means that the data regarding the scores of B deviates from the centre instead of concentrating at the centre.

This tendency of a data set to deviate from the mean is called dispersion and its value is called the measure of dispersion. Thus to come to a sensible conclusion from a given data set, we need to know the mean as well as the dispersion. The lesser the dispersion, the more reliable is the mean of the data.

Define Variance: Variance is a measure of dispersion from the mean. Just like how we saw in the example above, variance analysis helps us to understand dispersion of data from the mean so that we can decide better.

Formula for variance: For finding variance we use the following formula:
Variance = V =[ (X1-M)^2 + (X2-M)^2 + (X3-M)^2 + …. + (Xn-M)^2]/n
Where, X1,X2,X3,….Xn are the n observations and M is the mean of these n observations.