Variability:

We have elaborates the averages and the means of sets of values.  Although the mean is a useful tool in elaborating a characteristic of a set of numbers, a few times it is valuable to acquire information about the mean.  There is a second number that implies how representative the mean is of the data.   For instance, within the group of numbers, 100, 5, 20, 2 then the mean is 31.75.   If these data points show tank levels for four days then the use of the mean level, 31.75, to make a decision using tank usage could be misleading since none of the data points was close to the mean.

This spread, or distance, of each data point from the mean is called the variance. The variance of every data point is computed by:

Variance          x¯ = xi

where

xi         =          each data point

x¯          =          mean

The variance of each data point does not provide us along with any useful information.   But if the mean of the variances is computed, an extremely useful number is determined.  The mean variance is the average value of the variances of a set of data.  The mean variance is computed as follows:

The mean variance, or mean deviation, can be computed and used to make judgments through providing information on the quality of the data.   For instance, if you were trying to decide while to buy stock and all you knew was that this month's average price was $10, and today's price is $9, you might be tempted to buy some.  But, if you also knew in which the mean variance in the stock's price over the month was $6, you would realize the stock had fluctuated widely during the month. Thus, the stock represented a more risky purchase than just the average price indicated.

It can be seen that to make sound decisions using statistical data, it is important to analyze the data thoroughly before making any decisions.