February 15, 2012

Choosing An Appropriate Mathematical Statistic For a Data

Mathematical Statistics are the instruments that aids it's users to make decisions by using mathematical data. A bar diagram is a simple example of a mathematical statistic that makes use of two sets of mathematical data (each on one axis), to generate interpret-able information for its audience.

Most of the mathematical statistics can have a similar visual format but however it is a very essential key to select an appropriate statistic to produce a true result. It is important to note that there is a fine distinction between a mathematical statistic that gives a true (free from overstated-ness or understated-ness) figure and a mathematical statistic that gives a desirable figure.

To drive the point home, lets consider a simple mathematical data of the profits of 6 products as 2,50,50,45,55,100.

Now a desirable mathematical statistic will consider the average of profits as 2+50+50+45+55+100/6.
The result will be 50.333.
But a true and a more appropriate mathematical statistic will eliminate the 2 extreme figures in the data i.e 2 and 100.
Now the trimmed mathematical average of the profits will be 50+50+45+55/4 = 50. Thus avoiding an overstatement of 0.3333 of the profits.

The appropriateness of a mathematical statistic is not limited only to it being unbiased. But it also considers other factors such as:

Size of the data

For a large sized data, bar diagrams can be appropriate mathematical statistics ensuring that the entire data is enclosed into the length of the paper.

Data containing a few abnormally deviated figures

For a mathematical data that contains a few skewed figures a scattered diagram can be an appropriate mathematical statistic.

Data Showing Relationships / Not Showing Relationships

For a mathematical data the represents a relationship, for example, a data of the birth-rates of the last 5 decades, such a mathematical statistic should be used that can be graphically plotted. 

For the below table a bar mathematical statistic will be more appropriate.

Birth Rate (as compared to Death Rate)

But for a mathematical data that is not related to any other but it self a pie chart can be a more appropriate mathematical statistic.

The Use of More Than One Mathematical Statistic

Different mathematical statistics can be used to withdraw different interpretations from one data. So while using mathematical statistics to make important decisions, the use of more than one mathematical statistic is advisable.