## Statistics

Statistics is one of the branch of mathematics dealing with the collection, analysis and interpretation of numerical data. The word "statistics" has been derived from the Latin word “status” meaning a political state. We have four stages in statistics.

1.   Collection of data
i.         Primary data: All the data are collected by the investigator from the field for the specific purpose of study.
ii.        Secondary data: The primary data which have already been passed through the statistical process and used by someone else by someone else for the purpose of investigation are called secontary data. They are also called borrowed data.

2.   Presentation of data
The data collected from the field need to be presented by editing,   classifying, arranging, presenting in a graph, tabulating and showing in a   diagram. This process is called the presentation of data.

3.   Analysis of data
From the presentation of data, we should calculate central tendency and   dispersion for the analysis stages of data.

4.   Interpretation of data
In the analysis of data we write the conclusion of data which is called                    interpretation of data.

Example:
Let’s observe the marks secured by 20 students in a math test of 20 marks.
10,       8,         9,         8,         10,       10,       11,       12,       14,       15,
8,         9,         7,         8,         10,       10,       11,       12,       10,       8

The above data is called the raw data. Arranging the above data in ascending order, we have:

7,         8,         8,         8,         8,         8,         9,         9,         10,       10,       10,       10,       10,
10,       11,       11,       12,       12,       14,       15

In the above data:
7 is repeated one time, so its frequency is 1.
8 is repeated five times, so its frequency is 5.
9 repeated two times, so its frequency is 2.
10 is repeated six times, so its frequency is 6.
11 is repeated two times, so its frequency is 2.
12 is repeated two times, so its frequency is 2.
14 is repeated one time, so its frequency is 1.
15 is repeated one time, so its frequency is 1.

Thus, the frequency is the number of times of repetitions of a data.

We can represent the above data in a frequency distribution table, bar graph, line graph or pie-chart also as given in the following.

Frequency distribution table:

 Marks Frequency 7 8 9 10 11 12 14 15 1 5 2 6 2 2 1 1

Bar graph:

Line graph:

Pie-chart:

After representing the data, we can analyse and interpret it by calculating its different statistical values like mean, median, mode, range etc.

Go through the following articles for further studies on statistics:

-       Bar Graph

-       Line Graph

-       Pie-chart

-       Median

-       Quartiles

-       Mode | What is mode?

-       Range | What is range?
-       Quartile Deviation
-       Mean Deviation
-       Standard Deviation