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.********************
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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:
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