Frequency Distribution in Statistics

frequency distribution

Frequency distribution  in statistics refers to a graph or table which depicts or illustrate the occurrences of values.

Frequency distribution is very important in study of statistics, machine learning and data science area.  To  understand frequency distribution you have to understand organization of data.

Basically, there are three types of data organization techniques.

1- Individual Series Data

This type of data is basically raw data collected from somewhere. An example of students obtained marks in a class are given.

5, 12, 25, 15, 25, 15, 35, 28, 38, 25, 28, 38, 28, 45, 35, 38, 35, 35,35, 35, 35, 35, 45, 47,  45, 47, 45, 47, 45, 47, 45, 47, 45

47, 45, 47, 45, 47, 45, 47, 50, 47, 55, 50, 55, 50,  55, 50, 55, 50, 55, 50, 55, 50, 55, 50, 55, 55, 50, 55, 50, 58, 50, 58, 50, 58,

50, 58, 50, 58,  50, 62, 67, 62, 67, 62, 67, 62, 67, 62, 67, 62, 67, 62, 67, 62, 67, 62, 67, 71, 76, 71, 76, 71, 76, 71, 76, 82, 76, 82, 76, 82, 85, 91, 85, 94, 97, 85

The above data set  is individually organized and this type of arrangement of data is called individual series data. In this type of data set inferring information  takes lot of effort and time.

2- Discrete Series Data

The individual series data can be organized into more convenient tabular form using frequency distribution  which is called discrete series data. In which, there are two columns, the first column   contains values and the second one contains  their occurrences (frequency).  This type of data series can be easier to analyze compare  to individual series data.

Frequency Distribution

MarksNumber of Students
51
121
152
253
283
358
382
4510
4710
5015
5510
585
6210
6710
714
766
823
853
911
941
971

You can notice from the table row one that  marks 5 is obtained by only one student (frequency).

You can notice from the table row six that  marks 35 is obtained by only 8 student (frequency).

3- Continuous Series Data

The discrete series data table can also be made short using class intervals. In which   values are in a range  in first column and their occurrences in another column .  Which helps to analyze  and interpret  data in easier way.

See the same  table using class interval. This is more convenient to analyze  and understand  than discrete series data

Marks ( In Class Intervals )Number of Students (Frequency)
0-101
10-203
20-306
30-4010
40-5020
50-6030
60-7020
70-8010
80-906
90-1003

 

Furthermore, the frequency  distribution is also plotted below using bar graph. In graph at the x-axis marks and at the y-axis

number of students ( frequency ) are kept  which is depicted below.

 

frequency distribution

Conclusion-

In this post, I have explained about organization of data and  frequency distribution hope it will help you to understand these concepts in  statistics.

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