Frequency Distribution

A method of organizing and considering the raw data is the conversion of raw data into a grouped data.Here, the various items of data are classified into certain groups or classes and the no of items lying in each group or class is put against that group or class. The data organized and summarized in this way is known as Frequency Distribution.

Example:

                   The following are the marks out of 100 obtained by 25 students in the subject of physics at their final examination.

  45, 50, 51, 51, 54, 53, 53, 52, 55, 57, 54, 58, 60, 62, 59, 61, 61, 62, 64, 63, 48, 65, 53, 66, 65

The frequency distribution for the above data may be like given below:

Marks	Frequency	Class boundaries	Mid point (x)
45-49	2	44.5-49.5	47
50-54	9	49.5-54.5	52
55-59	4	54.5-59.5	57
60-64	7	59.5-64.5	62
65-69	3	64.5-69.5	67
Total	25

        Formation of Frequency Distribution (Tally Bar Method)

In this method the raw data or the ungrouped data are presented into a grouped data. Choice is yours to select the size of class interval. Generally, the size of class interval determined on the basis of total number of observations and the desired number of groups.

            Following are the steps in tally method.

(i)                  Find range of data.

(ii)                Find the size of class interval by dividing the range by the number of classes you wish to make. For example, the largest observation is 126 and the smallest observation is 20 and if we have to make 10 groups or classes, then

      

                Size of each class interval =        126  -   20

                                                                    10(groups)

                                                          =            106

                                                                         10

                                                          =          10.6 or 11 approximately

(iii)               Prepare three columns

(a)              Class interval

(b)              Tally marks

(c)              Frequencies.

(iv)              Select the data element one by one.

(v)                Look for the class in which each element of ungrouped data falls. Draw a small tally mark (/) against that class and also tick the element concerned with a tick mark sign. In this way you can remember that you have counted for the element. Continue this way with the next element unto the last element of the data set. If 5 or more tallies appear in any class, mark every fifth tally diagonally as(  )

(vi)              Count the number of tally marks against each class and write that number in the frequencies column.

Example:

                 Following are the numbers of telephone cells made in a week to 30teachers of a high school.

 5, 8, 11, 25, 13, 16, 20, 17, 15, 16, 30, 21, 14, 18, 19, 6, 22, 26, 15, 19, 35, 29, 31, 23, 25, 20, 10, 9, 7, 26.

Using 5 as class interval make a frequency distribution by tally method.

Solution:

                     

Class Interval	Tally Marks	Frequency (f)
5-9		5
10-14	////	4
15-19	///	8
20-24		5
25-29		5
30-34	//	2
35-39	/	1
Total	---	30

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