Frequency Distribution Data

A Frequency Distribution shows us a summarized grouping of data divided into mutually exclusive classes and the number of occurrences in a class. It is a way of showing unorganized data e.g. to show results of an election, income of people for a certain region, sales of a product within a certain period, student loan amounts of graduates, etc. Some of the graphs that can be used with frequency distributions are histograms, line graphs, bar charts and pie charts. Frequency distributions are used for both qualitative and quantitative data.

(Source: Wikipedia)

Types of Frequency Distribution data:

Different types of frequency distribution data are,

• Univariate frequency tables
• Joint frequency distribution

Univariate distribution tables:

                It is a list of values that can be ordered by the quantity. It can show the values for each value appear for number of times.

Joint frequency distribution:

                 It is used as two-way tables. It is also called as bivariate joint frequency distribution.

Example problem for Univariate frequency distribution data:

Example 1:
Construct the univariate frequency distribution table for the given data. For the following students in a class have marks in the exam.
Students scored marks in between 31-40 are 5
                                                        41-50 are 12
                                                        51-60 are 9
                                                        61-70 are 15
                                                        71-80 are 7
                                                        81-90 are 4
                                                        91-100 are 2
Solution:
         Determine the range:
                      100 – 31 = 70
         Determine the intervals:
                   Choose the interval as 10
         Construct the univariate frequency distribution table.

Marks	No of students	Cumulative frequency
31-40	5	5
41-50	12	17
51-60	9	26
61-70	15	41
71-80	7	48
81-90	4	52
91-100	2	54

Joint frequency distribution example problem:

Example 2:
In a school, boys and girls are participated in different sports competition that can be given. Using that set of values construct the joint frequency distribution.
Boys and girls are participated in running, long jump, and volley ball.
In running – 10 boys and 8 girls
In long jump – 8 boys and 7 girls
In volley ball –12 boys and 12 girls are participated.
Solution:
          Construct a joint frequency distribution table for the given set of data.

Joint frequency	Boys	Girls	Total
Running	10	8	18
Long jump	8	7	15
Volley ball	12	12	24
Total	30	27	57