Frequency Distribution

In economics and statistics, frequency distribution plays a very vital role. Frequency distribution helps to understand the number of times an action or a variable displays in a given time. It helps in understanding and analyzing data. Frequency distribution is the main helping hand in surveying data in survey methods. Frequency distribution holds an important reliance on group data. It aids the simplification of group data that is huge in respect of size and quantity. 

Frequency distribution also has two significant types and divisions. These are the cumulative frequency distribution, ungrouped and grouped frequency distribution. Let us understand these concepts separately with examples and their situational uses. 

What Is Frequency Distribution?

In general terms, frequency distribution refers to the representation of variables that occur during a particular interval. That is, the frequency distribution is either represented through graphs or data. This indicates the occurrence of an event in a given time. It tallies the total occurrence of a situation or outcome that has occurred. 

Let us understand frequency distribution with a theoretical and illustrated example. 

For example:

In a classroom, there are 10 students who attended a test of a total of 10 marks. The scores of these 10 students are: 2, 4, 10, 6, 8, 7, 9, 10, 4, 4. We want to know which students have scored the same range of marks. To know this, let us first create a frequency distribution table. 

 In the table, the left column represents the scores individually. The right column is representative of the frequency of scores, scored by the students. As per the tabular representation of the frequency distribution, the frequencies for the scores have been mentioned. There are 3 students who got 4 marks and 2 students who received 10 marks. 

There are no students who have received the scores of 1, 3 and 5. While, for the scores of 2, 6, 7, 8 and 9, there are one student each, who have received the scores. 

This is how we calculate the frequency distribution and form the table. Usually, we have the tally marks also, that are indicated as ‘I’. These are used to number the frequency occurrence. 

Implications of Frequency Distribution

Frequency distribution is used in various fields. The implications of frequency distribution are:

• Use for graphical representation in survey method

• Used for medical research

• Used for marketing and trend research

• Used for weather reports and assumptions

Types of Frequency Distribution

There are three broad classifications of frequency distribution, ungrouped, cumulative and grouped. These three types of frequency distribution hold various relevance in varied fields. Let us understand them closely and know more about them. 

Grouped Frequency Distribution

In the grouped frequency distribution, we organize the frequencies in a whole data set. We classify the frequencies in intervals and call them classes. The classes that we create are the same size. 

Let us understand grouped frequency distribution with an example

For example:

The price of the same chocolate, say Dairy Milk, is different across 10 shops. The prices are 25, 40, 20, 20, 30, 35, 45, 50, 20, 20. Let us group the price difference in a grouped frequency distribution. 

In the table, we have taken the same size of class interval or the classes. The class interval is the numerical width for classifying the different frequencies in the data. The difference between each class interval is 5. There are 4 stores that have a price range of 20-25 for the chocolate. While, the other class intervals include 1 shop each. 

Ungrouped Frequency Distribution

As the name suggests, ungrouped frequency distribution refers to putting in frequencies of data corresponding to its direct value. In this type of frequency distribution, we classify the data’s frequency directly without any class interval. This frequency distribution is used for both ordinal and nominal data. Ordinal data are quantitative data and nominal data are the named or qualitative data. 

Let us understand ungrouped frequency distribution with an example

For example:

10 part-time employees were asked how many hours they can work from home during weekdays. Their working hours as said were,1, 2,  5, 4, 6, 6, 4, 5, 3, 6. This can be tabulated in terms of ungrouped frequency distribution. Let us keep a range of 2 hours. 

In the table, we have considered the range of 2 hours to classify the frequency of working hours of 8 part-time employees. This gives as the result that the maximum number of part-time employees prefers to work for 6 hours. While, 2 part-time employees prefer to work for 4 and 5 hours. There are 1 part-time employee each, who prefer working for 1,2 and 3 hours respectively. 

Cumulative Frequency Distribution

A cumulative frequency distribution is a frequency distribution dealing with the divisions of data in the lower and upper classes. This type of frequency distribution depicts the data’s frequency as a cumulative process. That is, the data’s frequency is represented in a stair manner. The frequency is measured as what comes before each value. It helps understand the order of the observations or variables in data. 

Let us understand cumulative frequency distribution with an example

For example:

The scores of 12 students out of 100 marks are: 30, 30, 80, 75, 25, 80, 80, 35, 40, 75, 67, 80. To find out the cumulative frequency distribution, we need to tabulate it. For this we must have the class interval too. Let us take the class interval as 20 for classification.

In the table, the left column is the class interval. The right column is the cumulative frequency and the middle column is the frequency. Here, the cumulative frequency is calculated by adding the frequency of each class interval with the next frequency. That is, for the class interval 0-20, the cumulative frequency is 0. For class interval. 20-40, the cumulative frequency of the previous class interval (0) is added to the frequency of the corresponding class interval. 

So to find the cumulative frequency, you have to,

Cumulative Frequency (cf) – previous class interval ‘s cumulative frequency + absolute frequency of corresponding class interval. 

This is how we tabulate and calculate cumulative frequency distribution. 

Conclusion

Frequency distribution refers to the classification of the variables or observations that occur in a given time. The importance of frequency distribution lies in various fields such as election runs. It is also used in the marketing sector to understand what is in trend. 

There are three types of frequency distribution. These are:

• Grouped frequency distribution

• Ungrouped frequency distribution

• Cumulative frequency distribution

The explanation and examples for the concepts and sub-concepts imply the use of frequency distribution.