Bivariate Frequency Distribution | Calculation, Advantages and Disadvantages

What is Bivariate Frequency Distribution?

Bivariate Frequency Distribution is a statistical representation of the joint occurrence of two categorical variables. It shows how often specific combinations of values from two variables occur together. It provides information about how often specific combinations of categories or levels from two different variables occur together. This type of distribution is particularly useful when you want to examine relationships, associations, or dependencies between two categorical variables.

Power of Bivariate Frequency Distribution in Business Analysis

In the ever-evolving landscape of business studies, data is the key to informed decision-making. The ability to understand relationships between different variables can be a game-changer for businesses striving for success. One valuable statistical tool in this pursuit is the bivariate frequency distribution.

Why is Bivariate Frequency Distribution Significant in Business Research?

Bivariate frequency distribution holds immense significance in business research and decision-making for several reasons:

1. Decision-Making: In today’s data-driven world, businesses need to make decisions based on evidence rather than intuition. Bivariate Frequency Distribution provides a structured approach to understand how variables interact and ensure that decisions are grounded in data.

2. Market Segmentation: Businesses can use this tool to segment their market effectively. For instance, by analysing the relationship between customer demographics and purchase behaviour, they can tailor marketing strategies for specific customer groups.

3. Risk Assessment: Bivariate frequency distribution helps in risk assessment. For financial institutions, understanding the relationship between economic indicators and loan defaults is crucial for managing risk exposure.

4. Resource Allocation: It aids in resource allocation. Businesses can allocate resources more efficiently by examining how different factors, such as location and customer preferences, affect sales.

How to Calculate Bivariate Frequency Distribution?

1. The two variables involved in a bivariate set of data may be discrete, continuous, or one discrete and one continuous. One of these is represented horizontally, while the other is shown vertically.

2. Considering the nature of the variables involved and the magnitude of values in the data, an appropriate decision is taken regarding the individual values of the variable, how many classes, and what width is to be taken. In this way, a bivariate table is created.

3. After this, each pair of the values is considered and entered in the appropriate cell in the table by means of a tally bar.

4. Once all pairs are considered, and entries are made, the tally bars in each cell are counted, and frequencies for each of the cells are determined.

5. Finally, the row and column totals are obtained to get marginal frequencies.

Example 1:

Prepare a bivariate frequency distribution for the following data, taking class intervals for X as 25-35, 35-45, 45-55, etc., and for Y as 105-120, 120-135, etc. where X denotes the age in years and Y denotes blood pressure for a group of 20 people. 

The required data is: (45, 141); (26, 130); (62, 150); (28, 114); (55, 138); (36, 120); (48, 142); (40, 139); (28, 105); (32, 135); (31, 153); (37, 151); (59, 149); (50, 151); (48, 121); (47, 126); (33, 131); (42, 154); (49, 151); (34, 118).

Solution:

Given, X = Age in years, Y = Blood Pressure. 

Bivariate Frequency Distribution is to be prepared by taking class intervals for X as 25-35, 35-45, 45-55, etc., and for Y as 105-120, 120-135, etc.

Bivariate Frequency Distribution

Blood Pressure (Y)/ Age in years (X)	105-120	120-135	135-150	150-165	Total
25-35	|||	||	|	|	7
35-45		|	|	||	4
45-55		||	||	||	6
55-65			||	|	3
Total	3	5	6	6	20

Marginal Frequency Distribution of X:

Age in years (X)	25-35	25-35	45-55	55-65
Frequency	7	4	6	3

Marginal Frequency Distribution of Y:

Blood Pressure (Y)	105-120	120-135	135-150	150-165
Frequency	3	5	6	6

Advantages of Bivariate Frequency Distribution

1. Reveals Relationships: Bivariate Frequency Distribution helps uncover relationships or associations between two categorical variables. By examining the joint distribution of these variables, one can identify patterns and dependencies that might not be apparent when looking at each variable individually. This insight can inform strategic decisions.

2. Informs Decision-Making: Businesses can make more informed decisions based on the insights derived from bivariate frequency distributions. For example, HR departments can develop better employee management strategies, marketers can refine their targeting, and product development teams can focus on features that align with customer preferences.

3. Facilitates Data-driven Strategies: Bivariate analysis is a key component of data-driven decision-making. It provides businesses with quantitative evidence of relationships between variables, reducing the reliance on intuition and guesswork in strategic planning.

4. Identifies Areas for Improvement: Bivariate Frequency Distribution can pinpoint specific areas for improvement. For example, customer feedback analysis helps identify, which product features or aspects are consistently associated with negative sentiment, guiding product enhancement efforts.

Limitations of Bivariate Frequency Distribution

1. Bivariate frequency distributions are suitable only for analysing categorical data or discrete variables. They are not appropriate for continuous variables, which require different statistical methods.

2. Bivariate frequency distributions focus on the relationship between two variables. If one wants to analyse the joint distribution of more than two variables, one would need to use multivariate methods, which can be more complex.

3. Analysing large datasets using bivariate frequency distributions can be computationally intensive, and challenging to visualise, especially when there are many categories for each variable.