Univariate and Bivariate Analysis: An Easy Guide!!


In statistics, there are three kinds of techniques that are used in the data univariate data analysis. These are univariate analysis, bivariate analysis, and multivariate analysis. How the data analysis technique is selected is based on the variable number and the data type. The statistical inquiry focus is also something to be considered.


Univariate analysis is a basic kind of analysis technique for statistical data. Here the data contains just one variable and does not have to deal with the relationship of a cause and effect. Like for example consider a survey of a classroom. The analysts would want to count the number of boys and girls in the room. The data here simply talks about the number which is a single variable and the variable quantity. The main objective of the univariate analysis is to describe the data in order to find out the patterns in the data. This is done by looking at the mean, mode, median, standard deviation, dispersion, etc.

Univariate analysis is basically the simplest form to analyze data. Uni means one and this means that the data has only one kind of variable. The major reason for univariate analysis is to use the data to describe. The analysis will take data, summarise it, and then find some pattern in the data.

Univariate analysis is conducted in many ways and most of these ways are of a descriptive nature. These are the Frequency Distribution Tables, Frequency Polygons, Histograms, Bar Charts and Pie Charts

Let us get into details here of the kind of analysis that is done to analyze univariate data.

  • Frequency distribution table

Frequency means how often something takes place. The observation frequency tells the number of times for the occurrence of an event. The frequency distribution table may show categorical or qualitative and numeric or quantitative variables. The distribution gives a snapshot of the data and lets you find out the patterns

  • Bar chart

The bar chart is represented in the form of rectangular bars. The graph will compare various categories. The graph could be plotted vertically or these could be plotted horizontally. In maximum cases, the bar will be plotted vertically. The horizontal or the x-axis will represent the category and the vertical y-axis represents the category’s value. The bar graph looks at the data set and makes comparisons. Like for example, it may be used to see what part is taking the maximum budget?

Bar chart
  • Histogram

The histogram is the same as a bar chart which analysis the data counts. The bar graph will count against categories and the histogram displays the categories into bins. The bin is capable of showing the number of data positions, the range, or the interval.

  • Frequency Polygon

The frequency polygon is pretty similar to the histogram. However, these can be used to compare the data sets or in order to display the cumulative frequency distribution. The frequency polygon will be represented as a line graph.

Frequency Polygon
  • Pie Chart

The pie chart displays the data in a circular format. The graph is divided into pieces where each piece is proportional to the fraction of the complete category. So each slice of the pie in the pie chart is relative to categories size. The entire pie is 100 percent and when you add up each of the pie slices then it should also add up to 100.

Pie charts are used to understand how a group is broken down into small pieces.

Pie chart

The univariate data is the one that consists of just one variable. The analysis of univariate data is the simplest since the information has to deal with a single quantity only and the changes in it. It does have to study the relationship and cause and the analysis is used to describe the data and to find out the pattern that exists in it.

Like for example, the height of ten students in a class can be recorded and this is univariate data. There is only one variable which is the height and thus it does not have any relationship and cause attached to it. The description of the pattern that is found in this type of data is made by drawing out conclusions based on dispersion, central measures of tendency, spread, or data, and this is done through the histograms, frequency distribution table, bar charts, etc.

Univariate analysis works by examining its effect on a single variable on a given data set. Like for example, the frequency distribution table is a kind of univariate analysis. Here only one variable is involved in the data analysis. There could however be many alternate variables too like height, age, and weight. As soon as a secondary variable gets introduced in the analysis then this is a bivariate analysis. When there is three or more than three variable involved in the data analysis then this is the multivariate analysis.

Univariate is a common term that you use in statistics to describe a type of data that contains only one attribute or characteristic. The salaries of people in the industry could be a univariate analysis example. The univariate data could also be used to calculate the mean age of the population in a village.


Bivariate analysis means the analysis of the bivariate data. This is a single statistical analysis that is used to find out the relationship that exists between two value sets. The variables that are involved are X and Y.

  • Univariate analysis is when only one variable is analyzed.
  • Bivariate data analysis is when exactly two variables are analyzed.
  • Multivariate analysis is when more than two variables get analyzed.

The results that are obtained from the bivariate analysis are stored in a data table that has two columns. Bivariate analysis should not be confused with two sample data analyses where the x and y variables are not related directly.

Here is how the bivariate analysis is carried out.

  • Scatter plots — This gives an idea of the patterns that can be formed using the two variables
  • Regression Analysis — This uses a wide range of tools to determine how the data post could be related. The post may follow an exponential curve. The regression analysis gives the equation for a line or curve. It also helps to find the correlation coefficient.
  • Correlation Coefficients –The coefficient lets you know if the data in question are related. When the correlation coefficient is zero then this means that the variables are not related. If the correlation coefficient is a positive or a negative 1 then this means that the variables are perfectly correlated.

The kind of bivariate analysis is dependent on the kind of attributes and variables that is used to analyze the data. The variables may be ordinal, categorical, or numeric. The independent variable is categorical like a brand of a pen. In this case, probit regression or logit regression is used. If the dependent and the independent variables are both ordinal which means that they have a ranking or position then the rank correlation coefficient is measured.

In case the dependent attribute is ordinal then the ordered probit or the ordered logit is used. It is possible that the dependent attribute could be internal or a ratio like the scale of temperature. This is where regression is measured. Here is how we mention the kinds of bivariate data correlation.

  • Numerical and Numerical

In this kind of variable both the variables of the bivariate data which includes the dependent and the independent variable have a numerical value.

  • Categorical and Categorical

When both the variables in the bivariate data are in the static form then the data is interpreted and statements and predictions are made about it. During the research, the analysis will help to determine the cause and impact to conclude that the given variable is categorical.

  • Numerical and Categorical

This is when one of the variables is numerical and the other is categorical.

Bivariate analysis is a kind of statistical analysis when two variables are observed against each other. One of the variables will be dependent and the other is independent. The variables are denoted by X and Y. The changes are analyzed between the two variables to understand to what extent the change has occurred.

Numerical and Categorical.

Bivariate analysis is the analysis of any concurrent relation between either two-variable or attributes. The study will explore the relationship that is there between the two variables as well as the depth of the relationship. It helps to find out if there are any discrepancies between the variable and what the causes of the differences are.

The bivariate analysis examples are used is to study the relationship between two variables. Let us understand the example of studying the relationship between systolic blood pressure and age. Here you take a sample of people in a particular age group. Say you take the sample of 10 workers.

The first column will have the age of the worker and the second column records their systolic blood pressure.

The table then needs to be displayed in a graphical format to make some conclusion from it. The bivariate data is usually displayed through a scatter plot. Here the plots are made on a grid paper y-axis against the x-axis and this helps to find out the relationship between the data sets that are given.

A Scatter plot helps to form a relationship between the variables and tries to explain the relationship between the two. Once you apply the age on the y-axis and the systolic blood pressure on the x-axis you will notice possibly a linear relationship between them.

How to understand the relationship

The graph will show that there is a strong relationship between age and blood pressure and that the relationship is positive. This is because the graph has a positive correlation. So the older is one’s age the higher is the systolic blood pressure. The line of best fit also helps to understand the strength of the correlation. If there is little space between the points then the correlation is strong.

The correlation coefficient or R is a numerical value that ranges between -1 to 1. This indicates the strength of the linear relationship between two variables. To describe a linear regression the coefficient is called Pearson’s correlation coefficient. When the correlation coefficient is close to 1 then it highlights a strong positive correlation. When the correlation coefficient is close to -1 then this shows a strong negative correlation. When the correlation coefficient is equal to 0 then this shows no relationship at all.

Thanks for reading!!..




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