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In statistics, bivariate data is data on each of two variables, where each value of one of the variables is paired with a value of the other variable. [1] It is a specific but very common case of multivariate data. The association can be studied via a tabular or graphical display, or via sample statistics which might be used for inference.
Like univariate analysis, bivariate analysis can be descriptive or inferential. It is the analysis of the relationship between the two variables. [1] Bivariate analysis is a simple (two variable) special case of multivariate analysis (where multiple relations between multiple variables are examined simultaneously). [1]
Benford's law, which describes the frequency of the first digit of many naturally occurring data. The ideal and robust soliton distributions. Zipf's law or the Zipf distribution. A discrete power-law distribution, the most famous example of which is the description of the frequency of words in the English language.
A bivariate, multimodal distribution Figure 4. A non-example: a unimodal distribution, that would become multimodal if conditioned on either x or y. In statistics, a multimodal distribution is a probability distribution with more than one mode (i.e., more than one local peak of the distribution).
Finally, the fourth example (bottom right) shows another example when one outlier is enough to produce a high correlation coefficient, even though the relationship between the two variables is not linear. These examples indicate that the correlation coefficient, as a summary statistic, cannot replace visual examination of the data.
Bivariate data, that shows the relationship between two variables Bivariate analysis , statistical analysis of two variables Bivariate distribution, a joint probability distribution for two variables
This furnishes two examples of bivariate distributions that are uncorrelated and have normal marginal distributions but are not independent. The left panel shows the joint distribution of X 1 {\displaystyle X_{1}} and Y 2 {\displaystyle Y_{2}} ; the distribution has support everywhere but at the origin.
A bivariate map or multivariate map is a type of thematic map that displays two or more variables on a single map by combining different sets of symbols. [1] Each of the variables is represented using a standard thematic map technique, such as choropleth , cartogram , or proportional symbols .