Univariate vs Bivariate Data

Univariate vs Bivariate Data

Univariate and Bivariate distribution

“If it is proved true that in a large number of instances two variables tend always to fluctuate in the same or in opposite directions, we consider that the fact is established and that a relationship exists. This relationship is called correlation.”

  1. Univariate distribution: These are the distributions in which there is only one variable such as the heights of the students of a class.
  2. Bivariate distribution: Distribution involving two discrete variable is called a bivariate distribution. For example, the heights and the weights of the students of a class in a school.
  3. Bivariate frequency distribution: Let x and y be two variables. Suppose x takes the values x1, x2, …., xn and y takes the values y1, y2, ….., yn then we record our observations in the form of ordered pairs (x1, y1), where 1 ≤ i ≤ n, 1 ≤ j ≤ n. If a certain pair occurs fij times, we say that its frequency is fij.

The function which assigns the frequencies fij’s to the pairs (xi, yj) is known as a bivariate frequency distribution.

Difference between Univariate and Bivariate Data

Univariate data means “one variable” (one type of data).
Bivariate data means “two variables” (two types of data).

Univariate DataBivariate Data
  • involving a single variable
  • involving two variables
  • does not deal with causes or relationships
  • deals with causes or relationships
  • the major purpose of univariate analysis is to describe
  • the major purpose of bivariate analysis is to explain
  • central tendency – mean, mode, median
  • dispersion – range, variance, max, min, quartiles, standard deviation.
  • frequency distributions
  • bar graph, histogram, pie chart, line graph, box-and-whisker plot
  • analysis of two variables simultaneously
  • correlations
  • comparisons, relationships, causes,
    explanations
  • tables where one variable is contingent on the values of the other variable.
  • independent and dependent variables
Sample question:  How many of the students in the freshman class are female?Sample question:  Is there a relationship between the number of females in Computer Programming and their scores in Mathematics?

Covariance

Let (xi, yj); i = 1, 2, …., n be a bivariate distribution, where x1, x2, …., xn are the values of variable x and y1, y2, ….., yn those of y.  Then the covariance Cov (x, y) between x and y is given by
Univariate vs Bivariate Data 1
Covariance is not affected by the change of origin, but it is affected by the change of scale.