If there are more than one variable of observation for which values are being observed for each unit of observation , then we say that distribution is multivariate . But we are concerned with two distributions given below :
- Univariate distribution
A distribution in which there is only variable , is called a univariate distribution. For example , the marks obtained by students of a class form a univariate distribution.
2. Bivariate distribution
A distribution which involves two varriables is called a bivariate distribution . For example , the heights and weights of the students of a class in a school form a bivariate distribution.
In the bivariate distribution of two variables age and sex , one variable age is quantitative variable whereas second variable sex is a qualitative variable. We can have bivariate distributions in which both variables are qualitative or both are quantitative.
Further , if the two variables are denoted by x and y with possible values x1 , x2 ,x3 ......... x n and y1 , y 2 ,y 3 ,.......... yn respectively , the raw data would be represented by ordered pairs like ( x1, x2 ) ,(y1, y2) and so on , there being one ordered pair of value of the variables for each unit of observation. There are mn possible ordered pairs of values (xi ,yi ) , though not every one these m pairs may be observed in any particular situation.
Now we discuss two particular distributions.
- Marginal distribution
- Conditional distribution