Sunday, January 18, 2009

Introduction Of Distribution

We know that two terms " unit of observation and variable of observation are frequency used in frequency distribution. Each recorded or observed value of a variable of observation is associated with a particular person , place , object etc. and that term unit of observation is used to describe what the values of a variable of observation are attached to . Thus , when we are discussing data about examination results , the units of observation are students and the variable of observation is total marks obtained each recorded value of the variable denotes the total marks obtained by a particular student who has appeared in that examination
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 :
  1. 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
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