One Attribute

Suppose that there are 100 individuals in a certain sample, and the sample size is denoted by $$n$$. These 100 individuals are divided into two mutually exclusive groups on the basis of the attribute of height. Out of 100, 60 are tall and 40 are short. If tall is denoted by $$A$$ and short is denoted by $$\alpha $$, we can write:

\[\begin{array}{*{20}{c}} A&{}&\alpha &{}&{} \\ {60}&{}&{40}&{}&{n = 100} \end{array}\]

There are two groups and thus we say that there are two classes, $$A$$ and $$\alpha $$, and the class frequency under $$A$$ is 60. This is written as $$\left( A \right) = 60$$; similarly the number of individuals under $$\alpha $$ is written as $$\left( \alpha \right) = 40$$. Thus the attributes written within the brackets show their class frequencies. In this example the sample is divided into two groups, i.e.; two classes, tall and short. Dividing the data into two groups is called a dichotomy, which means cutting into two. In this example a single attribute ‘height’ divides the data in two groups. As only one attribute is involved, the data is called one-way classification. We can make a small table as below:

\[\begin{array}{*{20}{c}} {}&{}&{{\text{One – Way Classification}}}&{}&{} \\ {\text{A}}&{}&\alpha &{}&{} \\ {{\text{60 = }}\left( {\text{A}} \right)}&{}&{40 = \left( \alpha \right)}&{}&{n = 100} \end{array}\]


Clearly $$\left( A \right) + \left( \alpha \right) = n$$

The symbols $$\left( A \right)$$ and $$\left( \alpha \right)$$ are used to denote the frequency of individuals who possess $$A$$ and who do not possess $$A$$ ($$\alpha $$ means not ‘$$A$$’). It may be noted that the symbol ‘$$A$$’ is not necessarily fixed to mean tall. In some other discussions short may be denoted by $$A$$.