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