One Attribute

Suppose that there are 100 individuals in a certain sample, 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’ are denoted by A and short are denoted by \alpha , we can write:

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

There are two groups and we say that there are two classes A and \alpha and the class frequency under A is 60. It 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 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 for ‘tall. In some other discussion ‘short’ may be denoted by A.



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