Question

Out of 500 persons in a locality 300 were literate. Out of 500 persons 400 were employed of whom 250 were literate. Find out the degree of association between literacy and employment.

Answer 1

SOLUTION

GIVEN

Out of 500 persons in a locality 300 were literate. Out of 500 persons 400 were employed of whom 250 were literate.

TO DETERMINE

The degree of association between literacy and employment.

EVALUATION

Here it is given that Out of 500 persons in a locality 300 were literate. Out of 500 persons 400 were employed of whom 250 were literate.

Let

A : Persons who are literate

B : Persons who are employed

$\sf{ \alpha : Persons \: who \: are \: illiterate }$

$\sf{ \beta : Persons \: who \: are \: unemployed}$

We form the table from the given data

$\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c|c|c|c} \sf &\sf B&\sf \beta&\sf \:Total \\\frac{\qquad \qquad}{}&\frac{\qquad \qquad}{}&\frac{\qquad \qquad}{}&\frac{\qquad}{}\\\\ \sf A &\sf 250&\sf \: 50&\sf \:300\\\frac{\qquad \qquad}{}&\frac{\qquad \qquad}{}&\frac{\qquad \qquad}{}&\frac{\qquad}{}\\\\ \sf \alpha & \sf 150&\sf 50&\sf200 \\\frac{\qquad}{}&\frac{\qquad}{}&\frac{\qquad \qquad}{}\\\ \\ \sf Total &\sf 400&\sf \: 100&\sf \:500\\\frac{\qquad \qquad}{}&\frac{\qquad \qquad}{} &\frac{\qquad}{}& \sf & \end{array}}\end{gathered}\end{gathered}\end{gathered}$

Hence the required degree of association between literacy and employment

$\displaystyle \sf{ = \frac{(AB)( \alpha \beta ) - (A \beta )( \alpha B)}{(AB)( \alpha \beta ) + (A \beta )( \alpha B)} }$

$\displaystyle \sf{ = \frac{(250 \times 50) - (50 \times 150)}{(250 \times 50) + (50 \times 150)} }$

$\displaystyle \sf{ = \frac{50 \times 100}{50 \times 400} }$

$\displaystyle \sf{ = \frac{ 100}{ 400} }$

$\displaystyle \sf{ = 0.25}$

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