When the number of observation is large the data are often classified into two- way frequency distribution called a correlation table,

The class intervals for y are listed in the captions or column headings and those for X are listed in the studs at the left of the table the order can also be reversed. The frequencies for each cell of the table are determined by either tallying or card sorting just as in the case of frequency distribution of a single variable.

The formula for calculating the coefficient of correlation is:

R = N Σ f dx dy – Σ f dx Σ f dy

√(NΣ fd)²_x – (Σ f dx)² √ N Σ fd²_y – (Σ f dy)²

This formula is the same as the one discussed above for assumed mean. The only difference is that the deviations are also multiplied by the frequencies.

Steps.

Take the step deviations of the variable X and denote these deviations by dx.

Take the step deviations of the variable Y and denote these deviations by dy.

Multiply dx dy and respective frequency of each cell and write the figure obtained in right-hand upper corner of each cell.

Add togther all the cornered values as calculated in step (ii) and obtain the total Σ f dx.

Take the squares of the deviations of variable y and multiply them by the respective frequencies and obtain Σ fd²_x.

Multiply the frequencies of the variable y by the deviations of y and obtain the total Σ f dy.

Take the take the squares of the deviations of the variable y and multiply them by the respective frequencies and obtain Σ fd²_y

Substitute the values of Σ fd dx dy, Σ fd x, Σ f dx Σ fd²_x, Σ f dy and Σ f d²_y in the above formula and obtain the value of r.

Illustration

The following dare the marks obtained by the students of a class in statistics and accountancy.

Roll no. of students	Marks in statistics	Marks in accountancy	Roll no. of students	Marks in statistics	Marks in accountancy
1	15	13	13	14	11
2	0	1	14	9	3
3	1	2	15	8	5
4	3	7	16	13	11
5	16	8	17	10	10
6	2	9	18	13	11
7	18	12	19	11	14
8	5	9	20	11	7
9	4	17	21	12	18
10	17	16	22	18	15
11	6	6	23	15	15
12	19	18	24	7	3

Prepare a correlation table taking ht magnitude of each class interval as four marks and the first interval as equal to 0 and less than 4. Calculate Karl Pearson’s coefficient of correlation between the marks in statistics and marks in accountancy and comment on the correlation table.

Solution

Preparation of correlation table

                                                                                                 <-----Marks in Statistics----->

Marks in accountancy ↓	0-4	4-8	8-12	12-16	16-20	Total
0-4	2	1	1			4
4-8	1	1	2	1		5
8-12	1	1	1	2	1	6
12-16			2	1	2	5
16-20		1		1	2	4
Total	4	4	6	5	5	24

Let marks in statistics be denoted by X and marks in accountancy by y.

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