Calculation of Coefficient of Correlation

To calculate the coefficient of correlation, we need to find the sum of squares of differences in ranks of marks obtained in Physics and Chemistry by 10th students in a test.

Let's assume the ranks in Physics and Chemistry for the 10th students are as follows:

Physics: P1, P2, P3, P4, P5, P6, P7, P8, P9, P10
Chemistry: C1, C2, C3, C4, C5, C6, C7, C8, C9, C10

Step 1: Calculate the differences in ranks
We need to find the difference in ranks for each student between Physics and Chemistry. These differences can be calculated by subtracting the rank in Chemistry from the rank in Physics.

Differences: D1, D2, D3, D4, D5, D6, D7, D8, D9, D10

Step 2: Square the differences
Next, we need to square each difference calculated in Step 1 to get the sum of squares of differences.

Squares of Differences: D1^2, D2^2, D3^2, D4^2, D5^2, D6^2, D7^2, D8^2, D9^2, D10^2

Step 3: Calculate the sum of squares of differences
Add up all the squared differences calculated in Step 2 to get the sum of squares of differences.

Sum of Squares: D1^2 + D2^2 + D3^2 + D4^2 + D5^2 + D6^2 + D7^2 + D8^2 + D9^2 + D10^2

Given that the sum of squares of differences is 150, we can write the equation as:

D1^2 + D2^2 + D3^2 + D4^2 + D5^2 + D6^2 + D7^2 + D8^2 + D9^2 + D10^2 = 150

Step 4: Calculate the coefficient of correlation
The coefficient of correlation (r) can be calculated using the formula:

r = 1 - (6 * Sum of Squares) / (n * (n^2 - 1))

where n is the number of observations (in this case, 10).

Substituting the values, we can calculate the coefficient of correlation.

Conclusion
The coefficient of correlation can be calculated by finding the sum of squares of differences in ranks of marks obtained in Physics and Chemistry by 10th students in a test. By following the steps mentioned above, we can calculate the coefficient of correlation.

0.091