Question

Calculate the coefficient of rank correlation from the following data:-

Roll no. of Students : 1 2 3 4 5 6 7 8 9 10 11 12

Marks in X : 60 34 40 50 45 41 22 43 42 66 64 46

Marks in Y : 75 32 34 40 45 33 12 30 36 72 41 57​

Answer 1

Answer:-

0.8322

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Answer 2

Given:

Roll no. of Students :  1     2     3    4    5    6    7   8    9    10   11   12

              Marks in X : 60  34  40  50  45  41  22 43  42  66  64 46

              Marks in Y : 75  32  34  40  45  33  12  30  36  72  41  57​

To find:

The coeficient of rank correlation

Calculation:

Refer the table attached to find the value of ∑D²

Spearman’s rank corelation coefficient is given by

      $R=1-\frac{6\Sigma D^2}{N(N^2-1)}$

          $=1-\frac{6\times 48}{1728-12}$

          $=1-\frac{288}{1716}$

          $=\frac{1428}{1716}$

          $\approx 0.832$

Final answer:

The coeficient of rank correlation is 0.832