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Assign ranks to the marks in Accountancy (X) and Marks in Statistics (Y).

Mathematics

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Answer

0.5

Step-by-step solution

3 steps
  1. Assign ranks to the marks in Accountancy (X) and Marks in Statistics (Y).

    Marks in Accountancy (X)Rank (R_X)Marks in Statistics (Y)Rank (R_Y)
    485454
    353201
    171403
    232252
    474485
  2. Calculate the difference in ranks (d=RX−RYd = R_X - R_Y) and the squared difference (d2d^2).

    XYR_XR_Yd=RX−RYd = R_X - R_Yd2d^2
    48455411
    35203124
    174013-24
    23252200
    474845-11
    ∑d2=10\sum d^2 = 10
  3. Apply Spearman's rank correlation coefficient formula.

    The formula for Spearman's rank correlation coefficient (ρ\rho) is:

    ρ=1−6∑d2n(n2−1)\rho = 1 - \frac{6 \sum d^2}{n(n^2 - 1)}

    where nn is the number of pairs of observations. In this case, n=5n=5.

    Substitute the values into the formula:

    ρ=1−6×105(52−1)\rho = 1 - \frac{6 \times 10}{5(5^2 - 1)} ρ=1−605(25−1)\rho = 1 - \frac{60}{5(25 - 1)} ρ=1−605(24)\rho = 1 - \frac{60}{5(24)} ρ=1−60120\rho = 1 - \frac{60}{120} ρ=1−0.5\rho = 1 - 0.5 ρ=0.5\rho = 0.5

    The Spearman's rank correlation coefficient is 0.5.

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