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Worked Examples · Example 4
Q.

The marks obtained by 7 students in Statistics (X) and Accountancy (Y) are given below. Compute Spearman's Rank Correlation Coefficient, applying the correction for tied ranks.

StudentABCDEFG
Statistics (X)85857890657272
Accountancy (Y)75807088606568
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Step 1 — Rank the Statistics marks (X), highest = rank 1, averaging tied ranks. Sorted descending: D(90), A(85), B(85), C(78), F(72), G(72), E(65). A and B tie for 2nd/3rd ⇒\Rightarrow both get 2+32=2.5\frac{2+3}{2}=2.5. F and G tie for 5th/6th ⇒\Rightarrow both get 5+62=5.5\frac{5+6}{2}=5.5.

StudentXRxR_x
D901
A852.5
B852.5
C784
F725.5
G725.5
E657

Step 2 — Rank the Accountancy marks (Y), no ties. Sorted descending: D(88), B(80), A(75), C(70), G(68), F(65), E(60) ⇒\Rightarrow ranks 1–7 respectively, with no averaging needed.

Step 3 — Tabulate RxR_x, RyR_y, dd, d2d^2 by student.

StudentRxR_xRyR_yd=Rx−Ryd=R_x-R_yd2d^2
A2.53−0.50.25
B2.520.50.25
C4400
D1100
E7700
F5.56−0.50.25
G5.550.50.25
Total1.0

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