The Spearman's Rank correlation coefficient between Economics and Accountancy marks for a class student is $\dfrac{75}{99}$ and the sum of Square of differences in ranks for Economics and Accountancy marks is 40. What is the number of students in the class?
(A) 10
(B) 15
(C) 18
(

Question

The Spearman's Rank correlation coefficient between Economics and Accountancy marks for a class student is $\dfrac{75}{99}$ and the sum of Square of differences in ranks for Economics and Accountancy marks is 40. What is the number of students in the class?
(A) 10
(B) 15
(C) 18
(D) 20

Accepted Answer

> [!TLDR]
> Solve $1-\frac{6\sum d^2}{n(n^2-1)}=\frac{75}{99}$ → $n(n^2-1)=990$ → $n=10$.

### Step 1 — Write Spearman's rank correlation formula

> [!FORMULA]
> $$r=1-\dfrac{6\sum d^{2}}{n(n^{2}-1)}$$

### Step 2 — Isolate the fraction
With $r=\frac{75}{99}$ and $\sum d^2=40$:
$$\dfrac{6(40)}{n(n^2-1)}=1-\dfrac{75}{99}=\dfrac{24}{99}$$

### Step 3 — Solve for n
$$n(n^2-1)=\dfrac{240	imes 99}{24}=10	imes 99=990$$
Since $n(n^2-1)=990$ and $10	imes(100-1)=10	imes 99=990$, we get $n=10$. …

Student	Judge X rank	Judge Y rank	$d$	$d^{2}$
A	1	2	$-1$	1
B	2	1	$1$	1
C	3	4	$-1$	1
D	4	3	$1$	1
E	5	5	$0$	0

Spearman's Rank Correlation

How it works

Interpreting and adjusting

Quick example

Step 1 — Write Spearman's rank correlation formula

Step 2 — Isolate the fraction

Step 3 — Solve for n

Step 1 — Write Spearman's rank correlation formula

Step 2 — Isolate the fraction

Step 3 — Solve for n

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