From the following information, find the rank correlation coefficient between the sales (in thousand units) an

Question 35 of 42

From the following information, find the rank correlation coefficient between the sales (in thousand units) and the profit (in lakh ₹) :

Sales (thousand Units)	25	58	215	72	58	25	90	162
Profit (lakh ₹)	65	140	500	115	65	65	220	340

Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2025Subjective· 5mImportance★★★★★

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With average ranks for ties: $\Sigma d^2 = 6$ , tie correction $= 3$ , so $r = 1 - \dfrac{6(6+3)}{8(64-1)} = 1 - \dfrac{54}{504} \approx 0.893$ .

GSEB Class-12 Statistics, Linear Correlation (Spearman's rank correlation with ties):

Let $x$ = sales, $y$ = profit, $n = 8$ . Ranks are assigned by ascending order; tied values get the average of the ranks they occupy.

Sales ties: $25$ occurs twice (ranks 1, 2 → 1.5 each); $58$ occurs twice (ranks 3, 4 → 3.5 each).
Profit ties: $65$ occurs three times (ranks 1, 2, 3 → 2 each).

$x$	$y$	$R_x$	$R_y$	$d = R_x - R_y$	$d^2$
25	65	1.5	2	-0.5	0.25
58	140	3.5	5	-1.5	2.25
215	500	8	8	0	0
72	115	5	4	1	1
58	65	3.5	2	1.5	2.25
25	65	1.5	2	-0.5	0.25
90	220	6	6	0	0
162	340	7	7	0	0
					$\Sigma d^2 = 6$

Tie correction factor: $\sum \dfrac{m^3 - m}{12}$ for each tied group of size $m$ .

Sales: two groups of size 2 → $2 \times \dfrac{2^3 - 2}{12} = 2 \times \dfrac{6}{12} = 1$ …