The following ranks are obtained about the sales and profits of different electric companies. Find rank correl

Question 27 of 42

The following ranks are obtained about the sales and profits of different electric companies. Find rank correlation coefficient.

Ranks of Sales ( $X$ )	7.5	5.5	1	4	5.5	7.5	3	2
Ranks of Profit ( $Y$ )	7	4	1	5	7	7	3	2

Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2023Subjective· 3mImportance★★★★★

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$\sum d^2=6$ ; tie corrections: two pairs in $X$ ( $=1$ ) + one triple in $Y$ ( $=2$ ) $=3$ ; $r=1-\dfrac{6(6+3)}{8\cdot63}=0.8929\approx0.89$ .

Here $n=8$ and there are tied ranks, so we use the tie-corrected Spearman formula:

$r=1-\frac{6\left[\sum d^2+\sum\frac{m(m^2-1)}{12}\right]}{n(n^2-1)}.$

Step 1 — differences $d=X-Y$ and $d^2$ :

$X$	$Y$	$d=X-Y$	$d^2$
7.5	7	0.5	0.25
5.5	4	1.5	2.25
1	1	0	0
4	5	-1	1
5.5	7	-1.5	2.25
7.5	7	0.5	0.25
3	3	0	0
2	2	0	0
			$\sum d^2=6$

Step 2 — tie corrections $\dfrac{m(m^2-1)}{12}$ : …