(a) The following are the ranks obtained by 10 students in Commerce and Accountancy are given below : | Commerce | 6 | 4 | 3 | 1 | 2 | 7 | 9 | 8 | 10 | 5 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Accountancy | 4 | 1 | 6 | 7 | 5 | 8 | 10 | 9 | 3 | 2 | To what extent is the knowledge of students in two subjects related? OR (b) A person sells a 20% stocks of Face Value $\text{\rupee}\,10{,}000$ at a premium of 42%. With the money obtained he buys a 15% stock at a discount of 22%. What is the change in his income if the brokerage paid is 2%.

> > [!TLDR] > (a) Rank correlation $\rho\approx0.22$ — weak positive. (b) The person's income rises by ₹625. > > ## (a) Spearman's rank correlation > > | Commerce $R_1$ | 6 | 4 | 3 | 1 | 2 | 7 | 9 | 8 | 10 | 5 | > | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | > | Accountancy $R_2$ | 4 | 1 | 6 | 7 | 5 | 8 | 10 | 9 | 3 | 2 | > | $d$ | 2 | 3 | -3 | -6 | -3 | -1 | -1 | -1 | 7 | 3 | > | $d^2$ | 4 | 9 | 9 | 36 | 9 | 1 | 1 | 1 | 49 | 9 | > > $\sum d^{2}=128,\ n=10.$ > $$\rho=1-\frac{6\times128}{10(99)}=1-\frac{768}{990}=1-0.776=0.224\approx0.22.$$ > So the two subjects are only weakly (low) positively related. > > ## (b) Stocks with brokerage …

(a) The following are the ranks obtained by 10 stu – Class 11 Business Mathematics Statistics

Question 27 of 31

(a) The following are the ranks obtained by 10 students in Commerce and Accountancy are given below :

Commerce	6	4	3	1	2	7	9	8	10	5
Accountancy	4	1	6	7	5	8	10	9	3	2

To what extent is the knowledge of students in two subjects related?

(b) A person sells a 20% stocks of Face Value $\text{\text{₹}}\,10{,}000$ at a premium of 42%. With the money obtained he buys a 15% stock at a discount of 22%. What is the change in his income if the brokerage paid is 2%.

Puducherry TnboardTamil Nadu HSC First Year (DGE) Commerce Board 2024Subjective· 5mImportance★★★★★

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(a) Rank correlation $\rho\approx0.22$ — weak positive. (b) The person's income rises by ₹625.

(a) Spearman's rank correlation

Commerce $R_1$	6	4	3	1	2	7	9	8	10	5
Accountancy $R_2$	4	1	6	7	5	8	10	9	3	2
$d$	2	3	-3	-6	-3	-1	-1	-1	7	3
$d^2$	4	9	9	36	9	1	1	1	49	9

$\sum d^{2}=128,\ n=10.$

$\rho=1-\frac{6\times128}{10(99)}=1-\frac{768}{990}=1-0.776=0.224\approx0.22.$

So the two subjects are only weakly (low) positively related.

(b) Stocks with brokerage …

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(a) Spearman's rank correlation

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