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प्रश्न
An examination of 11 applicants for a accountant post was taken by a finance company. The marks obtained by the applicants in the reasoning and aptitude tests are given below.
| Applicant | A | B | C | D | E | F | G | H | I | J | K |
| Reasoning test | 20 | 50 | 28 | 25 | 70 | 90 | 76 | 45 | 30 | 19 | 26 |
| Aptitude test | 30 | 60 | 50 | 40 | 85 | 90 | 56 | 82 | 42 | 31 | 49 |
Calculate Spearman’s rank correlation coefficient from the data given above.
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उत्तर
| X | Y | RX | RY | d = RX − RY | d2 |
| 20 | 30 | 10 | 11 | − 1 | 1 |
| 50 | 60 | 4 | 4 | 0 | 0 |
| 28 | 50 | 7 | 6 | 1 | 1 |
| 25 | 40 | 9 | 9 | 0 | 0 |
| 70 | 85 | 3 | 2 | 1 | 1 |
| 90 | 90 | 1 | 1 | 0 | 0 |
| 76 | 56 | 2 | 5 | − 3 | 9 |
| 45 | 82 | 5 | 3 | 2 | 4 |
| 30 | 42 | 6 | 8 | − 2 | 4 |
| 19 | 31 | 11 | 10 | 1 | 1 |
| 26 | 49 | 8 | 7 | 1 | 1 |
| ∑d2 = 22 |
N = 11, Σd2 = 22
Rank correlation (ρ) = `1 - (6sum"d"^2)/("N"("N"^2 - 1))`
= `1 - (6 xx 22)/(11(121 - 1))`
= `1 - 12/120`
= 1 − 0.1
= 0.9
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If the sum of squares of differences of ranks for 10 pairs of observations is 66, find the rank correlation coefficient.
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| Marks by A | 81 | 72 | 60 | 33 | 29 | 11 | 56 | 42 |
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| Profit (₹ in lakh) | 6 | 5 | 7 | 7 | 8 | 12 | 11 |
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Variable of X = 9
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In a partially destroyed laboratory record of an analysis of regression data, the following data are legible :
Variable of X = 9
Regression equations : 8x - 10g + 66 = 0 and 40x- 18g = 214
Find Correlation coefficient between X and Y on the basis of the above information.
The ranks of the 10 students in Mathematics and Accountancy are as follows :
Two numbers given in the brackets denote the ranks of the students in Mathematics and Accountancy respectively.
(1. 1). (2. 10). (3. 3). (4. 4). (5. 5). (6. 7). (7. 2). (8. 6). (9. 8). (10. 9)
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| Commerce | 6 | 4 | 3 | 1 | 2 | 7 | 9 | 8 | 10 | 5 |
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| Rank of A | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
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