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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.
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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संबंधित प्रश्न
Coefficient of rank correlation between x and y is 0.5 and `sumd_i^2`= 42. Assuming that no ranks are repeated, find the number of pairs of observations.
If the sum of squares of differences of ranks for 10 pairs of observations is 66, find the rank correlation coefficient.
Calculate Spearman's Rank Correlation Coefficient between the following marks given by 'two' judges (A) and (B) to •eight' contestants in the elocution competition:
| Contestants | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Marks by A | 81 | 72 | 60 | 33 | 29 | 11 | 56 | 42 |
| Marks byB | 75 | 56 | 42 | 15 | 30 | 20 | 60 | 80 |
If the rank correlation coefficient is 0.6 and the sum of squares of differences of ranks is 66, then find the number of pairs of observations.
Draw scatter diagram for the following data and identify the type of correlation.
| capital (₹ in crore) | 2 | 3 | 4 | 5 | 6 | 8 | 9 |
| Profit (₹ in lakh) | 6 | 5 | 7 | 7 | 8 | 12 | 11 |
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 Mean values of X and Y on the basis of the above information .
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.
A random sample of recent repair jobs was selected and estimated cost and actual cost were recorded.
| Estimated cost | 300 | 450 | 800 | 250 | 500 | 975 | 475 | 400 |
| Actual cost | 273 | 486 | 734 | 297 | 631 | 872 | 396 | 457 |
Calculate the value of spearman’s correlation coefficient.
The rank of 10 students of the same batch in two subjects A and B are given below. Calculate the rank correlation coefficient.
| Rank of A | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Rank of B | 6 | 7 | 5 | 10 | 3 | 9 | 4 | 1 | 8 | 2 |
A random sample of recent repair jobs was selected and estimated cost, actual cost were recorded.
| Estimated cost | 30 | 45 | 80 | 25 | 50 | 97 | 47 | 40 |
| Actual cost | 27 | 48 | 73 | 29 | 63 | 87 | 39 | 45 |
Calculate the value of spearman’s correlation.
