Advertisements
Advertisements
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.
Advertisements
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
APPEARS IN
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.
Compute the coefficient of correlation for the following data :
n = 100 ; `bar x` = 62 , ` bar y` = 53 . σx = 10 ; σ y = 12 ,
`sum ("x"_1 - bar x) ("y"_1 - bar y) = 8000`
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 .
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 the two subjects related?
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 |
What are various steps for the calculation of rank order correlation?
