Arrange the correlation coefficients computed from the following information…
2024
Arrange the correlation coefficients computed from the following information on covariance i.e. cov(x,y) and standard deviation σx and σy, in increasing order.
A. cov(x,y)=18, σx=4, σy=9
B. cov(x,y)=15, σx=8, σy=3
C. cov(x,y)=16, σx=7, σy=4
D. cov(x,y)=21, σx=6, σy=5
Choose the most appropriate answer from the options given below:
Answer: A. A, C, B, D — ConceptFor two variables x and y, the Pearson correlation coefficient is r = cov(x,y)/(σx × σy). It standardizes covariance by the product of the standard…
- A.
A, C, B, D
- B.
B, C, D, A
- C.
C, B, A, D
- D.
D, B, A, C
Show answer & explanation
Correct answer: A
Concept
For two variables x and y, the Pearson correlation coefficient is r = cov(x,y)/(σx × σy). It standardizes covariance by the product of the standard deviations, so the resulting unit-free values can be compared.
Application
For A: rA = 18/(4 × 9) = 1/2 = 0.500.
For B: rB = 15/(8 × 3) = 5/8 = 0.625.
For C: rC = 16/(7 × 4) = 4/7 ≈ 0.571.
For D: rD = 21/(6 × 5) = 7/10 = 0.700.
Cross-check
An independent decimal comparison gives 0.500 < 0.571 < 0.625 < 0.700, which maps to A < C < B < D.
Data set | Correlation coefficient | Ascending position |
|---|---|---|
A | 0.500 | 1 |
C | 0.571 | 2 |
B | 0.625 | 3 |
D | 0.700 | 4 |
Therefore, the increasing order is A, C, B, D.