MCQ 11 Mark
Find out Karl Pearson’s coefficient of correlation in the following series relating to prices and demand of a commodity.
| Price (Rs.) | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Demand | 30 | 29 | 29 | 25 | 24 | 24 | 24 | 21 | 18 | 15 |
- A$0.92$
- ✓$0.94$
- C$0.98$
- D$0.96$
Answer
View full question & answer→Correct option: B.
$0.94$
(b) 0.94
Explanation:
$\begin{aligned} r & =\frac{N \sum d x d y-\sum d x \sum d y}{\sqrt{N \sum(d x)^2-\left(\sum d x\right)^2} \sqrt{N \sum(d y)^2-\left(\sum d y\right)^2}} \\ & =\frac{10(27)-(-1)(1)}{\sqrt{10(85)-(-1)^2} \sqrt{10(213)-(1)^2}}=0.94\end{aligned}$
Explanation:
| Price(X) | DD(Y) | dx | dy | dx2 | dy2 | dxdy |
| 11 | 30 | -5 | -6 | 25 | 36 | 30 |
| 12 | 29 | -4 | -5 | 16 | 25 | 20 |
| 13 | 29 | -3 | -5 | 9 | 25 | 15 |
| 14 | 25 | -2 | -1 | 4 | 1 | 2 |
| 15 | 24 | -1 | 0 | 1 | 0 | 0 |
| 16 | 24 | 0 | 0 | 0 | 0 | 0 |
| 17 | 24 | 1 | 0 | 1 | 0 | 0 |
| 18 | 21 | 2 | 3 | 4 | 9 | 6 |
| 19 | 18 | 3 | 6 | 9 | 36 | 18 |
| 20 | 15 | 4 | 9 | 16 | 81 | 36 |
| -1 | 1 | 85 | 213 | 127 |