1.26 Creative Questions
Given below are the daily income and expense of ten workers.
| Income (x) | 120 | 130 |
|---|---|---|
| Expense (y) | 80 | 120 |
From above data, prove
- \[\sum_{i=1}^{2}x_iy_i \ne (\sum_{i=1}^{2}x_i)(\sum_{i=1}^{2}y_j)\]
- \[\sum_{i=1}^{2} \sum_{j=1}^{2}x_iy_j=(\sum_{i=1}^{2}x_i)(\sum_{j=1}^{2}y_j)\]
- \[\sum_{i=1}^{2} \sum_{j=1}^{2}(x_i-y_j)=2 \times \sum_{i=1}^{2}x_i- 2 \times \sum_{j=1}^{2}y_j\]
Question 02
Given below are the daily income and expense of ten workers.
| Income (x) | 120 | 130 | 88 | 150 | 175 | 144 | 180 | 200 | 160 | 155 |
|---|---|---|---|---|---|---|---|---|---|---|
| Expense (y) | 80 | 120 | 70 | 100 | 160 | 114 | 170 | 195 | 140 | 131 |
- What do you mean by bivariate data?
- From above data, prove
\[\sum_{i=1}^{10} \sum_{j=1}^{10}x_iy_j=(\sum_{i=1}^{10}x_i)(\sum_{j=1}^{10}y_j)\] c. \[\sum_{i=1}^{10} \sum_{j=1}^{10}(x_i-y_j)=10 \times \sum_{i=1}^{10}x_i- 10 \times \sum_{j=1}^{10}y_j\] d. Prove \[\sum_{i=1}^{10}x_iy_i \ne (\sum_{i=1}^{10}x_i)(\sum_{i=1}^{10}y_j)\]