## 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
1. What do you mean by bivariate data?
2. 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 $\sum_{i=1}^{10}x_iy_i \ne (\sum_{i=1}^{10}x_i)(\sum_{i=1}^{10}y_j)$