Question

9. Given the following data, determine the nu- merical value of each of the expressions below. Person (i) X, 610 99/ 4 5 25 4 0 7 49 749 8 i.ΣΧ Xi 10. Given the data from Exercise 9 for X and Yan that c, a constant, equals 3, determine the nu merical value for the following expressions:

Answer 1

Question 9 :

Person	Xi	Yi	Xi +Yi	XiYi	Xi2	Yi2
1	6	9	15	54	36	81
2	4	5	9	20	16	25
3	6	3	9	18	36	9
4	0	7	7	0	0	49
5	7	8	15	56	49	64
Total	23	32	55	148	137	228

g) $\sum_{i=1}^{5}Xi^{2} = 137$

h) $\left ( \sum_{i=1}^{5}Xi \right )^{2} = 23^{2} = 529$

i) $\sum X= \sum_{i=1}^{5}Xi = 23$

j)  $\sum Y^{2}= \sum_{i=1}^{5}Yi^{2} =228$

k) $\left ( \sum Y \right )^{2} =\left ( \sum_{i=1}^{5}Y \right )^{2} = 32^{2} =1024$

l) $\sum X +\sum Y= 23 +32 = 55$

Question 10 :

c= 3

Person	Xi	Yi	C(Xi+Yi)	Cxi	Cyi	C*Xi * Yi
1	6	9	45	18	27	162
2	4	5	27	12	15	60
3	6	3	27	18	9	54
4	0	7	21	0	21	0
5	7	8	45	21	24	168
Total	23	32	165	69	96	444

a) $\sum_{i=1}^{5}cXi = 69$

b) $\sum cXY= \sum_{i=1}^{5}cXiYi =444$

c)$\sum c(X+Y)=\sum_{i=1}^{5}c(Xi+Yi) =165$

d) $\sum_{i=1}^{5}c=\sum_{i=1}^{5}3= 3 *5 = 15$

e) $\sum_{i=1}^{3}(X+c) = \sum_{i=1}^{3}Xi + \sum_{i=1}^{3} 3= ( 6+ 4 +6 ) + ( 3*3) = 25$