Question

For the following pairs of observations (1,10), (2, 9), (3, 9), (4, 8), (5, 6), (6, 12), (7, 4), (8, 3), (9, 13), (10, 1) Cov (x, y) =

• A. 1.05
• B. 2.45
• C. – 4.45
• D. – 4.9

Answer 1

Answer: (C)

– 4.45

Answer 2

Here $\bar{x} = 5.5,\bar{y} = 7.5$

$x - \bar{x}$	$y - \bar{y}$	$(x - \bar{x})(y - \bar{y})$
– 4.5	2.5	– 11.25
– 3.5	1.5	– 5.25
– 2.5	1.5	– 3.75
– 1.5	0.5	– 0.75
– 0.5	– 1.5	0.75
0.5	4.5	2.25
1.5	– 3.5	– 5.25
2.5	– 4.5	– 11.25
3.5	5.5	19.25
4.5	– 6.5	– 29.25

$Cov(x,y) = \frac{\sum(x - \bar{x})(y - \bar{y})}{n} = \frac{- 44.5}{10} = - 4.45$.