2. Covariance - Population Covariance, Sample Covariance Example-4 (X & Y)

We use cookies to improve your experience on our site and to show you relevant advertising. By browsing this website, you agree to our use of cookies. Learn more

Support us

Home > Statistical Methods calculators > Covariance - Population Covariance, Sample Covariance example

2. Covariance - Population Covariance, Sample Covariance example ( Enter your problem )

( Enter your problem )

Other related methods

Correlation Coefficient r
Covariance - Population Covariance, Sample Covariance

3. Example-3 (X & Y)
(Previous example)

4. Example-4 (X & Y)

4. Calculate Population cov(x,y), Sample cov(x,y) from the following data
X Y
300 800
350 900
400 1000
450 1100
500 1200
550 1300
600 1400
650 1500
700 1600

Solution:
Mean `bar x = (sum x_i)/n`

`=(300+350+400+450+500+550+600+650+700)/9`

`=4500/9`

`=500`

Mean `bar y = (sum y_i)/n`

`=(800+900+1000+1100+1200+1300+1400+1500+1600)/9`

`=10800/9`

`=1200`

`x`	`y`	`X=(x-500)/50`	`Y=(y-1200)/100`	*`XY`**
300	800	-4	-4	16
350	900	-3	-3	9
400	1000	-2	-2	4
450	1100	-1	-1	1
500	1200	0	0	0
550	1300	1	1	1
600	1400	2	2	4
650	1500	3	3	9
700	1600	4	4	16
---	---	---	---	---
`4500`	`10800`	`sum X=0`	`sum Y=0`	`sum X*Y=60`

Population Cov(x,y) :

Population `Cov(x,y) = (sum (x-bar x)(y-bar y))/(n)`

`=60/9`

`=6.6667`

Sample Cov(x,y) :

Sample `Cov(x,y) = (sum (x-bar x)(y-bar y))/(n-1)`

`=60/8`

`=7.5`

This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then Submit Here