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2. Covariance - Population Covariance, Sample Covariance example ( Enter your problem )
  1. Formula & Example-1 (Class-X & Y)
  2. Example-2 (Class-X & Y)
  3. Example-3 (X & Y)
  4. Example-4 (X & Y)
Other related methods
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  2. 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
XY
300800
350900
4001000
4501100
5001200
5501300
6001400
6501500
7001600


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``X*Y`
300800-4-416
350900-3-39
4001000-2-24
4501100-1-11
5001200000
5501300111
6001400224
6501500339
70016004416
---------------
`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.
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3. Example-3 (X & Y)
(Previous example)





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