1. Calculate Sample Coefficient of Variation from the following data
`3,13,11,15,5,4,2`

Solution:

`x`	`x^2`
3	9
13	169
11	121
15	225
5	25
4	16
2	4
---	---
`sum x=53`	`sum x^2=569`

Mean `bar x=(sum x)/n`

`=(3+13+11+15+5+4+2)/7`

`=53/7`

`=7.5714`

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Sample Standard deviation `S = sqrt((sum x^2 - (sum x)^2/n)/(n-1))`

`=sqrt((569 - (53)^2/7)/6)`

`=sqrt((569 - 401.2857)/6)`

`=sqrt(167.7143/6)`

`=sqrt(27.9524)`

`=5.287`

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Coefficient of Variation (Sample) `=S / bar x * 100 %`

`=5.287/7.5714 * 100 %`

`=69.83 %`

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2. Calculate Sample Coefficient of Variation from the following data
`10,50,30,20,10,20,70,30`

Solution:

`x`	`x - bar x = x - 30`	`(x - bar x)^2`
10	-20	400
50	20	400
30	0	0
20	-10	100
10	-20	400
20	-10	100
70	40	1600
30	0	0
---	---	---
`sum x=240`	`sum (x - bar x)=0`	`sum (x - bar x)^2=3000`

Mean `bar x=(sum x)/n`

`=(10+50+30+20+10+20+70+30)/8`

`=240/8`

`=30`

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Sample Standard deviation `S = sqrt((sum (x - bar x)^2)/(n-1))`

`=sqrt(3000/7)`

`=sqrt(428.5714)`

`=20.702`

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Coefficient of Variation (Sample) `=S / bar x * 100 %`

`=20.702/30 * 100 %`

`=69.01 %`

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3. Calculate Sample Coefficient of Variation from the following data
`85,96,76,108,85,80,100,85,70,95`

Solution:

`x`	`x - bar x = x - 88`	`(x - bar x)^2`
85	-3	9
96	8	64
76	-12	144
108	20	400
85	-3	9
80	-8	64
100	12	144
85	-3	9
70	-18	324
95	7	49
---	---	---
`sum x=880`	`sum (x - bar x)=0`	`sum (x - bar x)^2=1216`

Mean `bar x=(sum x)/n`

`=(85+96+76+108+85+80+100+85+70+95)/10`

`=880/10`

`=88`

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Sample Standard deviation `S = sqrt((sum (x - bar x)^2)/(n-1))`

`=sqrt(1216/9)`

`=sqrt(135.1111)`

`=11.6237`

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Coefficient of Variation (Sample) `=S / bar x * 100 %`

`=11.6237/88 * 100 %`

`=13.21 %`

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