Formula

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

2. Population Variance `sigma^2 = (sum x^2 - (sum x)^2/n)/n`

3. Population Standard deviation `sigma = sqrt((sum x^2 - (sum x)^2/n)/n)`

4. Coefficient of Variation (Population) `=sigma / bar x * 100 %`

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Examples
1. Calculate Population Variance `(sigma^2)`, Population Standard deviation `(sigma)`, Population Coefficient of Variation from the following data
3,13,11,15,5,4,2,3,2

Solution:

`x`	`x^2`
3	9 `9=3xx3`
13	169 `169=13xx13`
11	121 `121=11xx11`
15	225 `225=15xx15`
5	25 `25=5xx5`
4	16 `16=4xx4`
2	4 `4=2xx2`
3	9 `9=3xx3`
2	4 `4=2xx2`
---	---
`sum x=58`	`sum x^2=582`

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

`=(3 + 13 + 11 + 15 + 5 + 4 + 2 + 3 + 2)/9`

`=58/9`

`=6.4444`

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Population Variance `sigma^2 = (sum x^2 - (sum x)^2/n)/n`

`=(582 - (58)^2/9)/9`

`=(582 - 373.7778)/9`

`=208.2222/9`

`=23.1358`

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Population Standard deviation `sigma = sqrt((sum x^2 - (sum x)^2/n)/n)`

`=sqrt((582 - (58)^2/9)/9)`

`=sqrt((582 - 373.7778)/9)`

`=sqrt(208.2222/9)`

`=sqrt(23.1358)`

`=4.81`

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Coefficient of Variation (Population) `=sigma / bar x * 100 %`

`=4.81/6.4444 * 100 %`

`=74.64 %` 2. Calculate Population Variance `(sigma^2)`, Population Standard deviation `(sigma)`, Population 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 `-3=85-88`	9 `9=-3xx-3`
96	8 `8=96-88`	64 `64=8xx8`
76	-12 `-12=76-88`	144 `144=-12xx-12`
108	20 `20=108-88`	400 `400=20xx20`
85	-3 `-3=85-88`	9 `9=-3xx-3`
80	-8 `-8=80-88`	64 `64=-8xx-8`
100	12 `12=100-88`	144 `144=12xx12`
85	-3 `-3=85-88`	9 `9=-3xx-3`
70	-18 `-18=70-88`	324 `324=-18xx-18`
95	7 `7=95-88`	49 `49=7xx7`
---	---	---
`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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Population Variance `sigma^2 = (sum (x - bar x)^2)/n`

`=1216/10`

`=121.6`

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Population Standard deviation `sigma = sqrt((sum (x - bar x)^2)/n)`

`=sqrt(1216/10)`

`=sqrt(121.6)`

`=11.0272`

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Coefficient of Variation (Population) `=sigma / bar x * 100 %`

`=11.0272/88 * 100 %`

`=12.53 %`

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