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Find Standard Deviation for ungrouped Data
1. Calculate Coefficient of variation from the follwing data
69,66,67,69,64,63,65,68,72
Solution:
`x`
`x - bar x = x - 67`
`(x - bar x)^2`
69
2
`2=69-67`
4
`4=2xx2`
66
-1
`-1=66-67`
1
`1=-1xx-1`
67
0
`0=67-67`
0
`0=0xx0`
69
2
`2=69-67`
4
`4=2xx2`
64
-3
`-3=64-67`
9
`9=-3xx-3`
63
-4
`-4=63-67`
16
`16=-4xx-4`
65
-2
`-2=65-67`
4
`4=-2xx-2`
68
1
`1=68-67`
1
`1=1xx1`
72
5
`5=72-67`
25
`25=5xx5`
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`sum x=603`
`sum (x - bar x)=0`
`sum (x - bar x)^2=64`
Mean `bar x = (sum x)/n`
`=(69 + 66 + 67 + 69 + 64 + 63 + 65 + 68 + 72)/9`
`=603/9`
`=67`
`sigma = sqrt((sum (x - bar x)^2)/n)`
`=sqrt(64/9)`
`=sqrt(7.11)`
`=2.67`
Co-efficient of Variation `=sigma / bar x * 100 %`
`=2.67/67 * 100 %`
`=3.98 %`