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Find Standard Deviation(S.D.) and Coefficient of Variation for grouped data

Calculate Coefficient of variation from the follwing grouped data Class Frequency 2 - 4 3 4 - 6 4 6 - 8 2 8 - 10 1 Solution: Class `(1)` Frequency `(f)` `(2)` Mid value `(x)` `(3)` `f*x` `(4)=(2)xx(3)` `f*x^2=(f*x)xx(x)` `(5)=(4)xx(3)` 2-4 3  3 `3=(2+4)/2`  9 `9=3xx3` `(4)=(2)xx(3)`  27 `27=9xx3` `(5)=(4)xx(3)` 4-6 4  5 `5=(4+6)/2`  20 `20=4xx5` `(4)=(2)xx(3)`  100 `100=20xx5` `(5)=(4)xx(3)` 6-8 2  7 `7=(6+8)/2`  14 `14=2xx7` `(4)=(2)xx(3)`  98 `98=14xx7` `(5)=(4)xx(3)` 8-10 1  9 `9=(8+10)/2`  9 `9=1xx9` `(4)=(2)xx(3)`  81 `81=9xx9` `(5)=(4)xx(3)` --- --- --- --- --- -- `n = 10` -- `sum f*x=52` `sum f*x^2=306` Mean `bar x = (sum fx)/n` `=52/10` `=5.2` `sigma = sqrt((sum f*x^2)/n - ((sum f*x)/n)^2)` `=sqrt(306/10 - (52/10)^2)` `=sqrt(306/10 - 2704/100)` `=sqrt(30.6 - 27.04)` `=sqrt(3.56)` `=1.89` Co-efficient of Variation `=sigma / bar x * 100 %` `=1.89/5.2 * 100 %` `=36.28 %`