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Find Sample coefficient of variation {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}} [ Calculator, Method and examples ]

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Your problem -> Sample coefficient of variation {{10-20,15},{20-30,25},{30-40,20},{40-50,12},{50-60,8}}

 Class(1) Frequency (f)(2) Mid value (x)(3) d=(x-A)/h=(x-35)/10A=35,h=10(4) f*d(5)=(2)xx(4) f*d^2(6)=(5)xx(4) 10 - 20 15 15 15=(10+20)/2 -2 d=(15-35)/10=(-20)/10=-2d=(x-35)/10 -30 -30=15xx-2(5)=(2)xx(4) 60 60=-30xx-2(6)=(5)xx(4) 20 - 30 25 25 25=(20+30)/2 -1 d=(25-35)/10=(-10)/10=-1d=(x-35)/10 -25 -25=25xx-1(5)=(2)xx(4) 25 25=-25xx-1(6)=(5)xx(4) 30 - 40 20 35=A 35=(30+40)/2 0 d=(35-35)/10=(0)/10=0d=(x-35)/10 0 0=20xx0(5)=(2)xx(4) 0 0=0xx0(6)=(5)xx(4) 40 - 50 12 45 45=(40+50)/2 1 d=(45-35)/10=(10)/10=1d=(x-35)/10 12 12=12xx1(5)=(2)xx(4) 12 12=12xx1(6)=(5)xx(4) 50 - 60 8 55 55=(50+60)/2 2 d=(55-35)/10=(20)/10=2d=(x-35)/10 16 16=8xx2(5)=(2)xx(4) 32 32=16xx2(6)=(5)xx(4) --- --- --- --- --- --- n = 80 ----- ----- sum f*d=-27 sum f*d^2=129

Mean bar x = A + (sum fd)/n * h

=35 + -27/80 * 10

=35 + -0.3375 * 10

=35 + -3.375

=31.625

Sample Standard deviation S = sqrt((sum f*d^2 - (sum f*d)^2/n)/(n-1)) * h

=sqrt((129 - (-27)^2/80)/79) * 10

=sqrt((129 - 9.1125)/79) * 10

=sqrt(119.8875/79) * 10

=sqrt(1.5176) * 10

=1.2319 * 10

=12.3189

Co-efficient of Variation (Sample) =S / bar x * 100 %

=12.3189/31.625 * 100 %

=38.95 %

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