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Problem: coefficient of variation {{1,3},{2,4},{5,10},{6-10,23},{10-20,20},{20-30,20},{30-50,15},{50-70,3},{70-100,2}} [ Calculator, Method and examples ]

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Your problem -> coefficient of variation {{1,3},{2,4},{5,10},{6-10,23},{10-20,20},{20-30,20},{30-50,15},{50-70,3},{70-100,2}}

 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) 1 3 1 1=1 3 3=3xx1(4)=(2)xx(3) 3 3=3xx1(5)=(4)xx(3) 2 4 2 2=2 8 8=4xx2(4)=(2)xx(3) 16 16=8xx2(5)=(4)xx(3) 5 10 5 5=5 50 50=10xx5(4)=(2)xx(3) 250 250=50xx5(5)=(4)xx(3) 6 - 10 23 8 8=(6+10)/2 184 184=23xx8(4)=(2)xx(3) 1472 1472=184xx8(5)=(4)xx(3) 10 - 20 20 15 15=(10+20)/2 300 300=20xx15(4)=(2)xx(3) 4500 4500=300xx15(5)=(4)xx(3) 20 - 30 20 25 25=(20+30)/2 500 500=20xx25(4)=(2)xx(3) 12500 12500=500xx25(5)=(4)xx(3) 30 - 50 15 40 40=(30+50)/2 600 600=15xx40(4)=(2)xx(3) 24000 24000=600xx40(5)=(4)xx(3) 50 - 70 3 60 60=(50+70)/2 180 180=3xx60(4)=(2)xx(3) 10800 10800=180xx60(5)=(4)xx(3) 70 - 100 2 85 85=(70+100)/2 170 170=2xx85(4)=(2)xx(3) 14450 14450=170xx85(5)=(4)xx(3) --- --- --- --- --- n = 100 ----- sum f*x=1995 sum f*x^2=67991

Mean bar x = (sum fx)/n

=1995/100

=19.95

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

=sqrt((67991 - (1995)^2/100)/100)

=sqrt((67991 - 39800.25)/100)

=sqrt(28190.75/100)

=sqrt(281.9075)

=16.7901

Co-efficient of Variation (Population) =sigma / bar x * 100 %

=16.7901/19.95 * 100 %

=84.16 %

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