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Problem: Sample Standard Deviation {{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 -> Sample Standard Deviation {{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 3 3 2 4 2 8 16 5 10 5 50 250 6 - 10 23 8 184 1472 10 - 20 20 15 300 4500 20 - 30 20 25 500 12500 30 - 50 15 40 600 24000 50 - 70 3 60 180 10800 70 - 100 2 85 170 14450 --- --- --- --- --- n = 100 ----- sum f*x=1995 sum f*x^2=67991

Mean bar x = (sum fx)/n

=1995/100

=19.95

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

=sqrt((67991 - (1995)^2/100)/99)

=sqrt((67991 - 39800.25)/99)

=sqrt(28190.75/99)

=sqrt(284.7551)

=16.8747

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