Let the mean and standard deviation of marks of class A of 100 students be respectively 40 (0), and the mean and standard deviation of marks of class B of n students be respectively 55 and 30- . If…

Question

Let the mean and standard deviation of marks of class A of 100 students be respectively 40 (>0), and the mean and standard deviation of marks of class B of n students be respectively 55 and 30- . If the mean and variance of the marks of the combined class of 100 + n students are respectively 50 and 350, then the sum of variance of classes A and B is

Accepted Answer

Correct answer: A. (a) Solution A B A+B x_1=40 x_2=55 x=50 _1= _2=30- ^2=350 n_1=100 n_2=n 100+n x= 100 40+55n100+n 5000+50n=4000+55n 1000=5n n=200 _1^2= x_1^2100-55^2 350= ^2= x_i^2+ x_i^2300- (x )^2 350= (1600+ ^2) 100+((30- )^2+3025) 200300- (50 )^2 2850 3= ^2+2(30- )^2+1600+6050 8550= ^2+2(20- )^2+7650 ^2+2(30- )^2=900 ^2-40 +300=0 =10 ,30 _1^2+ _2^2=10^2+20^2=500

Solution

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