Let the mean and standard deviation of marks of class A of 100 students be respectively 40 and α > 0 , and the mean and standard deviation of marks of class B of n students be respectively 55 and 30 - α . 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 variances of classes A and B is

Step-by-step solution

Let the mean is denoted by x i ¯ , variance by σ i 2 , so standard deviation will be σ i , now as per given data we get, A   B   A + B x ¯ 1 = 40   x ¯ 2 = 55   x ¯ = 50 σ 1 = α   σ 2 = 30 - α   σ 2 = 350 n 1 = 100   n 2 = n   100 + n So, using the formula of mean in A + B we get, x ¯ = 100 × 40 + 55 n 100 + n = 50 ⇒     n = 200 Now using the formula of variance we get, σ 1 2 = ∑ x i 2