Statistics
Combined variance of two classes
nta_pyq_2023_jan
Grade 11
Question:
Let the mean and standard deviation of marks of class A of 100 students be respectively 40 and $\alpha(> 0)$, and the mean and standard deviation of marks of class B of $n$ students be respectively 55 and $30 - \alpha$. 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
Key Concept: From combined mean: $n = 200$. Use combined variance formula to set up equation in $\alpha$. Solve for $\alpha$ and then compute $\sigma_A^2 + \sigma_B^2$.
$n = 200$. Solving: $\alpha = 10$, $30-\alpha = 20$. $\sigma_A^2 + \sigma_B^2 = 100 + 400 = 500$.
Correct Answer: 1