Let the mean and standard deviation of marks of class A of students be respectively and , and the mean and standard deviation of marks of class B of students be respectively and . If the mean and variance of the marks of the combined class of students are respectively and , then the sum of variances of classes A and B is :

Explanation: Solution 1. Find using the combined mean: Combined Mean 2. Use the combined variance formula: , where and . and . Since standard deviation of B ( ) must be positive, cannot be . Thus, . 3. Sum of Variances: Variance A . Variance B . Sum . Correct Option: (4)

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

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 :

JEE 2023 — Mathematics PYQ

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