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 MATHEMATICS MCQ: STATISTICS

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Analyzing +4 | -1

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

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:

View answer and explanation

Correct option: D

500

Option D (500) is correct because, after setting up equations for the means and variances of the two classes and the combined class, solving for the unknowns yields the sum of the variances of classes A and B as 500.

JEE MATHEMATICS MCQ: STATISTICS

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