JEE Mains · Maths · STD 11 - 13. statistics
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
- A \(500\)
- B \(650\)
- C \(450\)
- D \(900\)
Answer & Solution
Correct Answer
(A) \(500\)
Step-by-step Solution
Detailed explanation
\(A\) \(B\) \(A+B\) \(\overline{ x }_1=40\) \(\overline{ x }_2=55\) \(\overline{ x }=50\) \(\sigma_1=\alpha\) \(\sigma_2=30-\alpha\) \(\sigma^2=350\) \(n _1=100\) \(n _2= n\) \(100+ n\) \(\overline{ x }=\frac{100 \times 40+55 n }{100+ n }\) \(5000+50 n =4000+55 n\) \(1000=5 n\)…
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