JEE Mains · Maths · STD 11 - 13. statistics
Let the mean and the variance of seven observations \(2, 4, \alpha, 8, \beta, 12, 14\), \(\alpha < \beta\), be \(8\) and \(16\) respectively. Then the quadratic equation whose roots are \(3\alpha + 2\) and \(2\beta + 1\) is :
- A \(x^2 - 35x + 306 = 0\)
- B \(x^2 - 41x + 420 = 0\)
- C \(x^2 - 45x + 506 = 0\)
- D \(x^2 - 37x + 342 = 0\)
Answer & Solution
Correct Answer
(B) \(x^2 - 41x + 420 = 0\)
Step-by-step Solution
Detailed explanation
Given the mean of the seven observations is \(8\): \(\dfrac{2 + 4 + \alpha + 8 + \beta + 12 + 14}{7} = 8\) \(\dfrac{40 + \alpha + \beta}{7} = 8\) \(\alpha + \beta = 16\) Given the variance of the observations is \(16\): \(\dfrac{\sum x_i^2}{n} - (\text{Mean})^2 = 16\)…
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