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AP EAMCET · Maths · Statistics

Let \(x_1, x_2, \ldots, x_{11}\) be the observations satisfying \(\sum_{i=1}^{11}\left(x_i-4\right)=22\) and \(\sum_{i=1}^{11}\left(x_i-4\right)^2=154\). If the mean and variance of the observations are \(\alpha\) and \(\beta\), then the quadratic equation having the roots \(\frac{\alpha}{\beta}\) and \(\frac{\beta}{\alpha}\) is

  1. A \(15 x^2-16 x+15=0\)
  2. B \(15 x^2-34 x+15=0\)
  3. C \(x^2-16 x+60=0\)
  4. D \(12 x^2-25 x+20=0\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(15 x^2-34 x+15=0\)

Step-by-step Solution

Detailed explanation

\(\bar{y} = \frac{\sum (x_i-4)}{11} = \frac{22}{11} = 2\) \(\alpha = \bar{x} = \bar{y} + 4 = 2+4 = 6\) \(\beta = \frac{\sum (x_i-4)^2}{11} - \left(\frac{\sum (x_i-4)}{11}\right)^2 = \frac{154}{11} - 2^2 = 14-4 = 10\) Roots: \(\frac{\alpha}{\beta} = \frac{6}{10} = \frac{3}{5}\),…
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