JEE Mains · Maths · STD 11 - 13. statistics
If the mean and the standard deviation of the data \(3,5,7, a, b\) are \(5\) and \(2\) respectively, then \(a\) and \(b\) are the roots of the equation
- A \(2 x^{2}-20 x+19=0\)
- B \(x^{2}-10 x+19=0\)
- C \(x^{2}-10 x+18=0\)
- D \(x^{2}-20 x+18=0\)
Answer & Solution
Correct Answer
(B) \(x^{2}-10 x+19=0\)
Step-by-step Solution
Detailed explanation
Mean \(=5\) \(\frac{3+5+7+a+b}{5}=5\) \(a+b=10\) S.d. \(=2 \Rightarrow \sqrt{\frac{\sum_{i=1}^{5}\left(x_{i}-\bar{x}\right)^{2}}{5}}=2\) \((3-5)^{2}+(5-5)^{2}+(7-5)^{2}+(a-5)^{2}+(b-5)^{2}=20\) \(\Rightarrow 4+0+4+(a-5)^{2}+(b-5)^{2}=20\) \(a^{2}+b^{2}-10(a+b)+50=12\)…
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