JEE Mains · Maths · STD 11 - 13. statistics
If the standard deviation of the numbers \( 2,3,a \) and \(11\) is \(3.5\) then which of the following is true ?
- A \(3{a^2} - 34a + 91 = 0\)
- B \(\;3{a^2} - 23a + 44 = 0\)
- C \(3{a^2} - 26a + 55 = 0\)
- D \(\;3{a^2} - 32a + 84 = 0\)
Answer & Solution
Correct Answer
(D) \(\;3{a^2} - 32a + 84 = 0\)
Step-by-step Solution
Detailed explanation
\(\mathrm{SD}=\sqrt{\frac{\Sigma \mathrm{x}_{\mathrm{i}}^{2}}{\mathrm{n}}-\left(\frac{\Sigma \mathrm{x}_{\mathrm{i}}}{\mathrm{n}}\right)^{2}}\) \(\frac{49}{4}=\frac{4+9+a^{2}+121}{4}-\left(\frac{16+a}{4}\right)^{2}\) \(3 a^{2}-32 a+84=0\)
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