If standard deviation of numbers 2,3,a and 11 is 3.5 then which of following is true ?

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13.Statistics

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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

$\;3{a^2} - 32a + 84 = 0$

(JEE MAIN-2016)

Solution

$\mathrm{SD}=\sqrt{\frac{\Sigma \mathrm{x}_{\mathrm{i}}^{2}}{\mathrm{n}}-\left(\frac{\Sigma \mathrm{x}_{\mathrm{i}}}{\mathrm{n}}\right)^{2}}$

$\frac{49}{4}=\frac{4+9+a^{2}+121}{4}-\left(\frac{16+a}{4}\right)^{2}$

$3 a^{2}-32 a+84=0$

Standard 11

Mathematics

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