Q50 / 90 · JEE Main 2016 (03 Apr) · Mathematics

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

A
$3 a^{2} - 34 a + 91 = 0.$
B
$3 a^{2} - 23 a + 44 = 0.$
C
$3 a^{2} - 26 a + 55 = 0.$
Correct answer
D
$3 a^{2} - 32 a + 84 = 0.$

Solution

$x$	$x^{2}$
$2$	$4$
$3$	$9$
$a$	$a^{2}$
$11$	$121$
$Sum \to 16 + a$	$Sum \to 134 + a^{2}$

σ = \sqrt{\frac{\sum x^{2}}{4} - {(\frac{\sum x_{i}}{4})}^{2}}

\sqrt{\frac{134 + a^{2}}{4} - {(\frac{16 + a}{4})}^{2}} = \frac{35}{10}

\frac{1}{2} \sqrt{134 + a^{2} - \frac{{(16 + a)}^{2}}{4}} = \frac{7}{2}

\sqrt{536 + 4 a^{2} - 256 - a^{2} - 32 a} =14

\Rightarrow 280 + 3 a^{2} - 32 a = 196

\Rightarrow 3 a^{2} - 32 a + 84 = 0.

Hence, the correct answer is option: 'D'.

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