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MathematicsStatisticsMean Square DeviationEasy2 minPYQ_2016

MathematicsEasysingle choice

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

Options:

Answer:

Solution:

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

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

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

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

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

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

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

Stream:JEESubject:MathematicsTopic:StatisticsSubtopic:Mean Square Deviation

⏱ 2mℹ️ Source: PYQ_2016

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