If the standard deviation of the numbers 2-3- a- and 11 is 3-5- then which of the following is trueA- 3 a 2-32 a -84-0- 3 a 2-34 a -91-0- 3 a 2-23 a -44-0D- 3 a 2-26 a -55-0

The correct option is A 3 a^2 32 a+84=0Standard deviation is given as, σ=√(∑ x^2_in (x)^2) Mean, x=16+a4 ⇒σ^2=∑ x^2_in (x)^2 ⇒(72)^2= 4+9+a^2+114 (16+a4)^2 ⇒ ...

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Standard XII

Mathematics

Standard Deviation about Mean

If the standa...

Question

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

3 a^{2} - 23 a + 44 = 0

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3 a^{2} - 26 a + 55 = 0

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

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3 a^{2} - 34 a + 91 = 0

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Solution

The correct option is C $3 a^{2} - 32 a + 84 = 0$
Standard deviation is given as,
$σ = \sqrt{\frac{\sum x_{i}^{2}}{n} - (¯ ¯ ¯ x)^{2}}$

Mean, $¯ ¯ ¯ x = \frac{16 + a}{4}$

$\Rightarrow σ^{2} = \frac{\sum x_{i}^{2}}{n} - (¯ ¯ ¯ x)^{2}$
$\Rightarrow {(\frac{7}{2})}^{2} = \frac{4 + 9 + a^{2} + 11}{4} - {(\frac{16 + a}{4})}^{2}$
$\Rightarrow 3 a^{2} - 32 a + 84 = 0$

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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

The correct option is C 3a2−32a+84=0Standard deviation is given as, σ=√∑x2in−(¯¯¯x)2 Mean, ¯¯¯x=16+a4 ⇒σ2=∑x2in−(¯¯¯x)2 ⇒(72)2=4+9+a2+114−(16+a4)2 ⇒3a2−32a+84=0

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