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

Engineering

Mathematics

Measure of Central Tendency

Question

3a² – 32a + 84 = 0

3a² – 23a + 44 = 0

3a² – 26a + 55 = 0

3a² – 34a + 91 = 0

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$\vec{x} = \frac{2 + 3 + a + 11}{4} = 4 + \frac{a}{4} \sum {(x_{i} - \bar{x})}^{2}$

$= {(2 + \frac{a}{4})}^{2} + {(1 + \frac{a}{4})}^{2} + {(4 - \frac{3 a}{4})}^{2} + {(7 - \frac{a}{4})}^{2}$

$= 70 + \frac{12 a^{2}}{16} - 8 a$

$∵ σ = 3 .5 = \frac{7}{2}$

$\Rightarrow σ^{2} = \frac{7}{2} = var (x) = \frac{70 + \frac{12 a^{2}}{16} - 8 a}{4}$ $\Rightarrow 49 = 70 + \frac{8 a^{2}}{4} - 8 a$

$\Rightarrow \frac{3 a^{2}}{4} - 8 a + 21 = 0 \Rightarrow 3 a^{2} - 32 a + 84 = 0$