Question:
If the mean and the standard deviation of the data $3,5,7, a$, $b$ are 5 and 2 respectively, then $a$ and $b$ are the roots of the equation:
Correct Option: , 3
Solution:
Mean $=\frac{3+5+7+a+b}{5}=5 \Rightarrow a+b=10$
Variance $=\frac{3^{2}+5^{2}+7^{2}+a^{2}+b^{2}}{5}-(5)^{2}=4$
$\Rightarrow a^{2}+b^{2}=62$
$\Rightarrow(a+b)^{2}-2 a b=62$
$\Rightarrow a b=19$
Hence, $a$ and $b$ are the roots of the equation,
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