Question:
If the mean and variance of six observations $7,10,11,15, \mathrm{a}, \mathrm{b}$ are 10 and $\frac{20}{3}$, respectively, then the value of $|a-b|$ is equal to :
Correct Option: , 4
Solution:
$10=\frac{7+10+11+15+a+b}{6}$
$\Rightarrow a+b=17$..(1)
$\frac{20}{3}=\frac{7^{2}+10^{2}+11^{2}+15^{2}+a^{2}+b^{2}}{6}-10^{2}$
$a^{2}+b^{2}=145$..(2)
Solve (i) and (ii) $a=9, b=8$ or $a=8, b=9$
$|a-b|=1$
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