If the mean and variance of six observations 7, 10, 11, 15, a, b are 10 and 203, respectiv…

Question

If the mean and variance of six observations 7, 10, 11, 15, a, b are 10 and $\dfrac{20}{3}$, respectively, then the value of $|a-b|$ is equal to

Accepted Answer

Mean $=10$: $7+10+11+15+a+b=60 \implies a+b=17$

Variance $=\dfrac{20}{3}$: $\dfrac{49+100+121+225+a^2+b^2}{6}-100=\dfrac{20}{3} \implies a^2+b^2=145$

Using $b=17-a$: $a^2+(17-a)^2=145 \implies 2a^2-34a+144=0 \implies a^2-17a+72=0$
$$(a-9)(a-8)=0 \implies a=9,b=8 \text{ or } a=8,b=9$$

$|a-b|=1$

Solutions · 1