Question

Given data $60, 60, 44, 58, 68, α, β, 56$ has mean $58$, variance = $66.2$, then find $α^2 + β^2$.

Answer 1

$\text{The formula for Variance is:}$ $\frac{\sum x^2}{n}-(\bar x)^2$

$\text{Substituting the data given in the question, we find,}$

$\frac{7200+1936+3364+4624+3136+\alpha^2+\beta^2}{8}-3364$ $=66.2$

$2532.5+\frac{\alpha^2+\beta^2}{8}-3364=66.2$

$=7181.6$ $\approx7182$

$\text{The correct answer is 7182.}$