jee-main 2023 Q74

jee-main · India · session2_06apr_shift2 Measures of Location and Spread
If the mean and variance of the frequency distribution
$x_{i}$246810121416
$f_{i}$44$\alpha$158$\beta$45

are 9 and 15.08 respectively, then the value of $\alpha^{2} + \beta^{2} - \alpha\beta$ is $\_\_\_\_$.
If the mean and variance of the frequency distribution
\begin{center}
\begin{tabular}{ c c c c c c c c l }
$x_{i}$ & 2 & 4 & 6 & 8 & 10 & 12 & 14 & 16 \\
$f_{i}$ & 4 & 4 & $\alpha$ & 15 & 8 & $\beta$ & 4 & 5 \\
\end{tabular}
\end{center}
are 9 and 15.08 respectively, then the value of $\alpha^{2} + \beta^{2} - \alpha\beta$ is $\_\_\_\_$.