If the mean and variance of the frequency distribution

$x_i$ $2$ $4$ $6$ $8$ $10$ $12$ $14$ $16$
$f_i$ $4$ $4$ $\alpha$ $15$ $8$ $\beta$ $4$ $5$

are $9$ and $15.08$ respectively, then the value of $\alpha^2+\beta^2-\alpha \beta$ is $............$.

  • [JEE MAIN 2023]
  • A

    $24$

  • B

    $23$

  • C

    $25$

  • D

    $22$

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