The mean and standard deviation of $15$ observations were found to be $12$ and $3$ respectively. On rechecking it was found that an observation was read as $10$ in place of $12$ . If $\mu$ and $\sigma^2$ denote the mean and variance of the correct observations respectively, then $15\left(\mu+\mu^2+\sigma^2\right)$ is equal to$...................$

  • [JEE MAIN 2024]
  • A

    $2521$

  • B

    $3562$

  • C

    $1245$

  • D

    $2356$

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