Let the mean and the variance of $5$ observations $x_{1}, x_{2}, x_{3}, x_{4}, x_{5}$ be $\frac{24}{5}$ and $\frac{194}{25}$ respectively. If the mean and variance of the first $4$ observation are $\frac{7}{2}$ and $a$ respectively, then $\left(4 a+x_{5}\right)$ is equal to

  • [JEE MAIN 2022]
  • A

    $13$

  • B

    $15$

  • C

    $17$

  • D

    $18$

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  • [JEE MAIN 2024]