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The mean and the standard deviation (s.d.) of $10$ observations are $20$ and $2$ resepectively. Each of these $10$ observations is multiplied by $\mathrm{p}$ and then reduced by $\mathrm{q}$, where $\mathrm{p} \neq 0$ and $\mathrm{q} \neq 0 .$ If the new mean and new s.d. become half of their original values, then $q$ is equal to

  • [JEE MAIN 2020]
  • A

    $-20$

  • B

    $10$

  • C

    $-10$

  • D

    $-5$

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