The mean and standard deviation of $10$ observations $x_1, x_2, x_3.....x_{10}$ are $\overline{x}$ and $\sigma$ respectively. Let $10$ is added to $x_1, x_2.....x_9$ and $90$ is subtracted from $x_{10}.$ If still, the standard deviation is the same, then $x_{10}-\overline{x}$ is equal to

• A

  $35$
• Correct answer
  B

  $45$
• C

  $55$
• D

  $50$

Hence, the correct answer is option: 'B'.