The mean and variance of $7$ observations are $8$ and $16$ respectively. If one observation $14$ is omitted a and $b$ are respectively mean and variance of remaining $6$ observation, then $a+3 b-5$ is equal to $..........$.

  • [JEE MAIN 2023]
  • A

    $36$

  • B

    $35$

  • C

    $34$

  • D

    $37$

Similar Questions

For a frequency distribution standard deviation is computed by applying the formula

If the standard deviation of the numbers $-1, 0, 1, k$ is $\sqrt 5$ where $k > 0,$ then $k$ is equal to

  • [JEE MAIN 2019]

Determine mean and standard deviation of first n terms of an $A.P.$ whose first term is a and common difference is d.

 

Find the standard deviation for the following data:

${x_i}$ $3$ $8$ $13$ $18$ $25$
${f_i}$ $7$ $10$ $15$ $10$ $6$

The mean and standard deviation of $40$ observations are $30$ and $5$ respectively. It was noticed that two of these observations $12$ and $10$ were wrongly recorded. If $\sigma$ is the standard deviation of the data after omitting the two wrong observations from the data, then $38 \sigma^{2}$ is equal to$.........$

  • [JEE MAIN 2022]