The variance of the numbers $8,21,34,47, \ldots, 320$, is______

  • [JEE MAIN 2025]
  • A
    $1059$
  • B
    $1238$
  • C
    $7562$
  • D
    $8788$

Similar Questions

If both the means and the standard deviation of $50$ observations $x_1, x_2, ………, x_{50}$ are equal to $16$ , then the mean of $(x_1 - 4)^2, (x_2 - 4)^2, …., (x_{50} - 4)^2$ is

  • [JEE MAIN 2019]

The variance of $10$ observations is $16$. If each observation is doubled, then standard deviation of new data will be -

Find the standard deviation for the following data:

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

Let $9 < x_1 < x_2 < \ldots < x_7$ be in an $A.P.$ with common difference $d$. If the standard deviation of $x_1, x_2 \ldots$, $x _7$ is $4$ and the mean is $\overline{ x }$, then $\overline{ x }+ x _6$ is equal to:

  • [JEE MAIN 2023]

The mean and standard deviation of $20$ observations are found to be $10$ and $2$ respectively. On rechecking, it was found that an observation $8$ was incorrect. Calculate the correct mean and standard deviation in each of the following cases:

If wrong item is omitted.