The variance of first $50$ even natural numbers is

  • [JEE MAIN 2014]
  • A

    $437$

  • B

    $\frac{{437}}{4}$

  • C

    $\frac{{833}}{4}$

  • D

    $833$

Similar Questions

The mean and standard deviation of some data for the time taken to complete . a test are calculated with the following results:

Number of observations $=25,$ mean $=18.2$ seconds, standard deviation $=3.25 s$

Further, another set of 15 observations $x_{1}, x_{2}, \ldots, x_{15},$ also in seconds, is now available and we have $\sum_{i=1}^{15} x_{i}=279$ and $\sum_{i=1}^{15} x_{i}^{2}=5524 .$ Calculate the standard deviation based on all 40 observations.

Let $n \geq 3$. A list of numbers $x_1, x, \ldots, x_n$ has mean $\mu$ and standard deviation $\sigma$. A new list of numbers $y_1, y_2, \ldots, y_n$ is made as follows $y_1=\frac{x_1+x_2}{2}, y_2=\frac{x_1+x_2}{2}$ and $y_j=x_j$ for $j=3,4, \ldots, n$.

The mean and the standard deviation of the new list are $\hat{\mu}$ and $\hat{\sigma}$. Then, which of the following is necessarily true?

  • [KVPY 2014]

The variance of first $50$ even natural numbers is

Calculate mean, variance and standard deviation for the following distribution.

Classes $30-40$ $40-50$ $50-60$ $60-70$ $70-80$ $80-90$ $90-100$
${f_i}$ $3$ $7$ $12$ $15$ $8$ $3$ $2$

The mean and standard deviation of $20$ observations are found to be $10$ and $2$, respectively. On respectively, it was found that an observation by mistake was taken $8$ instead of $12$ . The correct standard deviation is

  • [JEE MAIN 2024]