The variance of first $50$ even natural numbers is
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.
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?
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
The variance of first $50$ even natural numbers is
Calculate mean, variance and standard deviation for the following distribution.
Classes
$30-40$
$40-50$
$50-60$
$60-70$
$70-80$
$80-90$
$90-100$
${f_i}$
$3$
$7$
$12$
$15$
$8$
$3$
$2$
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
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]