In a series of $2n$ observations, half of them equal to $a$ and remaining half equal to $-a$. If the standard deviation of the observations is $2$, then $|a|$ equals
In a series of $2n$ observations, half of them equal to $a$ and remaining half equal to $-a$. If the standard deviation of the observations is $2$, then $|a|$ equals
- [AIEEE 2004]
- A
$\frac{{\sqrt 2 }}{n}$
- B
$\sqrt 2 $
- C
$2$
- D
$\frac{1}{n}$
Similar Questions
Find the mean, variance and standard deviation using short-cut method
Height in cms
$70-75$
$75-80$
$80-85$
$85-90$
$90-95$
$95-100$
$100-105$
$105-110$
$110-115$
No. of children
$3$
$4$
$7$
$7$
$15$
$9$
$6$
$6$
$3$
Find the mean, variance and standard deviation using short-cut method
| Height in cms | $70-75$ | $75-80$ | $80-85$ | $85-90$ | $90-95$ | $95-100$ | $100-105$ | $105-110$ | $110-115$ |
| No. of children | $3$ | $4$ | $7$ | $7$ | $15$ | $9$ | $6$ | $6$ | $3$ |
The sum of squares of deviations for $10$ observations taken from mean $50$ is $250$. The co-efficient of variation is.....$\%$
The sum of squares of deviations for $10$ observations taken from mean $50$ is $250$. The co-efficient of variation is.....$\%$
Let the mean and the variance of 6 observation $a, b$, $68,44,48,60$ be $55$ and $194 $, respectively if $a>b$, then $a+3 b$ is
Let the mean and the variance of 6 observation $a, b$, $68,44,48,60$ be $55$ and $194 $, respectively if $a>b$, then $a+3 b$ is
- [JEE MAIN 2024]
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.
If the standard deviation of the numbers $-1, 0, 1, k$ is $\sqrt 5$ where $k > 0,$ then $k$ is equal to
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]