For a frequency distribution standard deviation is computed by applying the formula
- A$\sigma = \sqrt {\left( {\frac{{\sum \,fd}}{{\sum \,f}}} \right) - \frac{{\sum \,f{d^2}}}{{\sum \,f}}} $
- B$\sigma = \sqrt {\frac{{\sum \,f{d^2}}}{{\sum \,f}} - {{\left( {\frac{{\sum \,f{d^2}}}{{\sum \,f}}} \right)}^2}} $
- C$\sigma = \sqrt {{{\left( {\frac{{\sum \,fd}}{{\sum \,f}}} \right)}^2} - \frac{{\sum \,f{d^2}}}{{\sum \,f}}} $
- D$\sigma = \sqrt {\frac{{\sum \,f{d^2}}}{{\sum \,f}} - {{\left( {\frac{{\sum \,fd}}{{\sum \,f}}} \right)}^2}} $
Similar Questions
If the variance of the first $n$ natural numbers is $10$ and the variance of the first m even natural numbers is $16$, then $m + n$ is equal to
If the variance of the first $n$ natural numbers is $10$ and the variance of the first m even natural numbers is $16$, then $m + n$ is equal to
- [JEE MAIN 2020]
The mean and the standard deviation $(s.d.)$ of five observations are $9$ and $0,$ respectively. If one of the observations is changed such that the mean of the new set of five observations becomes $10,$ then their $s.d.$ is?
The mean and the standard deviation $(s.d.)$ of five observations are $9$ and $0,$ respectively. If one of the observations is changed such that the mean of the new set of five observations becomes $10,$ then their $s.d.$ is?
- [JEE MAIN 2018]
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.....$\%$
For the frequency distribution :
Variate $( x )$
$x _{1}$
$x _{1}$
$x _{3} \ldots \ldots x _{15}$
Frequency $(f)$
$f _{1}$
$f _{1}$
$f _{3} \ldots f _{15}$
where $0< x _{1}< x _{2}< x _{3}<\ldots .< x _{15}=10$ and
$\sum \limits_{i=1}^{15} f_{i}>0,$ the standard deviation cannot be
For the frequency distribution :
| Variate $( x )$ | $x _{1}$ | $x _{1}$ | $x _{3} \ldots \ldots x _{15}$ |
| Frequency $(f)$ | $f _{1}$ | $f _{1}$ | $f _{3} \ldots f _{15}$ |
where $0< x _{1}< x _{2}< x _{3}<\ldots .< x _{15}=10$ and
$\sum \limits_{i=1}^{15} f_{i}>0,$ the standard deviation cannot be
- [JEE MAIN 2020]
Consider the statistics of two sets of observations as follows :
Size
Mean
Variance
Observation $I$
$10$
$2$
$2$
Observation $II$
$n$
$3$
$1$
If the variance of the combined set of these two observations is $\frac{17}{9},$ then the value of $n$ is equal to ..... .
Consider the statistics of two sets of observations as follows :
| Size | Mean | Variance | |
| Observation $I$ | $10$ | $2$ | $2$ |
| Observation $II$ | $n$ | $3$ | $1$ |
If the variance of the combined set of these two observations is $\frac{17}{9},$ then the value of $n$ is equal to ..... .
- [JEE MAIN 2021]