Let $r$ be the range and ${S^2} = \frac{1}{{n - 1}}\sum\limits_{i = 1}^n {{{({x_i} - \bar x)}^2}} $ be the $S.D.$ of a set of observations ${x_1},\,{x_2},\,.....{x_n}$, then
$S \le r\sqrt {\frac{n}{{n - 1}}} $
$S = r\sqrt {\frac{n}{{n - 1}}} $
$S \ge r\sqrt {\frac{n}{{n - 1}}} $
None of these
The mean and variance of $5$ observations are $5$ and $8$ respectively. If $3$ observations are $1,3,5$, then the sum of cubes of the remaining two observations is
If the variance of the frequency distribution is $160$ , then the value of $\mathrm{c} \in \mathrm{N}$ is
$X$ | $c$ | $2c$ | $3c$ | $4c$ | $5c$ | $6c$ |
$f$ | $2$ | $1$ | $1$ | $1$ | $1$ | $1$ |
The mean and variance of $10$ observations were calculated as $15$ and $15$ respectively by a student who took by mistake $25$ instead of $15$ for one observation. Then, the correct standard deviation is$.....$
For a given distribution of marks mean is $35.16$ and its standard deviation is $19.76$. The co-efficient of variation is..
One set containing five numbers has mean $8$ and variance $18$ and the second set containing $3$ numbers has mean $8$ and variance $24$. Then the variance of the combined set of numbers is