The $S.D.$ of a variate $x$ is $\sigma$. The $S.D.$ of the variate $\frac{{ax + b}}{c}$ where $a, b, c$ are constant, is
$\left( {\frac{a}{c}} \right)\,\sigma $
$\left| {\frac{a}{c}} \right|\,\sigma $
$\left( {\frac{{{a^2}}}{{{c^2}}}} \right)\,\sigma $
None of these
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
The mean of the numbers $a, b, 8, 5, 10$ is $6$ and the variance is $6.80.$ Then which one of the following gives possible values of $a$ and $b$ $?$
Find the variance and standard deviation for the following data:
${x_i}$ | $4$ | $8$ | $11$ | $17$ | $20$ | $24$ | $32$ |
${f_i}$ | $3$ | $5$ | $9$ | $5$ | $4$ | $3$ | $1$ |
Let $X=\{11,12,13, \ldots ., 40,41\}$ and $Y=\{61,62$, $63, \ldots ., 90,91\}$ be the two sets of observations. If $\bar{x}$ and $\bar{y}$ are their respective means and $\sigma^2$ is the variance of all the observations in $X \cup Y$, then $\left|\overline{ x }+\overline{ y }-\sigma^2\right|$ is equal to $.................$.
Consider three observations $a, b$ and $c$ such that $b = a + c .$ If the standard deviation of $a +2$ $b +2, c +2$ is $d ,$ then which of the following is true ?