Suppose values taken by a variable $x$ are such that $a \le {x_i} \le b$, where ${x_i}$ denotes the value of $x$ in the $i^{th}$ case for $i = 1, 2, ...n.$ Then..
$a \le {\rm{Var}}(x) \le b$
${a^2} \le {\rm{Var}}(x) \le {b^2}$
$\frac{{{a^2}}}{4} \le {\rm{Var}}(x)$
${(b - a)^2} \ge {\rm{Var}}(x)$
The mean and standard deviation of six observations are $8$ and $4,$ respectively. If each observation is multiplied by $3,$ find the new mean and new standard deviation of the resulting observations.
The variance of the first $n$ natural numbers is
Variance of $^{10}C_0$ , $^{10}C_1$ , $^{10}C_2$ ,.... $^{10}C_{10}$ is
If the standard deviation of the numbers $-1, 0, 1, k$ is $\sqrt 5$ where $k > 0,$ then $k$ is equal to