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..
$a \le {\rm{Var}}(x) \le b$
${a^2} \le {\rm{Var}}(x) \le {b^2}$
$\frac{{{a^2}}}{4} \le {\rm{Var}}(x)$
${(b - a)^2} \ge {\rm{Var}}(x)$
Find the standard deviation for the following data:
${x_i}$ | $3$ | $8$ | $13$ | $18$ | $25$ |
${f_i}$ | $7$ | $10$ | $15$ | $10$ | $6$ |
Consider $10$ observation $\mathrm{x}_1, \mathrm{x}_2, \ldots, \mathrm{x}_{10}$. such that $\sum_{i=1}^{10}\left(x_i-\alpha\right)=2$ and $\sum_{i=1}^{10}\left(x_i-\beta\right)^2=40$, where $\alpha, \beta$ are positive integers. Let the mean and the variance of the observations be $\frac{6}{5}$ and $\frac{84}{25}$ respectively. The $\frac{\beta}{\alpha}$ is equal to :
In a series of $2n$ observation, half of them are equal to $'a'$ and remaining half observations are equal to $' -a'$. If the standard deviation of this observations is $2$ then $\left| a \right|$ equals
The variance of $10$ observations is $16$. If each observation is doubled, then standard deviation of new data will be -
The variance of first $50$ even natural numbers is