The frequency distribution:
$\begin{array}{|l|l|l|l|l|l|l|} \hline X & 2 & 3 & 4 & 5 & 6 & 7 \\ f & 4 & 9 & 16 & 14 & 11 & 6 \\ \hline \end{array}$
Find the standard deviation.
$\begin{array}{|c|c|c|c|c|} \hline x_{i} & f_{i} & d_{i}=x_{i}-4 & f_{i} d_{i} & f_{i} d_{i}^{2} \\ \hline 2 & 4 & -2 & -8 & 16 \\ \hline 3 & 9 & -1 & -9 & 9 \\ \hline 4 & 16 & 0 & 0 & 0 \\ \hline 5 & 14 & 1 & 14 & 14 \\ \hline 6 & 11 & 2 & 22 & 44 \\ \hline 7 & 6 & 3 & 18 & 54 \\ \hline \text { Total } & n=60 & & \Sigma f_{i}=37 & \Sigma f_{i} d_{i}^{2}=137 \\ \hline \end{array}$
$ \therefore \quad SD =\sqrt{\frac{\Sigma f_{i} d_{i}^{2}}{n}-\left(\frac{\Sigma f_{i} d_{i}}{n}\right)^{2}}=\sqrt{\frac{137}{60}-\left(\frac{37}{60}\right)^{2}}=\sqrt{2.2833-(0.616)^{2}} $
$=\sqrt{2.2833-0.3794}=\sqrt{1.9037}=1.38 $
The mean and the variance of five observations are $4$ and $5.20,$ respectively. If three of the observations are $3, 4$ and $4;$ then the absolute value of the difference of the other two observations, is
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 ?
What is the standard deviation of the following series
class | $0-10$ | $10-20$ | $20-30$ | $30-40$ |
Freq | $1$ | $3$ | $4$ | $2$ |
Let $x_1, x_2, x_3, x_4, .......... , x_n$ be $n$ observations and let $\bar x$ be their arithmetic mean and $\sigma ^2$ be their variance.
Statement $-1$ : Variance of observations $2x_1, 2x_2, 2x_3, ......, 2x_n$ is $4\sigma ^2$ .
Statement $-2$ : Arithmetic mean of $2x _1, 2x_2, 2x_3, ......, 2x_n$ is $4\bar x$ .
If $x_1, x_2,.....x_n$ are $n$ observations such that $\sum\limits_{i = 1}^n {x_i^2} = 400$ and $\sum\limits_{i = 1}^n {{x_i}} = 100$ , then possible value of $n$ among the following is