Based on the following statements, choose the correct option.
Statement I The variance of the first $n$ even natural numbers is $\frac{n^2-1}{4}$.
Statement II The difference between the variance of the first 20 even natural numbers and their arithmetic mean is 112 .
The coefficient of variation for the frequency distribution is
$$ \begin{array}{|c|l|l|l|} \hline \boldsymbol{x}_{\boldsymbol{i}} & 4 & 3 & 1 \\ \hline \boldsymbol{f}_{\boldsymbol{i}} & 1 & 3 & 5 \\ \hline \end{array} $$
Mean deviation about the mean for the following data is
$$ \begin{array}{llllll} \hline \text { Class Interval } & 0-6 & 6-12 & 12-18 & 18-24 & 24-30 \\ \hline \text { Frequency } & 1 & \,2 & \,3 & \,2 & \,1 \\ \hline \end{array} $$
If the mean deviation about the mean is $m$ and variance is $\sigma^2$ for the following data, then $m+\sigma^2=$
| $\mathbf{x}$ | 1 | 3 | 5 | 7 | 9 |
| $\mathbf{f}$ | 4 | 24 | 28 | 16 | 8 |
If the mean deviation of the data $$1,1+d 1+2 d, \ldots, 1+100 d,(d>0)$$ from their mean is 255, then '$$d$$' is equal to
If the mean of the data $$p, 6,6,7,8,11,15,16$$, is 3 times $$p$$, then the mean deviation of the data from its mean is
The mean deviation about the mean for the following data.
$$5,6,7,8,6,9,13,12,15 \text { is }$$
The mean deviation from the mean of the set of observation $$-1,0,4$$ is
Let an angle of a triangle is 60$$^\circ$$. If the variance of the angles of the triangle is 1014$$^\circ$$, then the other two angles are
For the random variable X with probability distribution is given by the table
| $$X=x$$ | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| $$P(X=x)$$ | $$K$$ | $$K+\frac{1}{7}$$ | $$2K$$ | $$\frac{2}{5}$$ |
The mean of X is
The mean and variance of $$n$$ observations $$x_1, x_2, x_3, \ldots . . x_n$$ are 5 and 0 respectively. If $$\sum_{i=1}^n x_i^2=400$$, then the value of $$n$$ is equal to
The variance of the variates 112, 116, 120, 125 and 132 about their AM is
Which of the following set of data has least standard deviation?