If $\sum_{i=1}^9\left(x_i-5\right)=9$ and $\sum_{i=1}^9\left(x_i-5\right)^2=45$, then the standard deviation of the nine observations $x_1, x_2, \ldots, x_9$ is

The mean deviation from the median for the following data is

$ \begin{array}{llllll} \hline x_1 & 9 & 3 & 7 & 2 & 5 \\ \hline f_1 & 1 & 6 & 2 & 8 & 4 \\ \hline \end{array} $

The mean deviation about the mean for the following data is

$ \begin{array}{llllll} \hline \text { Class Interval } & 0-2 & 2-4 & 4-6 & 6-8 & 8-10 \\ \hline \text { Frequency } & 1 & 3 & 4 & 1 & 2 \\ \hline \end{array} $

Let $x_1, x_2, \ldots, x_{11}$ be the observations satisfying $\sum\limits_{i=1}^{11}\left(x_i-4\right)=22$ and $\sum\limits_{i=1}^{11}\left(x_i-4\right)^2=154$. If the mean and variance of the observations are $\alpha$ and $\beta$, then the quadratic equation having the roots $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$ is

The mean and variance of the observations $x_1, x_2, x_3 \ldots x_{15}$ are respectively 2 and 4 . If the mean and variance of the observations $y_1, y_2 \ldots, y_{10}$ are respectively 2 and 5 , then the variance of the observations $x_1, x_2 \ldots, x_{15}, y_1, y_2 \ldots, y_{10}$ is

Variance of the following discrete frequency distribution is

$ \begin{array}{llllll} \hline \text { Class Interval } & 0-2 & 2-4 & 4-6 & 6-8 & 8-10 \\ \hline \text { Frequency } & 2 & 3 & 5 & 3 & 2 \\ \hline \end{array} $

The following data represents the frequency distribution of 20 observations

$ \begin{array}{ccccccc} \hline x_i & 3 & 4 & 5 & 8 & 10 & 11 \\ \hline f_i & \alpha+2 & (\alpha-1)^2 & 4 & \alpha-1 & 2 & \alpha \\ \hline \end{array} $

Then, its mean deviation about the mean is

If the variance of the first $n$ natural numbers is 10 and the variance of the first $m$ even natural numbers is 16 , then $n: m=$

The variance of ungrouped data $2,12,3,11,5,10,6,7$, is

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 $m+\sigma^2=$

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.

$5,6,7,8,6,9,13,12,15 \text { is }$

If the mean of a data x is 10 and if all the observations are multiplied by 2, then the mean of new data 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

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?