Statistics

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

Variance of the following continuous frequency distribution is
$$ \begin{array}{cc} \hline \text { Class Interval } & \text { Frequency } \\ \hline 0-4 & 1 \\ \hline 4-8 & 2 \\ \hline 8-12 & 2 \\ \hline 12-16 & 1 \\ \hline \end{array} $$

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

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,...

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 th...

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, it...

Variance of the following discrete frequency distribution is
$$ \begin{array}{llllll} \hline \text { Class Interval } & 0-2 & 2-4 & 4-6 & 6-8 & 8-10 \\ \hline \text { Frequency } & 2 & 3 & 5 & 3 & 2 \\ \hline \end{array} $$

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

If the mean of the data $7,8,9,7,8,7, \lambda$ and 8 is 8 , then variance of the data is equal to

If $x_1, x_2, x_3, \ldots . x_n$ are $n$ observations such, that $\Sigma\left(x_i+2\right)^2=28 n$ and $\Sigma\left(x_1-2\right)^2=12 n$, then the variance 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 the...

Mean deviation about the mean for the following data is

$$ \begin{array}{llllll} \hline \text { Class Interval } & 0-6 & 6-12 & 12-18 & 18-24 & 24-30 \\ \hline \text { Frequency } & 1 & \,2 & \,3 & \,2 & \,1 \\ \hline \end{array} $$

The coefficient of variation for the frequency distribution is
$$ \begin{array}{|c|l|l|l|} \hline \boldsymbol{x}_{\boldsymbol{i}} & 4 & 3 & 1 \\ \hline \boldsymbol{f}_{\boldsymbol{i}} & 1 & 3 & 5 \\ \hline \end{array} $$

$x$ and $y$ are the arithmetic means of the runs of two batsmen $A$ and $B$ in 10 innings respectively and $\sigma_A, \sigma_B$ are the standard deviations of their runs in them. If batsman $A$ is more consistent than $B$, then he is also a...

If the mean deviation about the mean is $m$ and variance is $\sigma^2$ for the following data, then $m+\sigma^2=$ .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:A...

If $m$ and $M$ denote the mean deviations about mean and about median respectively of the data $20,5,15,2$, $7,3,11$, then the mean deviation about the mean of $m$ and $M$ is

For a set of observations, if the coefficient of variation is 25 and mean is 44 , then the variance is

The variance of 20 observations is 5. If each one of the observations is multiplied by 2 , then the variance of the resulting observations is

The mean of 5 observations is 4.4 and their variance is 8.24. If three of those observations are 1,2 and 6 , then the other two observations are

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

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 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

For the random variable X with probability distribution is given by the table

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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

The mean deviation from the mean of the set
of observation \(-1,0,4\) 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

Which of the following set of data has least standard deviation?

The variance of the variates 112, 116, 120, 125 and 132 about their AM 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