Statistics

If the variance of the data $2,3,5,8,12$ is $\sigma^2$ and the mean deviation from the median for this data is M , then $\sigma^2-\mathrm{M}=$

The arithmetic mean of the data $0,1,2, \ldots \ldots, n$ with frequencies $1,{ }^{4} \mathrm{C}_{1}{ }^{4} \mathrm{C}_{2}, \ldots . .,{ }^{\infty} \mathrm{C}_{\mathrm{a}}$ is

Coefficient of variation of two distributions are $50$ and $60$ and their arithmetic means are $30$ and $25$, respectively. Difference of their standard deviation is

Find the value of \(\lim _{x \rightarrow 0} \frac{\sqrt{\left(1+x^2\right)}-\sqrt{1-x^2}}{x^2}\)

The mean of n items is X . If the first item is increased by 1 , second by 2 and so on, the new mean is :

If the value of mode and mean is 60 and 66 respectively, then the value of median is

If sample A contains 100 observations $101,102, \ldots$ 200 and sample B contains 100 obsections $151,152,$ $\ldots$ 250, then ratio of variance $\mathrm{v}_{\mathrm{A}} / \mathrm{v}_{\mathrm{B}}=$

IfM. D. is 12, the value of S.D. will be

The mean of five observations is $4$ and their variance is $5.2$. If three of these observations are $1$,$2$ and $6$ , then the other two are

If the function $f(x)$, defined below, is continuous on the interval $[0,8]$, then $f(x)=\left\{\begin{array}{cc}x^2+a x+b & , 0 \leq x \lt 2 \\ 3 x+2, & 2 \leq x \leq 4 \\ 2 a x+5 b, & 4 \lt x \leq 8\end{array}\right.$

The standard deviation of 5 scores $1,2,3,4,5$ is $\sqrt{a}$. The value of ' $a$ ' is

The arithmetic mean of a set of observation is $\vec{X}$. If each observation is divided by $α$ and increased by $10$, then the mean of the new series is