Statistics

For a data consisting of 15 observations $x_i$, $i=1,2,3, \ldots, 15$ the following results are obtained : $\sum_{i=1}^{15} x_i=170 ; \sum_{i=1}^{15} x_i^2=2830$. If one of the observation namely 20 was found wrong and…

If the mean deviation about the mean is $m$ and variance is $\sigma^2$ for the following data, then $m+\sigma^2=$ $\begin{array}{|c|c|c|c|c|c|} \hline \text{x} & 1 & 3 & 5 & 7 & 9 \\ \text{f} & 4 & 24 & 28 & 16 & 8 \\…

The coefficient of variation of \(9,3,11,5,7\), is

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

Variance of the following discrete frequency distribution is Class Interval0-22-44-66-88-10Frequency23532

The mean and variance of the observations $\mathrm{x}_1, \mathrm{x}_2, \mathrm{x}_3, \ldots, \mathrm{x}_{15}$ are respectively 2 and 4. If the mean and variance of the observations $y_1, y_2, \ldots, y_{10}$ are…

A random variable $\mathrm{X}$ takes the values $0,1,2$. Its mean is $1 \cdot 2 .$ If $\mathrm{P}(\mathrm{X}=0)=0.3$, then $\mathrm{P}(\mathrm{X}=1)=$

For two data sets each of size 5 , the variance are given to be 4 and 5 and the corresponding means are given to be 2 and 4 respectively. The variance of the combined data set is

If the standard deviation of data is 12 and mean is 72 , then coefficient of variation is

The arithmetic mean of the observations $10,8,5, a, b$ is 6 and their variance is 6.8 , then $a b$ is equal to

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

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…