Statistics

The outcome of each of $30$ items was observed; $10$ items gave an outcome $\dfrac{1}{2}$- d each, $10$ items gave outcome $\dfrac{1}{2}$ each and the remaining $10$ items gave outcome $\dfrac{1}{2}+$ d each. If the variance of this outcome data is $\dfrac{4}{3}$ then $|d|$ equals:-

If both the mean and the standard deviation of $50$ observations ${ x }{ 1 },{ x }{ 2 },......,{ x }{ 50 }$ are equal to $16$, then the mean of ${ \left( { x }{ 1 }-4 \right) }^{ 2 },{ \left( { x }{ 2 }-4 \right) }^{ 2 },.....{ \left( { x }{ 50 }-4 \right) }^{ 2 }$ is:

If $\displaystyle \sum_{i = 1}^{9}(x_{i} - 5) = 9$ and $\displaystyle \sum_{i = 1}^{9}(x_{i} - 5)^{2} = 45$, then the standard deviation of the $9$ items $x_{1}, x_{2}, ...., x_{9}$ is

Let $\overline X$ and M.D. be the mean and the mean deviation about $\overline X$ of n observations $x_i, i=1, 2, ....., n.$ If each of the observations is increased by 5, then the new mean and the mean deviation about the new mean, respectively, are :

Let $x_{1},x_{2},\cdots\cdot x_{n}$ be $\mathrm{n}$ observations, and let $\bar{x}$ be their arithmetic mean and $\sigma^{2}$ be their variance. Statement 1: Variance of $2x_{1},2x_{2},\ldots,2x_{n}$ is $4\sigma^{2}$. Statement 2: Arithmetic mean of $2x_{1},2x_{2},\ldots,2x_{n}$ is $4\bar{x}$.

If the mean deviation about the median of the numbers $\mathrm{a},\ 2\mathrm{a},\ \ldots$ , $50\mathrm{a}$ is $50$, then $|\mathrm{a}|$ is equal

If the mean deviation of the numbers $1$, $1+\mathrm{d}$, $1 +2\mathrm{d},\ \ldots$ , $1+100\mathrm{d}$ from their mean is $255$, then the $\mathrm{d}$ is equal to

If $x_{1}, x_{2}, ..., x_{n}$ be $n$ observations such that $\displaystyle \sum ^{n}{i=1} x{i}^{2} = 400$ and $\displaystyle \sum ^{n}{i=1} x{1} = 80$. Then, a possible value of $n$ among the following is

In an experiment with $15$ observations on $x$, then following results were available: $\sum x^2=2830, : : \sum x=170$ One observation that was $20$ was found to be wrong and was replaced by the correct value $30$. Then the corrected variance is:

If the combined mean of the two group is $\dfrac { 40 }{ 3 } $ and if the mean of one group with $10$ observations is $15$, then the mean of the other group with $8$ observations is

Coefficients of variation of two distributions are $50$ and $60$ and their arithmetic mean are $30$ and $25$ respectively. Difference of their standard deviation is