The first of the two samples in a group has $100$ items with mean $15$ and standard deviation $3$. If the whole group has $250$ items with mean $15.6$ and standard deviation $\sqrt{13.44}$,then the standard deviation of the second sample is:

The mean and the standard deviation of $10$ observations are $20$ and $2$ respectively. Each of these $10$ observations is multiplied by $p$ and then reduced by $q$,where $p \neq 0$ and $q \neq 0$. If the new mean and new standard deviation (s.d.) become half of the original values,then $q$ is equal to

The average age of a group of men and women is $30$ years. If the average age of men is $32$ years and that of women is $27$ years,what is the percentage of women in the group?

Two distributions $A$ and $B$ have the same mean. If their coefficients of variation are $6$ and $2$ respectively and $\sigma_A$ and $\sigma_B$ are their standard deviations,then:

The mean of $n$ observations $x_{1}, x_{2}, \ldots, x_{n}$ is $\bar{x}$. If an observation $x_{q}$ is replaced by $x_{q}^{\prime}$, then the new mean is:

If $x_1, x_2, \ldots, x_n$ are $n$ observations and $\bar{x}$ is their mean. If $\sum_{i=1}^{n}(x_i - \bar{x})^2$ is almost zero,then which of the following statements is true?