The means of two groups of size $200$ and $300$ are $25$ and $10$ respectively. Their standard deviations are $3$ and $4$ respectively. What is the variance of the combined sample of size $500$?

The variance of the data $2, 3, 5, 11, 13, 17, 19$ is nearly

If $\sum_{i=1}^9(x_i-5)=9$ and $\sum_{i=1}^9(x_i-5)^2=45$,then the standard deviation of the nine observations $x_1, x_2, \ldots, x_9$ is

Find the coefficient of variation of the first $n$ natural numbers.

Let the observations $x_{i} (1 \leq i \leq 10)$ satisfy the equations $\sum_{i=1}^{10}(x_{i}-5)=10$ and $\sum_{i=1}^{10}(x_{i}-5)^{2}=40$. If $\mu$ and $\lambda$ are the mean and the variance of the observations $x_{1}-3, x_{2}-3, \dots, x_{10}-3$,then the ordered pair $(\mu, \lambda)$ is equal to:

Let $X = \{x \in \mathbb{N} : 1 \le x \le 19\}$ and for some $a, b \in \mathbb{R}$, $Y = \{ax + b : x \in X\}$. If the mean and variance of the elements of $Y$ are $30$ and $750$, respectively, then the sum of all possible values of $b$ is