Let $r$ be the range and $S^2 = \frac{1}{n - 1} \sum_{i = 1}^n (x_i - \bar{x})^2$ be the variance of a set of observations $x_1, x_2, \dots, x_n$. Then:

Let $a$ and $b$ be two real numbers. If the arithmetic mean and the variance of $a, b, 8, 5$ and $10$ are respectively $6$ and $6.8$,then an ordered pair $(a, b) =$

Let the median and the mean deviation about the median of $7$ observations $170, 125, 230, 190, 210, a, b$ be $170$ and $\frac{205}{7}$ respectively. Then the mean deviation about the mean of these $7$ observations is:

The average marks of boys in a class is $52$ and that of girls is $42$. The average marks of boys and girls combined is $50$. The percentage of boys in the class is:

The class marks of a distribution are $6, 10, 14, 18, 22, 26, 30$. The class size is:

The mean and standard deviation of $100$ observations are $40$ and $5.1$,respectively. By mistake,one observation is taken as $50$ instead of $40$. If the correct mean and the correct standard deviation are $\mu$ and $\sigma$ respectively,then $10(\mu+\sigma)$ is equal to