The mean of $9$ observations is $15$. If a new observation is added,the new mean becomes $16$. What is the value of the new observation?

The number of values of $a \in N$ such that the variance of $3, 7, 12, a, 43-a$ is a natural number is (Mean $= 13$).

$A$ $100$ mark examination was administered to a class of $50$ students. Despite only integer marks being given,the average score of the class was $47.5$. The maximum number of students who could have received marks greater than the class average is:

The range of the data $35, 12, 21, 24, 15, 7, 16, 12, 30, 32, 13, 17$ is

The average weight of students in a class of $35$ students is $40 \ kg$. If the weight of the teacher is included,the average weight increases by $0.5 \ kg$. The weight of the teacher is.....$kg$.

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?