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?

Let $n \geq 3$. $A$ list of numbers $x_1, x_2, \ldots, x_n$ has mean $\mu$ and standard deviation $\sigma$. $A$ new list of numbers $y_1, y_2, \ldots, y_n$ is made as follows: $y_1 = \frac{x_1+x_2}{2}$,$y_2 = \frac{x_1+x_2}{2}$ and $y_j = x_j$ for $j = 3, 4, \ldots, n$. The mean and the standard deviation of the new list are $\hat{\mu}$ and $\hat{\sigma}$. Which of the following is necessarily true?

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

The mean of $5$ observations is $4.4$ and the variance is $8.24$. If three of the five observations are $1, 2,$ and $6$,then the values of the other two observations are:

Consider the frequency distribution of the given numbers. If the mean is known to be $3$,then the value of $f$ is:

Value	$1$	$2$	$3$	$4$
Frequency	$5$	$4$	$6$	$f$

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?