Find the range of the given numbers: $10, 8, 12, 11, 14, 9, 6$.

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:

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 mean and standard deviation of a group of $100$ observations were found to be $20$ and $3$,respectively. Later on,it was found that three observations were incorrect,which were recorded as $21, 21,$ and $18$. Find the mean and standard deviation if the incorrect observations are omitted.

Let ${x_1}, {x_2}, ..., {x_n}$ be $n$ observations such that $\sum x_i^2 = 400$ and $\sum x_i = 80$. Then a possible value of $n$ among the following is:

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?