The average income of individuals in one group is $\bar{x}$ and the average income of another group is $\bar{y}$. If the ratio of the number of individuals in both groups is $4:3$,what is the average income of the combined group?

Which of the following is not a measure of central tendency?

Suppose a class has $7$ students. The average marks of these students in the mathematics examination is $62$,and their variance is $20$. $A$ student fails in the examination if they get less than $50$ marks. In the worst-case scenario,what is the maximum number of students who can fail?

The mean and variance of $n$ observations are $8$ and $16$, respectively. If the sum of the first $(n - 1)$ observations is $48$ and the sum of squares of the first $(n - 1)$ observations is $496$, then the value of $n$ is:

If the coefficients of variation of two distributions are $60$ and $70$ and their standard deviations are $21$ and $16$ respectively,then their arithmetic means are respectively:

Let $n \geq 3$. $A$ list of numbers $0 < x_1 < x_2 < \ldots < x_n$ has mean $\mu$ and standard deviation $\sigma$. $A$ new list of numbers is formed as follows: $y_1=0, y_2=x_2, \ldots, y_{n-1}=x_{n-1}, y_n=x_1+x_n$. The mean and the standard deviation of the new list are $\hat{\mu}$ and $\hat{\sigma}$. Which of the following is necessarily true?