If $\bar{x}_1$ and $\bar{x}_2$ are the means of two distributions such that $\bar{x}_1 < \bar{x}_2$ and $\bar{x}$ is the mean of the combined distribution,then

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

If the arithmetic mean of the following frequency distribution is $50$,find the values of $f_1$ and $f_2$.

Class	Frequency
$0 - 20$	$17$
$20 - 40$	$f_1$
$40 - 60$	$32$
$60 - 80$	$f_2$
$80 - 100$	$19$
Total	$120$

The mean life of a sample of $60$ bulbs was $650$ hours and the standard deviation was $8$ hours. $A$ second sample of $80$ bulbs has a mean life of $660$ hours and standard deviation $7$ hours. Find the overall standard deviation.

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?

The mean and $S.D.$ of the marks of $200$ candidates were found to be $40$ and $15$ respectively. Later,it was discovered that a score of $40$ was wrongly read as $50$. The correct mean and $S.D.$ respectively are...