If the information gathered by an investigator is from an already existing source of data,then such information is called .........

The mean of $25$ observations is $36$. If the mean of the first $13$ observations is $32$ and the mean of the last $13$ observations is $40$,find the $13^{\text{th}}$ observation.

Find the median of the observation: $62, 67, 82, 71, 75, 77, 63, 91$.

The mean of the following distribution is $50$. Find the value of $a$ and hence the frequencies of $30$ and $70$.

$x$	$f$
$10$	$17$
$30$	$5a+3$
$50$	$32$
$70$	$7a-11$
$90$	$19$

The class marks of a continuous distribution are: $1.04, 1.14, 1.24, 1.34, 1.44, 1.54$ and $1.64$. Is it correct to say that the last interval will be $1.55-1.73$? Justify your answer.

The mean of $10$ observations is calculated as $22.7$. It was later noticed that one observation was taken as $15$ instead of $51$ by mistake. Then,the correct mean of the data is ........