From the record on sizes of shoes sold in a shop, one can compute the following to determine the most preferred shoe size.

If the variables $x$ and $z$ are so related that $z = ax + b$ for each where $a$ and $b$ are constant, then $\bar{z} = a\bar{x} + b$.

If the mean of the following distribution is $6$, then the value of $P$ is: $ \begin{array}{|c|c|c|c|c|c|} \hline $X$ & 2 & 4 & 6 & 10 & $P+5$ \\ \hline $F$ & 3 & 2 & 3 & 1 & 2 \\ \hline \end{array} $

There are $n$ numbers. When 50 is subtracted from each of these number the sum of the numbers so obtained is $-10$. When 46 is subtracted from each of the original $n$ numbers, then the sum of numbers so obtained is 70. What is the mean of the original $n$ numbers?

Which measure is suitable for open-end classification?

$50^{th}$ Percentile is equal to

Find the median of the following. Class: 0-10, 10-20, 20-30, 30-40, 40-50; Freq: 2, 3, 4, 5, 6