Which of the following results hold for a set of distinct positive observations?

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

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

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

Which measure is suitable for open-end classification?

$\displaystyle 50^{th}$ 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