A page is selected at random from a book. The probability that the digit at units place of the page number chosen is less than $7$ is,

The mean of the following frequency distribution is $62.8$ and the sum of all frequencies is $50$. Compute the missing frequencies $f_1$ and $f_2$.

$\begin{array}{|ccccccc|}\hline \mathrm{Class}\mathrm{Interval} & 0-20& 20-40& 40-60& 60-80& 80-100& 100-120\\ \mathrm{Frequency} & 5& f_1& 10& f_2& 7& 8\\ \hline\end{array}$

The diameter of circles (in $\mathrm{mm}$) drawn in a design are given in the table. Calculate the standard deviation.

$\begin{array}{|cccccc|}\hline \text{ Diameters }& 33-36& 37-40& 41-44& 45-48& 49-52\\ \text{ Number of clrcles }& 15& 17& 21& 22& 25\\ \hline\end{array}$

In the frequency distribution table, $k$ is a positive integer, has a variance of $160$. Determine the value of $k$.

$\begin{array}{|ccccccc|}\hline x& k& 2k& 3k& 4k& 5k& 6k\\ f& 2& 1& 1& 1& 1& 1\\ \hline\end{array}$