Question 6

100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:

$$\begin{array}{|c|c|c|c|c|c|c|}

\hline
\text{Number of letters} & 1 - 4 & 4 - 7 & 7 - 10 & 10 - 13 & 13 - 16 & 16 - 19 \\
\hline
\text{Number of surnames} & 6 & 30 & 40 & 16 & 4 & 4 \\
\hline
\end{array}$$

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames.