Question

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

$\begin{array}{ccccccc}\text{Number of letters}& 1-4& 4-7& 7-10& 10-13& 13-16& 16-19\\ \text{Number of surnames}& 6& 30& 40& 16& 4& 4\end{array}$
Determine the median number of letters in the surnames.

• A. 8.05
• B. 9.05
• C. 10.05
• D. 7.55

Answer 1

The correct option is A 8.05

$\begin{array}{ccc}\text{C.I}& \text{Frequency}& \text{C.F}\\ 1-4& 6& 6\\ 4-7& 30& 36\\ 7-10& 40& 76\\ 10-13& 16& 92\\ 13-16& 4& 96\\ 16-19& 4& 100\end{array}$

Here $n=100$ & $\frac{n}{2}=50$
hence median class = 7-10

Now, we see that the 50th observation on the graph by extending it to the ogive.

The value for median seen from the graph is 8.05.