Question

Compute mode of the following series:

$\begin{array}{cccccccccc}\text{Mid-values}& 5& 10& 15& 20& 25& 30& 35& 40& 45\\ \text{Frequency}& 7& 13& 19& 24& 32& 28& 17& 8& 6\end{array}$

Answer 1

Since we are given mid-values (i.e, central size), first we determine the lower and upper limits of the classes.

$\begin{array}{cc}\text{Classes}& \text{f}\\ 2.5-7.5& 7\\ 7.5-12.5& 13\\ 12.5-17.5& 19\\ 17.5-22.5& 24\\ 22.5-27.5& 32\\ 27.5-32.5& 28\\ 32.5-37.5& 17\\ 37.5-42.5& 8\\ 42.5-47.5& 6\end{array}$

By inspection, we observe that the modal class is 22.5-27.5 and it has the highest frequency

$Z=l_1+\frac{D_1}{D_1+D_2}\times i$

$=22.5+\frac{8}{8+4}\times 5=25.83$