Question

Compute the mode from the following series:

Size	45-55	55-65	65-75	75-85	85-95	95-105	105-115
Frequency	7	12	17	30	32	6	10

Answer 1

As the class 85-95 has the maximum frequency, it is the modal class.

$$\begin{gathered} \mathrm{Now},x_k=85,h=10,f_k=32,f_{k-1}=30\mathrm{and}{f}_{k+1}=6 \\ \therefore \mathrm{Mode},M_0=x_k+\left\{h\times \frac{\left(f_k-f_{k-1}\right)}{\left(2f_k-f_{k-1}-f_{k+1}\right)}\right\} \\ =85+\left\{10\times \frac{\left(32-30\right)}{\left(2\times 32-30-6\right)}\right\} \\ =85+\left\{10\times \frac{2}{28}\right\} \\ =\left(85+.71\right) \\ =85.71 \end{gathered}$$

Hence, mode=85.71