Question

Compute the mode from the following data:

Age (in years)	0-5	5-10	10-15	15-20	20-25	25-30	30-35
Number of patients	6	11	18	24	17	13	5

Answer 1

As the class 15-20 has the maximum frequency, it is the modal class.
$$\begin{gathered} \mathrm{Now},x_k=15,h=5,f_k=24,f_{k-1}=18\mathrm{and}{f}_{k+1}=17 \\ \therefore \mathrm{Mode},M_0=x_k+\left\{h\times \frac{\left(f_k-f_{k-1}\right)}{\left(2f_k-f_{k-1}-f_{k+1}\right)}\right\} \\ =15+\left\{5\times \frac{\left(24-18\right)}{\left(2\times 24-18-17\right)}\right\} \\ =15+\left\{5\times \frac{6}{13}\right\} \\ =\left(15+2.3\right) \\ =17.3 \end{gathered}$$

Hence, mode=17.3 years