Question

Calculate mode of the following series:

Class Interval	30−59	60−89	90−119	120−149	150−179	180−209	210−239
Frequency	4	7	12	15	18	6	5

Answer 1

Class Interval	Exclusive Class interval	Frequency
30 − 59 60 − 89 90 − 119 120 − 149	29.5 − 59.5 59.5 − 89.5 89.5 − 119.5 119.5 − 149.5	4 7 12 15 f0
150 − 179	(l₁) 149.5 − 179.5	18 f1
180 − 209 210 − 239	179.5 − 209.5 209.5 − 239.5	6 f2 5

A glance at the above table reveals that 149.5 − 179.5 is the model class interval as it has the highest frequency i.e.18.

Calculating the mode of the series:

$$\begin{gathered} \mathrm{Z}=l_1+\frac{f_1-f_0}{2f_1-f_0-f_2}\times i \\ \mathrm{or},\mathrm{Z}=149.5+\frac{18-15}{2\left(18\right)-15-6}\times 30 \\ \mathrm{or},\mathrm{Z}=149.5+\frac{3}{36-21}\times 30 \\ \mathrm{or},\mathrm{Z}=149.5+\frac{3\times 30}{15} \\ \mathrm{or},\mathrm{Z}=149.5+6 \\ \Rightarrow \mathrm{Z}=155.5 \end{gathered}$$

Hence, the modal value of the above series is 155.5