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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

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Solution

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:

Z=l1+f1-f02f1-f0-f2×ior, Z =149.5+18-15218-15-6×30or, Z =149.5+336-21×30or, Z =149.5+3×3015or, Z =149.5+6 Z =155.5

Hence, the modal value of the above series is 155.5

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