Find the mode of the following distribution.
(i)
Class-interval: | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
Frequency: | 5 | 8 | 7 | 12 | 28 | 20 | 10 | 10 |
(ii)
Class-interval: | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 | 35-40 |
Frequency: | 30 | 45 | 75 | 35 | 25 | 15 |
(iii)
Class-interval: | 25-30 | 30-35 | 35-40 | 40-45 | 45-50 | 50-60 |
Frequency: | 25 | 34 | 50 | 42 | 38 | 14 |
(i)
Class interval | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
Frequency | 5 | 8 | 7 | 12 | 28 | 20 | 10 | 10 |
Here, the maximum frequency is 28 then the corresponding class 40-50 is the model class
l= 40, h= 50-40= 10, f= 28, f1=12, f2 =20
Mode = l + 
= 40 + 
=40 + 6.67
=46.67
(ii)
Class interval | 10 -15 | 15 -20 | 20 -25 | 25 -30 | 30 -35 | 35 -40 |
Frequency | 30 | 45 | 75 | 35 | 25 | 15 |
Here, the maximum frequency is 75, then the corresponding interval 20- 25 is modal class
l= 20, h=5, f=75, f1=45, f2 =35
Mode = l + 
= 20 + 
=20 + 2.14
=22.14
(iii)
Class interval | 25-30 | 30-35 | 35-40 | 40-45 | 45-50 | 50-55 |
Frequency | 25 | 34 | 50 | 42 | 38 | 14 |
Here, the maximum frequency is 50, then the corresponding interval 35-40 is modal class
l= 35, h=5, f=50, f1=34, f2 =42
Mode = l + 
= 35 + 
=35 + 3.33
=38.33