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
Answers
Mode of the following distribution is:
• Estimated Mode is given by formula,
L + [ (f1 - fo)/2f1 - fo - f2 ]×w
Where,
• L is the lower class boundary of the modal group
• fo is the frequency of the group before the modal group
• f1 is the frequency of the modal group
• f2 is the frequency of the group after the modal group
• w is the group width
Mode is the maximum number of data occurring in a given distribution.
1. 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
In 1st distribution, modal class = 40 - 50
Mode=40+[ (28-12)/2×28-12+20 ]×10
= 40 + 260/64 = 40+3.75 = 43.75
2. class interval: 10-15 15-20 20-25 25-30 30-35 35-40
Frequency: 30 45 75 35 25 15
Modal class = 20-25
Mode = 20+[(75-45)/75×2-45+35]×5
= 20 + 150/140 = 20+1.07 = 21.07
3. Do it by yourself now.