Calculate the mode of the following frequency distribution
Seconds |
51-55 |
56-60 |
61-65 |
66-70 |
Frequency |
2 |
7 |
8 |
4 |
Given
Modal class = 61 – 65 ( Highest frequency = 8)
L = 61
I = 4
f_{o} = 7
f_{1} = 8
f_{2} = 4
Formula
Mode = L + [(f_{1} – f_{0})/(2f_{1} – f_{0 – }f_{2})] × I
I = class interval or class size
f1 = frequency of modal class
fo = frequency of pre modal class
f2 = frequency of success modal class
L = lower limit of modal class
Calculation
Seconds |
Frequency |
51 – 55 |
2 |
56 - 60 |
7 |
61 – 65 |
8 |
66 - 70 |
4 |
Mode = 61 + [(8 – 7)/(2 × 8 – 7 – 4)] × 4
⇒ 61 + [(1/(16 – 11)] × 4
⇒ 61 + (1/5) × 4
⇒ 61 + 4/5
∴ The mode is 61.8