01 · MODAL CLASS
What is the Modal Class?
In a grouped frequency distribution, the Modal Class is the class interval with the maximum frequency (f₁).
02 · FORMULA
Mode Formula for Grouped Data
Mode = l + [ (f₁ - f₀) / (2f₁ - f₀ - f₂) ] × h
l
Lower limit of the modal class.
h
Size of the class interval (assuming all class sizes equal).
f₁
Frequency of the modal class.
f₀
Frequency of the class preceding the modal class.
f₂
Frequency of the class succeeding the modal class.
03 · SOLVED NCERT EXAMPLE
Step-by-Step Problem Solving
EXAMPLE 1
A survey conducted on 20 households in a locality resulted in the following frequency table for family size
Family Size | Number of Families (fᵢ)
1 - 3 | 7
3 - 5 | 8 ◄ MAX FREQUENCY (Modal Class!)
5 - 7 | 2
7 - 9 | 2
9 - 11 | 1
1 - 3 | 7
3 - 5 | 8 ◄ MAX FREQUENCY (Modal Class!)
5 - 7 | 2
7 - 9 | 2
9 - 11 | 1
Identifying Parameters:
Modal Class = 3 - 5
Lower Limit l = 3, Class Size h = 2
f₁ = 8 (modal class frequency)
f₀ = 7 (preceding frequency)
f₂ = 2 (succeeding frequency)
Lower Limit l = 3, Class Size h = 2
f₁ = 8 (modal class frequency)
f₀ = 7 (preceding frequency)
f₂ = 2 (succeeding frequency)
Calculating Mode:
Mode = 3 + [ (8 - 7) / (2(8) - 7 - 2) ] × 2
Mode = 3 + [ 1 / (16 - 9) ] × 2 = 3 + (2 / 7) = 3 + 0.286 = 3.286
Mode = 3 + [ 1 / (16 - 9) ] × 2 = 3 + (2 / 7) = 3 + 0.286 = 3.286
The mode of the data is 3.286.
04 · QUICK SUMMARY
Key Takeaways
01
Modal class has the highest frequency f₁.
02
Mode formula: Mode = l + [ (f₁ - f₀) / (2f₁ - f₀ - f₂) ] × h.
03
Mode always lies inside the modal class interval.