Calculate Mode for Grouped Data with Step-by-Step Derivation
Class Intervals (lower-upper)
Frequencies (corresponding to classes)
Results
Mode
Modal Class
Max Frequency
Class Width
Lower Limit (L)
Frequency Distribution
Class
Frequency
Step-by-Step Derivation
Mode Formula for Grouped Data
Mode = L + [(f₁ - f₀) / (2f₁ - f₀ - f₂)] × h
Where L=lower limit of modal class, f₁=frequency of modal class, f₀=frequency before, f₂=frequency after, h=class width.
⚠Modal class is the class with the highest frequency. The formula interpolates within this class.
What is Mode for Grouped Data?
Mode for grouped data is an estimated value that represents the most frequent class interval. Since individual data points are not available, we use a formula to estimate the mode within the modal class.
Modal Class
Class with highest frequency
Interpolation
Estimates mode within modal class
Class Width
Size of each class interval
Adjacent Classes
Frequencies of classes before and after modal
💡 Example: Classes [0-10,10-20,20-30,30-40,40-50] with frequencies [5,12,18,10,5]. Modal class = 20-30, mode ≈ 25.71.
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