Calculate Median for Grouped Data with Step-by-Step Derivation
Class Intervals (lower-upper)
Frequencies (corresponding to classes)
Results
Median
Median Class
Total (n)
Class Width
Lower Limit (L)
Cumulative Frequency Distribution
Class
Frequency
Cumulative
Step-by-Step Derivation
Median Formula for Grouped Data
Median = L + [(n/2 - CF) / f] × h
Where L=lower limit of median class, CF=cumulative frequency before, f=frequency of median, h=class width.
⚠Median class is where cumulative frequency first reaches or exceeds n/2. The formula interpolates within this class.
What is Median for Grouped Data?
Median for grouped data is an estimated value that represents the middle value of the dataset. Since individual data points are not available, we use cumulative frequency to locate the median class and interpolate within it.
Median Class
Class where cumulative frequency ≥ n/2
Cumulative Frequency
Running total of frequencies
Interpolation
Estimates median within median class
Middle Value
Divides data into two equal halves
💡 Example: Classes [0-10,10-20,20-30,30-40,40-50] with frequencies [5,12,18,10,5]. Median ≈ 24.44.
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