Median of Grouped Data
Locate the Median in Grouped Data
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What is Median of Grouped Data?
What is Median of Grouped Data?
It’s the middle value of data organized in class intervals and frequencies, helping divide the dataset into two equal halves for analysis.
Why Use Grouped Data?
Grouped data summarizes large datasets using class intervals, making it easier to spot patterns and calculate central values like the median.
Step 1: Create a Frequency Table
List class intervals and their frequencies. This table organizes data for further calculations and helps identify where the median lies.
Step 2: Calculate Cumulative Frequency
Add up frequencies cumulatively for each class. The last value gives the total number of observations (n).
Step 3: Find the Median Class
Locate the class interval where the cumulative frequency just exceeds n/2. This is called the median class.
Step 4: Median Formula
Use the formula:
Median = l + [(n/2 − c)/f] × h
Where l = lower limit, c = cumulative frequency before median class, f = frequency, h = class size.
Why Median Matters
The median of grouped data gives a reliable central value, especially for skewed distributions, and is less affected by outliers than the mean.