1. What is the Median for Grouped Data?

The median for grouped data is the middle value when all observations are arranged in order, estimated from frequency distribution tables when individual data points are not available.

2. How Does the Calculator Work?

The calculator uses the median formula for grouped data:

Where:

• \( L \) — Lower boundary of the median class
• \( n \) — Total number of observations
• \( cf \) — Cumulative frequency of the class before the median class
• \( f \) — Frequency of the median class
• \( h \) — Class width (size of median class interval)

Explanation: The formula estimates the median by interpolating within the median class based on the position of the median value.

3. Importance of Median Calculation

Details: The median is a robust measure of central tendency that is less affected by outliers than the mean. For grouped data, it provides the best estimate when individual values are not available.

4. Using the Calculator

Tips:

• Ensure the cumulative frequency is correctly calculated up to the class before the median class
• Class width should be consistent across all classes
• Total frequency should equal the sum of all individual frequencies

5. Frequently Asked Questions (FAQ)

Q1: How do I identify the median class?
A: The median class is the first class where the cumulative frequency exceeds n/2 (where n is total frequency).

Q2: What's the difference between median for grouped and ungrouped data?
A: For ungrouped data, we can find the exact median value. For grouped data, we estimate based on class intervals.

Q3: When should I use median instead of mean?
A: Use median when your data is skewed or contains outliers, as it's less affected by extreme values.

Q4: Can I use this for open-ended classes?
A: No, this formula requires all classes to have defined limits and equal width.

Q5: How accurate is the median for grouped data?
A: It's an estimate that assumes uniform distribution within the median class. Accuracy improves with smaller class widths.