Calculate mean, variance, and standard deviation from frequency distribution data. Ideal for analyzing grouped or binned datasets.
Last updated: March 2026
Each line: range (e.g., 10-20) and frequency count
| Class | Midpoint | Frequency | f·x | f·x² |
|---|---|---|---|---|
| 10-20 | 15.00 | 5 | 75.00 | 1125.00 |
| 20-30 | 25.00 | 8 | 200.00 | 5000.00 |
| 30-40 | 35.00 | 12 | 420.00 | 14700.00 |
| 40-50 | 45.00 | 10 | 450.00 | 20250.00 |
| 50-60 | 55.00 | 5 | 275.00 | 15125.00 |
Grouped data refers to raw data that has been organized into classes or intervals (ranges) with their associated frequencies. Rather than working with individual data points, grouped data summarizes information by showing how many observations fall into each class.
This approach is useful when dealing with large datasets where individual values are numerous. For example, age data might be grouped into 10-20, 20-30, etc., with the frequency showing how many people fall into each age range. Grouped data loses some precision (we don't know exact values within each class) but gains efficiency in handling and visualization.
To analyze grouped data, we use the midpoint of each class as a representative value for that class, then calculate statistics using these midpoints weighted by their frequencies.
Student Test Scores Distribution
When individual values are unknown, the midpoint represents the center of the class. It assumes data within the class is uniformly distributed. This is the standard approach for grouped data analysis.
Raw data uses individual values; grouped data uses class intervals and frequencies. Grouped data loses precision but handles large datasets efficiently. Results are approximations based on midpoints.
Use sample (n-1) if your data is a sample from a larger population. Use population (n) if your data represents the entire population. When in doubt, use sample standard deviation.
This calculator works with any class widths. However, unequal class widths can create misleading visualizations. Consider using frequency density (frequency/width) for proper analysis.
Yes. You can enter ranges like 10.5-20.5, 20.5-30.5, etc. The calculator will extract the lower and upper bounds and compute the midpoint accordingly.
Accuracy depends on class width and data distribution. Narrower classes provide more accuracy but less data compression. Results are approximations—actual values within classes are unknown.
Variance measures spread of data around the mean. It's in squared units (e.g., if data is in dollars, variance is in dollars²). Standard deviation (√variance) is more interpretable in original units.
Use this when you have frequency distribution data (already grouped). If you have individual raw values, use a raw data standard deviation calculator for more accuracy.
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