Frequency Distribution Calculator - Create Frequency Tables
Generate frequency distribution tables with class intervals, frequencies, relative frequencies, and cumulative frequencies from your dataset
Enter Your Data
Summary Statistics
Frequency Distribution Table
| Class Interval | Class Boundaries | Midpoint | Frequency | Relative Freq. | Cumulative Freq. |
|---|
What is a Frequency Distribution Calculator?
A Frequency Distribution Calculator organizes raw data into class intervals and displays the frequency (count) of observations in each interval, along with relative and cumulative frequencies.
This calculator is used for:
- Data Organization - Summarizing large datasets
- Pattern Recognition - Identifying data distribution shapes
- Statistical Analysis - Preparing data for histograms
- Quality Control - Monitoring process variations
To visualize your frequency distribution with bar charts, explore our Histogram Calculator to create graphical representations with properly sized bins.
To determine optimal interval widths for your data, check out our Class Width Calculator to calculate appropriate class intervals for frequency tables.
To create line graph visualizations, visit our Frequency Polygon Calculator to display distribution trends with connected points.
To analyze your data with chi-square tests, use our Chi-Square Calculator to test if observed frequencies differ from expected distributions.
How Frequency Distribution Works
The calculator uses these formulas:
Key components:
- Class Intervals - Range of values in each class
- Class Boundaries - True limits eliminating gaps
- Midpoint = (Lower limit + Upper limit) / 2
Key Concepts Explained
Class Width
The size of each interval. All classes should have equal width for proper frequency distribution.
Relative Frequency
Proportion of observations in each class. Sum of all relative frequencies equals 1 (or 100%).
Cumulative Frequency
Running total showing how many observations fall at or below each class's upper boundary.
How to Use This Calculator
Enter Your Dataset
Input numbers separated by commas or spaces
Specify Number of Classes
Choose between 2-20 classes (typically 5-10 works best)
View Frequency Table
Review generated table with all frequency statistics
Benefits of This Calculator
- Automatic Calculation - Instantly generates complete frequency table
- Multiple Metrics - Frequency, relative, cumulative all included
- Class Boundaries - Calculates true statistical boundaries
- Midpoint Calculation - Provides class midpoints automatically
- Flexible Classes - Choose optimal number of classes
- Educational Tool - Perfect for statistics students and researchers
Important Considerations
- Number of Classes - Too few loses detail; too many creates noise
- Sturges' Rule - Use k = 1 + 3.322 × log₁₀(n) as guide
- Equal Width - All classes should have same width
- No Gaps - Class intervals should be continuous
- Sample Size - Larger datasets support more classes
- Rounding - Class width may be rounded for convenience
Frequently Asked Questions
What is a frequency distribution?
A frequency distribution is a table that displays how data values are distributed across different class intervals, showing the count (frequency) of observations in each interval.
How do you calculate class width?
Class width is calculated as: (Maximum value - Minimum value) / Number of classes. Round up to a convenient number for better readability.
What is relative frequency?
Relative frequency is the proportion of observations in a class interval relative to the total number of observations. It's calculated as: (Class frequency) / (Total observations).
What are class boundaries?
Class boundaries are the true limits of class intervals that eliminate gaps between classes. Lower boundary = lower limit - 0.5; upper boundary = upper limit + 0.5 (for integer data).
How many classes should a frequency distribution have?
Typically, use 5-20 classes. Sturges' rule suggests: k = 1 + 3.322 × log₁₀(n), where k is the number of classes and n is the sample size.
What is cumulative frequency?
Cumulative frequency is the running total of frequencies up to and including a particular class. It shows how many observations fall below the upper boundary of each class.