Frequency Distribution Calculator
Create frequency tables, cumulative distributions, and statistical summaries from your data
Data Input
Enter numeric values. Empty fields will be ignored.
Example: Test Scores Analysis
Sample Data
Student Test Scores: 85, 92, 78, 85, 90, 88, 85, 95, 82, 87
Sample Size: 10 students
Frequency Distribution
| Score | Frequency | Percentage |
|---|---|---|
| 78 | 1 | 10% |
| 82 | 1 | 10% |
| 85 | 3 | 30% |
| 87 | 1 | 10% |
| 88 | 1 | 10% |
| 90 | 1 | 10% |
| 92 | 1 | 10% |
| 95 | 1 | 10% |
Analysis
Mean: 86.7 points
Median: 86.5 points
Mode: 85 (appears 3 times)
Interpretation: Most students scored around 85-90, with 85 being the most common score
Distribution Types
Ungrouped Data
Each unique value gets its own frequency count
Best for discrete data with few unique values
Grouped Data
Values are grouped into intervals (classes)
Best for continuous data or large datasets
Cumulative Frequency
Running total of frequencies
Shows total count up to each value
Key Concepts
Analysis Tips
Use ungrouped data for small datasets
Group data when you have many unique values
Mode shows the most common value
Cumulative frequency helps find percentiles
Understanding Frequency Distribution
What is Frequency Distribution?
Frequency distribution is a statistical method that shows how often each value appears in a dataset. It organizes data into a table or chart that displays the frequency (count) of each value or group of values, making it easier to understand the pattern and distribution of your data.
Types of Frequency Distribution
- •Ungrouped: Each unique value has its own frequency count
- •Grouped: Data is organized into class intervals
- •Cumulative: Shows running totals of frequencies
- •Relative: Shows frequencies as percentages
Key Statistical Measures
Measures of Central Tendency:
- Mean: Average of all values
- Median: Middle value when sorted
- Mode: Most frequently occurring value
Measures of Dispersion:
- Range: Difference between max and min
- Variance: Average squared deviation from mean
- Standard Deviation: Square root of variance
Frequency Formulas:
- Relative Frequency: f/n
- Percentage: (f/n) × 100
- Cumulative Frequency: ∑f up to that point
Applications and Uses
Academic Research
Analyzing test scores, survey responses, and experimental data to understand distributions and patterns.
Business Analytics
Examining sales data, customer demographics, and performance metrics for business insights.
Quality Control
Monitoring manufacturing processes, tracking defect rates, and ensuring product consistency.
Best Practices
- • Choose appropriate class intervals for grouped data (typically 5-20 classes)
- • Ensure class intervals are equal width when possible
- • Consider the data type when deciding between grouped and ungrouped distribution
- • Use cumulative frequency to find percentiles and quartiles
- • Visualize data with histograms or bar charts for better understanding