Frequency Analysis Calculator
Example Data Table
This example shows a small dataset you can test instantly.
| Observation | Value | Observation | Value | Observation | Value |
|---|---|---|---|---|---|
| 1 | 12 | 6 | 18 | 11 | 24 |
| 2 | 15 | 7 | 21 | 12 | 24 |
| 3 | 15 | 8 | 21 | 13 | 27 |
| 4 | 18 | 9 | 24 | 14 | 30 |
| 5 | 18 | 10 | 24 | 15 | 30 |
Formula Used
Absolute Frequency: f(x) = number of times a value appears.
Relative Frequency: rf = f / n
Percentage Frequency: percentage = (f / n) × 100
Cumulative Frequency: running total of all previous frequencies.
Mean: x̄ = Σx / n
Variance: sample s² = Σ(x − x̄)² / (n − 1), population σ² = Σ(x − x̄)² / n
Standard Deviation: square root of the selected variance.
Grouped Midpoint: midpoint = (lower class limit + upper class limit) / 2
How to Use This Calculator
- Paste or type numeric values into the dataset box.
- Use commas, spaces, new lines, or semicolons as separators.
- Set class width when you want grouped intervals or a histogram style summary.
- Add class start if your grouped analysis needs a custom opening boundary.
- Choose decimal precision and the variance method.
- Select ascending or descending display order.
- Press Analyze Frequency to calculate the table, summary measures, and chart.
- Use the export buttons to save the summary as CSV or PDF.
Frequently Asked Questions
1. What does a frequency analysis tool do?
It counts how often each value appears in a dataset. It also summarizes relative frequency, cumulative totals, central tendency, and spread, making patterns easier to interpret.
2. When should I use grouped classes?
Use grouped classes when your dataset has many distinct values or covers a wide range. Grouping condenses the distribution into intervals, which simplifies reading and charting.
3. What is the difference between relative and cumulative frequency?
Relative frequency shows each category’s share of the whole dataset. Cumulative frequency adds counts progressively, helping you see how totals build across sorted values or class intervals.
4. Why does the tool offer sample and population variance?
Sample variance is used when your data represents part of a larger population. Population variance applies when the dataset contains every observation you want to describe.
5. Can this tool handle decimals and repeated values?
Yes. Decimal numbers are accepted, and repeated values are central to frequency analysis. The tool counts duplicates accurately and uses them in all summary metrics.
6. How is the mode reported?
The mode is the value or set of values with the highest frequency. If several values tie for the greatest count, the result lists each one.
7. Why might grouped frequencies differ from raw value counts?
Grouped frequencies combine several raw values into intervals. The grouped table summarizes ranges rather than individual numbers, so it is broader by design but still based on the same dataset.
8. What does the chart help me understand?
The chart makes concentration, gaps, clusters, and skew easier to spot. It quickly shows which values or intervals dominate the dataset and how counts are distributed.