Calculator
Example Data Table
| Category | Frequency | Relative Frequency | Percent |
|---|---|---|---|
| A | 12 | 0.2667 | 26.67% |
| B | 18 | 0.4000 | 40.00% |
| C | 9 | 0.2000 | 20.00% |
| D | 6 | 0.1333 | 13.33% |
Formula Used
Relative frequency measures how common a value is within a dataset. It is a normalized frequency that sums to 1 across all categories.
- Total frequency: N = Σ fᵢ
- Relative frequency: rᵢ = fᵢ / N
- Percentage: pᵢ = (fᵢ / N) × 100%
- Cumulative frequency: Fᵢ = Σ fₖ up to row i
- Cumulative relative: Rᵢ = Σ rₖ up to row i
How to Use This Calculator
- Choose a mode: Use a frequency table or raw values.
- Enter data: Add labels and counts, or paste values.
- Pick options: Set decimals, sorting, and fraction display.
- Click Calculate: Results show above the form instantly.
- Export: Use download buttons for CSV or PDF.
For raw data, repeated values are counted automatically. For grouped data, ensure each category frequency is correct.
Relative Frequency Guide
1) What relative frequency tells you
Relative frequency turns a raw count into a share of the whole. If a category appears 18 times out of 45 total, its relative frequency is 18 ÷ 45 = 0.4000. This makes categories comparable even when sample sizes differ.
2) From counts to probability intuition
In large samples, relative frequency often behaves like an estimated probability. For example, if “Defect A” occurs 12 times in 200 units, r = 0.06 suggests about a 6% defect rate. Your calculator also shows percent for faster interpretation.
Sample size matters: 6% from 20 observations is noisy, while 6% from 2,000 observations is usually more stable. For fair comparisons, keep the same measurement rule across groups.
3) Cumulative columns for ordered categories
When categories have a natural order (like score ranges 0–10, 11–20, 21–30), cumulative frequency sums counts up to each row. Cumulative relative frequency sums r-values, ending near 1.0000. This is useful for percentiles and “at or below” statements.
4) Raw data mode vs frequency table mode
Use raw data mode when you have individual entries (like survey answers: yes/no/maybe). The tool counts repeats automatically. Use the frequency table when you already have grouped counts, such as 5 bins of a histogram or classroom grade bands.
5) Rounding and reporting
Rounding affects how clean your report looks. Many worksheets use 3–4 decimals for r-values and 1–2 decimals for percent. If rounding causes the displayed totals to look slightly off, remember the exact values still sum to 1 before rounding.
A simple check is to confirm the total frequency N matches your dataset size (or total weight). If N is wrong, every relative frequency shifts.
6) Sorting for clearer insights
Sorting by highest frequency highlights the most common outcomes first. Alphabetical sorting is better for named categories (cities, brands, colors). Keeping “as entered” preserves your original order, which is important for ordered bins and cumulative interpretation.
7) Quick check using a real mini dataset
Suppose a 50-response poll gives: A=22, B=15, C=9, D=4. Total N=50. Relative frequencies are 0.44, 0.30, 0.18, 0.08. Cumulative relative becomes 0.44, 0.74, 0.92, 1.00. This pattern immediately shows how much of the distribution is covered by the top categories.
FAQs
What is the difference between frequency and relative frequency?
Frequency is the raw count for a category. Relative frequency is the count divided by the total, so it represents the category’s share of the dataset and allows comparison across different sample sizes.
Do relative frequencies always add up to 1?
Yes, using exact values they sum to 1. If you round to a few decimals, the displayed values may sum to 0.9999 or 1.0001 due to rounding, but the underlying totals remain consistent.
When should I use cumulative relative frequency?
Use cumulative relative frequency when categories are ordered, such as ranges or time intervals. It answers “up to this point” questions, supports percentile ideas, and helps you see coverage of the distribution quickly.
Can I use decimal or weighted frequencies?
Yes. In frequency table mode, frequencies can be decimals to represent weights. The calculator still divides by the total weight to produce relative frequencies, percentages, and cumulative values.
Why does raw data mode change my labels to lowercase?
By default it treats values case-insensitively to avoid splitting “Blue” and “blue” into two categories. If you need exact casing, enable the case-sensitive option before calculating.
How do I export my results?
After you calculate, use the “Download CSV” button for spreadsheets, or “Download PDF” for a printable summary. Exports include the label, frequency, relative frequency, percent, and cumulative columns.