Relative Frequency Calculator
Build a full frequency distribution — frequency, relative frequency, cumulative frequency and cumulative relative frequency — from raw data or a pre-tallied table, with a bar chart / histogram and an ogive.
What is relative frequency?
Relative frequency is the proportion of the total observations that fall into a given category or class interval — it converts a raw count into a share of the whole. When accumulated top-to-bottom, the same idea produces cumulative frequency and the classic ogive curve.
Frequency distributions, piece by piece
Relative frequency
The frequency of a category divided by the total number of observations. It converts a raw count into a share of the whole, so categories become directly comparable regardless of sample size.
Percentage form
Multiply a relative frequency by 100 to get a percentage. Percentages are easier to read and are what you'd typically put on a chart or in a headline number, but the underlying arithmetic is identical.
Cumulative frequency
A running total of the frequencies as you read the table top-to-bottom. Row i's cumulative frequency answers 'how many observations fall at or below this category?' — the last row always equals N.
Cumulative relative frequency (ogive)
The running total of relative frequencies — always rising from 0 to 1. Plotted against the upper class boundary it produces the ogive curve, which reads off percentiles at a glance.
Relative frequency vs probability
Relative frequency comes from actually observed data (empirical), while probability is a theoretical proportion for a random experiment. In the frequentist interpretation of probability, relative frequency is our best estimate of probability — and by the law of large numbers, it converges to the true probability as the number of observations grows.
If you already know or assume a theoretical model (a fair coin, a normal distribution, etc.), use the Probability Calculator to compute probabilities directly instead of estimating them from a sample.
Common mistakes
- Reporting frequency when relative frequency is what's asked. A count of 8 is meaningless without knowing the total; 8/20 = 40% is the interpretable number.
- Forgetting the sum-to-1 sanity check. Relative frequencies across all categories must sum to 1 (or 100%). Rounding may leave ±0.01; anything larger indicates a missing/duplicated category.
- Non-monotonic cumulative values. Cumulative frequency and cumulative relative frequency must never decrease. If they do, a frequency was entered as a negative number.
- Bar chart vs histogram confusion. Use gaps between bars for categorical/discrete data; use touching bars (histogram) for grouped continuous data — the touching bars signal that the x-axis is a continuous number line, not a set of labels.
- Overlapping class intervals. "10–20, 20–30" doesn't say where 20 goes. Use half-open intervals like [10, 20), [20, 30) — the convention this calculator follows.
Features of this calculator
- Three input modes: raw categorical/discrete tally, raw numeric grouped into class intervals, or a pre-tallied frequency table.
- Full distribution table with frequency, relative frequency (decimal + %), cumulative frequency and cumulative relative frequency in one view.
- Automatic class width via Sturges' rule for grouped numeric data — or set your own width.
- Bar chart for categorical/discrete data, histogram (touching bars) for grouped continuous data.
- Ogive (cumulative relative frequency) chart — the second chart most competing calculators skip.
- Show/hide step-by-step working with the total, division for each category and the running cumulative check.
- Copy the full table as tab-separated text (paste-ready into Excel or Sheets) or download the result panel as a PNG.
Frequently asked questions
+What's the difference between frequency and relative frequency?
Frequency is a raw count of observations in a category. Relative frequency divides that count by the total, giving a proportion (0–1) or percentage (0–100%).
+Do the relative frequencies always sum to 1?
Yes — that's a definitional property. If they don't, you either miscounted the total, missed a category, or double-counted an observation. Small ±0.01 rounding is normal after formatting.
+When should I use a histogram instead of a bar chart?
Use a histogram (bars touching) for grouped continuous numeric data — heights, weights, times. Use a bar chart (with gaps) for categorical or discrete data — colours, brands, or integer counts.
+What is an ogive?
An ogive is a line chart of cumulative relative frequency against the class boundary. It always rises from 0 to 1. You can read off percentiles directly — find 0.5 on the y-axis and drop down to get the median class.
+How does the calculator choose class widths automatically?
It uses Sturges' rule (k ≈ 1 + log₂ n) as the initial number of classes, then rounds the class width to a "nice" 1/2/5-times-power-of-ten value so the bin edges read cleanly.
+Can I paste data straight from Excel or Google Sheets?
Yes. Tabs, spaces, commas, semicolons and line breaks all work as separators for both raw-data modes.