Foundations · Frequency distributions
Relative Frequency Calculator
The whole frequency distribution table from your raw data — how often each value or category occurs (frequency), what share of the total that is (relative frequency), and how the shares build up (cumulative frequency). Works for discrete values, words and categories, or grouped numeric classes, with a histogram and cumulative curve drawn out.
“Auto” lists each distinct value when there are only a few, and groups numbers into equal-width classes when there are many. Categories (words) are always counted individually.
Result
In plain English
A frequency distribution just answers “how often does each thing happen?”, then re-expresses those counts as shares of the whole so different-sized datasets can be compared. The relative frequency of an outcome is the closest thing data alone can give you to its probability.
- frequency (f)
- The plain count: how many times a value or category appears in the data.
- relative frequency
- That count as a share of the total, f ∕ n — written as a proportion (0.30) or a percentage (30%). All the relative frequencies add up to 1 (100%).
- cumulative frequency
- A running total: the number of observations at or below each class. The last one equals n; as a percentage it ends at 100%.
- class (bin)
- When numbers take many values, they are grouped into equal-width intervals. The count in each interval is its frequency. Wider classes mean fewer, taller bars.
- relative frequency ≈ probability
- Over many independent trials, the relative frequency of an outcome settles down toward its true probability (the law of large numbers). With little data it is a noisy estimate, not the truth.
Frequently asked
What is relative frequency?
Relative frequency is how often something happens as a share of all observations: the count for a value divided by the total number of observations, f ∕ n. A value that occurs 6 times in 20 observations has a relative frequency of 6 ∕ 20 = 0.30, or 30%. Every relative frequency in a dataset adds up to 1 (100%).
What is the difference between frequency and relative frequency?
Frequency is the raw count — how many times a value appears. Relative frequency rescales that count to a proportion of the total, so it does not depend on how many observations you collected. Relative frequencies let you compare a sample of 20 with a sample of 2,000 on the same footing, and they are what you plot when you want a distribution rather than a tally.
Is relative frequency the same as probability?
Not quite — it is an estimate of probability. The law of large numbers says that as you gather more independent observations, the relative frequency of an outcome converges on its true probability. But from a small sample the relative frequency can be well off; treat it as the best guess the data support, not a guarantee.
What is cumulative relative frequency?
It is the running total of the relative frequencies as you move up the values or classes — the share of the data at or below each point. It always ends at 100%, and plotted against the values it traces the ogive, the S-shaped cumulative curve. From the ogive you can read medians, quartiles and percentiles straight off: find the height you want (50% for the median) and drop down to the value beneath it.