How this instrument works
Frequency, in the statistics sense, just means how many times something happened — 15 customers chose the blue option, 8 students scored above 90, 3 defective parts turned up in a batch. On its own, a frequency count is hard to interpret because it says nothing about the size of the group it came from. Relative frequency fixes that by expressing the count as a proportion (or, multiplied by 100, a percentage) of the total number of observations.
The calculation itself is one division: relative frequency equals the frequency of the outcome divided by the total number of observations, then multiplied by 100 to read as a percentage. If 15 of 50 survey respondents picked a given answer, the relative frequency is 15/50 = 0.30, or 30%. Add up the relative frequencies of every possible outcome in a dataset and, by construction, they sum to exactly 100%.
Relative frequency is the practical, everyday cousin of probability: in a large enough sample, an outcome's relative frequency is often used as an estimate of its true underlying probability, which is the entire basis of the frequentist approach to statistics. It shows up constantly in frequency tables, histograms, and survey results — anywhere a raw tally needs to be turned into a share of the whole that can be compared across groups of different sizes.
- Enter how many times the outcome occurred into Frequency (count of this outcome).
- Enter the total number of observations in the full dataset into Total number of observations — this must be greater than zero and at least as large as the frequency.
- Read Relative frequency (%) — this is frequency divided by total, multiplied by 100.
- Repeat for each outcome in your dataset if you're building a full frequency table; the relative frequencies of all outcomes should add up to 100%.
Worked example — 15 out of 50 total observations
Enter 15 into Frequency (count of this outcome) and 50 into Total number of observations. The instrument divides 15 by 50 to get 0.30, then multiplies by 100.
Relative frequency (%) reads 30.0000 exactly. So this outcome accounts for 30% of all 50 observations — a figure you could now directly compare against another outcome's relative frequency from a completely different-sized sample, something the raw count of 15 alone couldn't tell you.
Questions
What's the difference between frequency and relative frequency?
Frequency is the raw count — how many times something happened, with no context about the size of the group it came from. Relative frequency divides that count by the total number of observations, turning it into a proportion (or percentage) that can be compared fairly across datasets of different sizes. A frequency of 15 means very little on its own; a relative frequency of 30% is immediately interpretable.
Do relative frequencies always add up to 100%?
Yes, as long as your outcomes are mutually exclusive and cover every observation in the dataset (which is the standard setup for a frequency table). Each observation is counted in exactly one outcome's frequency, so summing every outcome's relative frequency necessarily recovers the whole dataset, which is 100%.
Is relative frequency the same thing as probability?
They're closely related but not identical. Relative frequency is an empirical, observed proportion from actual data you collected. Probability is a theoretical or long-run concept. In practice, as a sample grows very large, its relative frequencies tend to converge toward the true underlying probabilities — this convergence is the basis of the 'frequentist' interpretation of probability — but a relative frequency from a small sample can differ noticeably from the true probability just by chance.
What if the frequency is larger than the total?
That's not a valid input — a single outcome's count can never exceed the total number of observations it's drawn from, since the total is supposed to include that outcome's count as part of it. If you see this, double-check that you haven't mixed up which number is the subgroup count and which is the grand total.