Relative frequency answers the question “what fraction of the time did this happen?” It is a frequency divided by the total number of observations. If a football team lost 4 of its 11 matches, the relative frequency of a loss is 4/11 ≈ 0.364, or 36.4%. Relative frequencies always lie between 0 and 1 and add up to exactly 1 across all outcomes.
Because it is a proportion, relative frequency is also an estimate of probability – the experimental (empirical) probability. Toss a coin 10 times and you might see 7 heads (0.7); toss it 10,000 times and the relative frequency will be very close to the theoretical 0.5. This is the law of large numbers at work.
Relative frequency tables make groups of different sizes comparable: 30 of 120 and 10 of 40 are both 25%. The cumulative column tells you the proportion of observations at or below each value, and its last entry is always 1. Use grouped mode for continuous data, and the “value of interest” field to read off the relative frequency of a single outcome.
How to use the Relative Frequency Calculator
- Data set
- Type of data
- Start of the first class — Lower limit of the first class; must not be above the smallest value.
- Class width — Each class runs from its lower limit up to, but not including, the next one.
- Value of interest — The calculator reports the relative frequency of this value (or of the class that contains it).
- Chart shows
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
The data are counted per distinct value or per equal-width class. Each count is divided by n for the relative frequency, multiplied by 100 for the percentage, and accumulated for the cumulative relative frequency. The value of interest is matched exactly in ungrouped mode or to the class that contains it in grouped mode.
Worked example
A team scored 0, 1, 2, 1, 3, 0, 1, 2, 2, 1, 4, 1, 0, 2, 1, 3, 1, 2, 0, 1 goals in 20 matches. One goal occurred 8 times, so its relative frequency is 8 ÷ 20 = 0.40 (40%). The full table is 0 goals: 0.20, 1: 0.40, 2: 0.25, 3: 0.10, 4: 0.05, which sums to 1. The cumulative relative frequency at 1 goal is 0.20 + 0.40 = 0.60 – the team scored at most one goal in 60% of its matches.
Relative frequency and probability
The relative frequency of an event in n independent trials is an estimate of its probability, and its standard error is √(p(1 − p)/n). For p = 0.4 that is about 0.11 with 20 trials but only 0.015 with 1,000 trials, which is why relative frequencies from small samples bounce around and those from large samples are stable.
Formula
Relative frequency = f ÷ n · Percentage = f ÷ n × 100% · Cumulative relative frequency = (f₁ + … + fᵢ) ÷ n
Worked example
Inputs — Data set: 0, 1, 2, 1, 3, 0, 1, 2, 2, 1, 4, 1, 0, 2, 1, 3, 1, 2, 0, 1; Type of data: Ungrouped – one row per distinct value; Value of interest: 1; Chart shows: Relative frequency.
Results — Relative frequency of the value of interest = 40 %; Matched value or class = Value 1; Its frequency = 8; Cumulative relative frequency up to it = 60 %; Relative frequency table = Value f Rel. f Rel. % Cum. rel. f Cum. %
──────────────────────────────────────────────────
0 4 0.2 20% 0.2 20%
1 8 0.4 40% 0.6 60%
2 5 0.25 25% 0.85 85%
3 2 0.1 10% 0.95 95%
4 1 0.05 5% 1 100%; Total observations (n) = 20.
Key terms
- Relative frequency
- Frequency divided by the total number of observations.
- Experimental probability
- The probability of an outcome estimated from its relative frequency in trials.
- Cumulative relative frequency
- The proportion of observations at or below a value.
- Law of large numbers
- As trials increase, the relative frequency settles near the true probability.
Frequently asked questions
How do you calculate relative frequency?
Divide the number of times an outcome occurs by the total number of observations. 8 matches with one goal out of 20 matches → 8 ÷ 20 = 0.4 = 40%.
What is the difference between frequency and relative frequency?
Frequency is the count (8); relative frequency is the proportion (0.4). Relative frequencies of all outcomes sum to 1.
Is relative frequency the same as probability?
It is an estimate of probability based on observed data – the experimental probability. It approaches the true probability as the number of trials grows.
What is cumulative relative frequency?
The running total of relative frequencies: the share of observations at or below a value. Its final value is always 1 (100%).
How do I express relative frequency as a percentage?
Multiply by 100. 0.25 → 25%.
Can relative frequency be greater than 1?
No. It ranges from 0 (never happened) to 1 (happened every time). Values above 1 mean a counting mistake.
What is a relative frequency histogram?
A histogram whose bar heights are proportions or percentages instead of counts – choose grouped data to draw one.