Quick Answer

In the data set {A, B, A, C, A, B, A}, the value A appears 4 times out of 7 total, giving a relative frequency of 4/7 = 0.5714, or 57.14%.

Data Values

Separate values with commas, spaces, or newlines. Works with numbers, text, or categories.

Common Examples

Input	Result
A, B, A, C, A, B, A	A: 0.5714 (57.14%), B: 0.2857 (28.57%), C: 0.1429 (14.29%)
1, 2, 2, 3, 3, 3	3: 0.5000 (50.00%), 2: 0.3333 (33.33%), 1: 0.1667 (16.67%)
red, blue, red, red, green, blue	red: 0.5000, blue: 0.3333, green: 0.1667
5, 5, 5, 5	5: 1.0000 (100.00%)

How It Works

Relative frequency measures how often a particular value occurs relative to the total number of observations. The formula is:

Relative Frequency = f / n

Where:

• f = the frequency (count) of a specific value
• n = the total number of data points

The result is always a number between 0 and 1 (inclusive). Multiply by 100 to express it as a percentage. The sum of all relative frequencies in a data set always equals 1 (or 100%).

Frequency Distribution Table

A frequency distribution table lists each unique value alongside its count, relative frequency, and percentage. This is one of the most fundamental tools in descriptive statistics, providing a clear summary of how data is distributed across categories or values.

Cumulative Relative Frequency

In more advanced analysis, cumulative relative frequency adds up the relative frequencies from the smallest value to the largest. This is useful for determining what proportion of data falls at or below a given value. This calculator focuses on individual relative frequencies.

Applications

Relative frequency is used in probability estimation, survey analysis, quality control, and any scenario where understanding the proportion of each category matters. In probability, the relative frequency of an outcome in a large number of trials approximates its theoretical probability (the law of large numbers).

Worked Example

Consider a bag of colored marbles drawn with the following results: red, blue, red, green, blue, red, red, green, blue, red. There are 10 draws total. Red appears 5 times, blue appears 3 times, and green appears 2 times. Relative frequency of red = 5/10 = 0.50 (50%). Relative frequency of blue = 3/10 = 0.30 (30%). Relative frequency of green = 2/10 = 0.20 (20%). The sum of all relative frequencies is 0.50 + 0.30 + 0.20 = 1.00 (100%), as expected.

Related Calculators

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Frequently Asked Questions

What is the difference between frequency and relative frequency?

Frequency is the raw count of how many times a value appears in a data set. Relative frequency is that count divided by the total number of observations, giving a proportion between 0 and 1. For example, if 'A' appears 4 times in 20 observations, its frequency is 4 and its relative frequency is 4/20 = 0.20.

Do all relative frequencies add up to 1?

Yes. The sum of all relative frequencies in a complete data set always equals exactly 1 (or 100% when expressed as percentages). This is because every data point belongs to exactly one category, and dividing all counts by the same total guarantees they sum to 1.

Can relative frequency be used to estimate probability?

Yes. The relative frequency of an outcome across a large number of trials is a common way to estimate its probability. This is known as the frequentist interpretation of probability. As the number of observations increases, the relative frequency converges toward the true probability (the law of large numbers).

Does this calculator work with text values?

Yes. This calculator treats each entry as a string value, so it works with numbers, words, categories, codes, or any other text. Values are compared exactly, so 'Red' and 'red' are treated as different values. For consistent results, use the same capitalization throughout your data.

What is the difference between relative frequency and cumulative frequency?

Relative frequency shows the proportion for each individual value. Cumulative frequency is a running total that adds up frequencies from the smallest to the largest value. Cumulative relative frequency shows what proportion of the data falls at or below each value.