Frequency Distribution Calculator

Background.

A frequency distribution turns a list of observations into a count for every distinct entered value. It answers two simple questions: which values occur, and how often does each occur? This calculator reports exact-value frequencies rather than choosing class intervals. It also divides each count by the total observation count to show relative frequency as a percentage. All repeated entries are retained in the total, while each distinct numeric value receives one row.

Paste finite numbers separated by commas. Decimal and scientific notation are accepted, and values are compared numerically with Decimal.js, so 2, 2.0, and 2e0 belong to the same numeric row. Empty tokens, words, NaN, and infinity are rejected instead of being skipped. The table is ordered by numeric value, not lexicographic text, which ensures 9 appears before 10 and negative values appear in the expected order.

For each distinct value v_j, the calculator evaluates f_j = count(x_i = v_j). Relative frequency is f_j/n, displayed as a percentage, where n is the complete observation count. The outputs include both n and the number of distinct values, allowing the table to be checked: all frequencies must sum to n, and all relative frequencies must sum to 100 percent apart from display rounding. No intermediate count is estimated or smoothed.

Exact-value grouping is appropriate for discrete outcomes, categories already encoded as numbers, and small datasets where individual values matter. It is often unhelpful for continuous measurements because tiny measurement or rounding differences can create many one-observation rows. A histogram or grouped frequency table requires a bin origin, bin width, and endpoint convention; this page deliberately does not select those choices on the user's behalf.

The table describes only the entered observations. It does not infer a probability distribution, correct selection bias, weight survey responses, impute missing values, or establish independence. Preserve the measurement units and collection method with the result. When comparing datasets, confirm that they use the same rounding precision and definitions before treating apparently equal or different values as meaningfully comparable.

To verify the table, add every row count and compare the sum with the reported observation count. Then add the unrounded relative frequencies; they must total one. A discrepancy usually indicates a copied token, inconsistent rounding, or a category that was encoded two different ways. Keep the raw list so apparently similar rows can be traced back to the measurements rather than merged by assumption. Document units and counting rules with the saved table.

What is frequency distribution calculator?

Frequency Distribution Calculator is a transparent implementation of f_j = count(x_i = v_j), relative f_j = f_j/n.

How to use this calculator.

1. 01Paste finite comma-separated numbers.
2. 02Keep paired lists in matching order.
3. 03Review the parsed count.
4. 04Read the result with its scope statement.
5. 05Retain appropriate precision.

The formula.

The implementation parses every token explicitly and then evaluates f_j = count(x_i = v_j), relative f_j = f_j/n with Decimal.js. It rejects malformed or incomplete data instead of coercing it.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NIST/SEMATECH e-Handbook, Frequency Distributions.
2. [2]OpenStax, Introductory Statistics 2e.
3. [3]NIST/SEMATECH e-Handbook of Statistical Methods.