Frequency Distribution Calculator

Background.

Raw data rarely says much in the order it was collected. Fifty answers to a question about household size read as a jumble of 2s, 4s and 3s until someone tallies them: how many households of one person, how many of two, and so on. That tally, value by value, is a frequency distribution. It is usually the first step with a fresh column of numbers, because it shows at a glance which values are common, which are rare, and whether something odd — a 44 among the 4s — has crept in.

The table built here is the exact-value kind. Every distinct number in your list gets its own row with two figures: its frequency, the number of times it occurs, and its relative frequency, that count as a percentage of all observations. Rows run from smallest to largest, and alongside the table come the total number of observations and the number of distinct values.

Exact-value tables suit data that naturally repeats: numbers of children or cars, dice rolls, marks on a short quiz, shoe sizes, survey answers coded 1 to 5. They suit continuous measurements badly. Record forty heights to the millimetre and nearly every value will be unique, giving forty rows each with a frequency of 1 — correct, and useless. Data like that needs grouping into class intervals for a histogram, and choosing the interval width is a judgement left to you.

Values are matched by numeric value, not by how they were typed, so 2, 2.0 and 02 share a row while 3.1 and 3.14 stay apart. Entries must be separated by commas; a space alone does not split them. There is no weighting column either, so a value seen 50 times has to appear 50 times.

What is frequency distribution calculator?

A frequency distribution lists each value that occurs in a data set together with how often it occurs. The absolute frequency f of a value is its count; the relative frequency is f divided by n, the total number of observations, often written as a percentage. Relative frequencies across all rows add up to 100%. An ungrouped distribution, like the one produced here, gives every distinct value its own row, whereas a grouped distribution pools values into class intervals.

How to use this calculator.

1. 01Type or paste the observations into the Values box, separated by commas. Line breaks are fine as long as a comma still sits between each pair of numbers; a comma left dangling at the end is reported as an empty item.
2. 02Include every observation, repeats and all: a value that occurred 12 times must appear 12 times, because there is no separate count column.
3. 03For measurements recorded to many decimal places, round them to a sensible precision first, otherwise most rows will hold a single observation.
4. 04Read the observation count and the number of distinct values, then the table, where each row gives a value, its frequency and its percentage of the total.

The formula.

For each distinct value vⱼ, the frequency is fⱼ = count(xᵢ = vⱼ), the number of observations xᵢ equal to it. The relative frequency is fⱼ ÷ n, where n is the total number of observations; the table shows it multiplied by 100 as a percentage, to eight significant figures, so one-sixth appears as 16.666667%. The frequencies always sum to n, and the percentages to 100% apart from that final rounding. Equality is numeric: 2.50 and 2.5 are the same value, but 2.5 and 2.49 are not, so any rounding or grouping has to happen before the data is entered. The table holds everything the usual summaries need. The mode is the row with the largest frequency, and the mean is Σ vⱼ fⱼ ÷ n, the values weighted by their counts.

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.