Mode Calculator

Mode = the value with the highest frequency; the frequency and the number of tied values are reported alongside it

xᵢ

One value in the data set. Its size is irrelevant — only the number of times it repeats matters, so a mode can be computed for labels that cannot be added or averaged

f

The frequency: how many times the reported value occurs. A frequency of 1 means no value repeats at all, and then every value in the list is tied for first place

mode

The most frequent value. When several values tie for the highest frequency, the smallest of them is printed and the number of ties is given separately — one number cannot say "2 and 5 are equally common"

ties

How many distinct values share the highest frequency. Two is a bimodal data set, three or more is multimodal, and a count equal to the number of values means there is no mode

n

How many values the list holds, up to 200 here. It sets the ceiling for the frequency, and comparing it with the tie count is what identifies the no-mode case

Use the mode when the values are categories rather than measurements: sizes, colours, models, error codes, the option people picked most often. Means and medians need arithmetic and ordering, and there is no meaningful average of "blue" — but there is a most common one, and it answers real questions such as which size to stock or which fault to fix first. It is also worth a look on numeric data with repeated values, since a mode far from the mean and median points at a cluster worth investigating. What it will not do is summarise a continuous measurement: take enough readings of a temperature and every value occurs once, so the mode has nothing to report — which is what a tie count equal to the list length means. It also ignores every value except the winner, so it says nothing about the rest of the data.

1. One clear winner: 4 appears three times

   1. Count how many times each value appears: 2 once, 4 three times, 5 twice, 7 once, 9 once
   2. The highest count is 3, reached only by 4
   3. Mode: 4, frequency 3, and one value tied for the top — so this data set is unimodal

   Read the frequency together with the tie count or the answer is ambiguous: frequency 3 with one tie is a clean single mode, while frequency 3 with three ties would mean three different values all appear three times. Those two data sets have the same frequency and completely different shapes.

2. Two modes: 2 and 5 are equally common

   1. Counts: 2 appears twice, 5 appears twice, 9 appears once
   2. The highest count is 2, and two distinct values reach it
   3. Mode: 2 is printed — the smaller of the pair — with frequency 2 and a tie count of 2

   A data set like this is called bimodal, and it often means two groups were mixed together by accident — a cluster of 2s and a cluster of 5s, which is exactly what a histogram would show as two humps. The tool prints the smaller value so that one line has something in it, but the honest reading is "2 and 5, both twice", and the tie count is what says so.

3. No mode at all, because every value is different

   1. Every value appears exactly once
   2. The highest frequency is therefore 1
   3. Three values share that frequency — that is, all of them
   4. The panel reports frequency 1 with a tie count of 3, which is how this page says "there is no mode"

   A frequency of 1 with a tie count equal to the number of values is the signature of a data set with no repeated values, and it is the normal outcome for continuous measurements rather than a sign that something went wrong. The value shown is simply the smallest in the list — something has to occupy that row, and the two counts beside it are what tell you not to read it as a winner.

The mode uses only the winning value and ignores everything else, so it is by far the least informative of the three measures of centre: two data sets can share a mode and differ in every other way. On continuous data it is close to useless — round a set of measurements finely enough and no value repeats, so there is nothing to report, while rounding them coarsely invents a mode out of the rounding. It is also unstable: change a single value and the winner can change, so a mode computed from a small list should not be trusted much. A data set can have several modes or none, which is why this page reports the frequency and the tie count rather than a single number, and why there is no frequency table in the results: the table would have to be built from your data, and nothing on this page can see your data before you type it. The list is capped at 200 values, and values are counted exactly as typed — 2.5 and 2.50 are the same number, but no rounding is applied to make near-identical readings match.

How do I find the mode of a list of numbers?

Count how many times each value appears and take the one with the highest count. In 2, 4, 4, 4, 5, 5, 7, 9 the counts are 1, 3, 2, 1 and 1, so the mode is 4 with a frequency of 3. Nothing is added and nothing is sorted, which is why a mode can be found for labels — the most common size, the most common colour — where an average makes no sense.

Can a data set have more than one mode?

Yes, and it is common. If two values tie for the highest frequency the set is bimodal, and three or more make it multimodal. 2, 2, 5, 5, 9 has two modes because 2 and 5 both appear twice, and a bimodal shape usually means two groups have been mixed together — a cluster around each mode. The panel prints the smaller of the tied values and reports the count of ties beside it, because naming only one of them would be misleading.

What does it mean when there is no mode?

It means every value occurs the same number of times, so nothing is more frequent than anything else. This page does not leave that row blank; it reports a frequency of 1 and a tie count equal to the number of values, so 1, 2, 3 comes back as three modes. That is the expected answer for a short list with no repeats, and for continuous measurements it is the usual one — round the readings finely enough and no two are identical.

Why does the mode row show a value when there is no mode?

Because a blank row is harder to read than a row with a number in it plus two counts that explain it. When every value ties, the value shown is the smallest one in the list, the frequency is 1, and the tie count equals the number of values. Read the three together and the answer is "nothing repeats"; read the value alone and you would think 1 had won, which is why the two counts sit next to it.

Is the mode useful for continuous measurements?

Rarely. Measure anything precisely enough and every reading is different, so there is no repeat to report — frequency 1, ties equal to the list length, no mode. Round the same readings coarsely and an apparent mode appears that is really an artefact of where the rounding boundaries happened to fall. The mode earns its place on categories and on genuinely repeated numeric values, such as how many people chose each of five options.

Is there a sample version and a population version of the mode?

No. The mode is a count of repetitions, so there is no divisor to adjust and no switch on this page for it. The n − 1 correction belongs to the measures of spread, where a sum of squared deviations is divided by a count. A mode is the same whether your list is a sample or the entire group.

• Measures of Location — e-Handbook of Statistical Methods, section 1.3.5.1 — National Institute of Standards and Technology (NIST)
• Measures of the Center of the Data — Introductory Statistics 2e, section 2.5 — OpenStax, Rice University
• GB/T 3358.1-2009, Statistics — Vocabulary and symbols, Part 1 (the Chinese national vocabulary standard covering the mode and the other measures of location; the record page notes that no online full text is offered) — State Administration for Market Regulation, China