Mode Calculator

StatisticsLast updated: August 22, 2026

The mode is the value that occurs most often in a data set. Unlike the mean and the median it requires no arithmetic; it is found simply by counting frequencies. That is why the mode is the only measure of central tendency available for categorical data that cannot be ordered (brand, color, occupation, blood type).

This calculator counts the data, builds the frequency table, and states separately whether the distribution has one mode (unimodal), two (bimodal), or more (multimodal). If no value repeats, the amodal case is reported explicitly. Mode, mean, and median are also shown together; the ordering of these three gives the first clue about the skewness of the distribution.

Separate the numbers with commas, spaces, or line breaks. A decimal comma is accepted as the decimal separator (3,14).
With continuous measurements no value may repeat exactly; rounding can reveal a meaningful peak value.

Mode formulas

Raw data:        Mode = the value with the highest frequency
                 f(Mode) = max{f(x₁), f(x₂), …, f(xₖ)}
Grouped data:    Mode = L + [Δ₁ / (Δ₁ + Δ₂)] · h
                 Δ₁ = f_mode − f_previous ,  Δ₂ = f_mode − f_next
                 L = lower bound of the modal class, h = class width
Empirical rule:  Mode ≈ 3·Median − 2·x̄
Symmetric case:  Mode = Median = x̄

For raw data the mode is found by counting frequencies; like Excel's MODE.MULT, this calculator lists every peak value that shares the highest frequency.

How to Calculate

  1. Paste your data values into the box; commas, spaces, and line breaks are all accepted.
  2. If you are entering continuous measurements, choose a counting precision — without rounding, no value may repeat at all.
  3. Find the row with the highest frequency in the frequency table; the mode is the value in that row.
  4. Check the mode type: unimodal, bimodal, multimodal, or amodal is reported separately.
  5. Compare the mode with the mean and the median; the ordering of the three shows the direction of the skew.
  6. If the bar chart shows more than one peak, ask whether your data is made up of subgroups.

Worked Examples

A unimodal data set

Among 8 observations the value 7 appears 3 times and the value 9 appears twice; since the highest frequency is 3, the mode is 7 and the data is unimodal (the mode makes up 37.5% of the data). In the same data the mean is 8.75 and the median is 8; the mean exceeding the mode points to right skew. The Pearson estimate gives 3·8 − 2·8.75 = 6.50.

Number of values (n): 8 · Mode: 7.00 · Mode type: Unimodal (one mode)

Bimodal data

Because the values 12 and 15 each appear twice, the data is bimodal; the modes are 12 and 15. The mean is 14.13 and the median is 14.50. Two peaks suggest the data may come from two different subgroups rather than a single homogeneous population.

Number of values (n): 8 · Modes: 12.00 and 15.00 · Mode type: Bimodal (two modes)

Amodal data (no mode)

All five values appear exactly once, so the highest frequency is 1 and the data set has no mode. In this case the median (8) or the mean (8.20) should be reported as the measure of center; the mean and median being nearly equal indicates a nearly symmetric distribution.

Number of values (n): 5 · Mode: None · Mode type: No mode (amodal) — no value repeats

Frequently Asked Questions

Can a data set have more than one mode?
Yes. Every value that shares the highest frequency is a mode: if two values share it the data is bimodal, and if three or more share it the data is multimodal. This calculator lists all of the equally frequent peak values together. More than one peak is usually a sign that the data mixes several subgroups.
What is the mode when no value repeats?
Such a data set is amodal and no mode is reported. This happens very often with continuous measurements; the finer the measurement precision, the lower the chance of a repeat. The remedy is to round the values or to group the data into class intervals and find the modal class.
What is the difference between mode, mean, and median?
The mean finds the center by summing all values and dividing, and it is the measure most affected by outliers. The median is the middle of the ordered data and resists extreme values. The mode simply names the most frequent value and involves no arithmetic at all. In a symmetric distribution all three coincide; in skewed distributions they separate.
Can the mode be used with categorical data?
Yes — in fact the mode is the only measure of central tendency that works with categorical (nominal) data. The most preferred brand, the most common blood type, or the largest occupational group are all modes. The mean and the median are undefined for such data because categories cannot be added or meaningfully ordered.
How is the mode computed in Excel and SPSS?
In Excel, MODE.SNGL returns only the first mode and MODE.MULT returns all of them; if nothing repeats it gives an #N/A error. The SPSS Frequencies output shows the smallest mode when there are several and adds a footnote below the table. This calculator removes that confusion by listing all modes together.
When does Pearson's 3·Median − 2·Mean relation hold?
This empirical relation is only an approximation, and only for unimodal, mildly skewed distributions. With pronounced skew, multimodal distributions, or small samples it can drift far from the true mode. That is why it is presented as an estimate; the actual mode is always found by counting frequencies.
What should I do when I see a bimodal distribution?
First check whether the data comes from different subgroups (gender, branch, shift, measurement period); two peaks usually arise when two different populations are mixed. Separating the subgroups and analyzing them individually is far more informative than reporting a single mean for the mixed data.