Math · Live
Mode Calculator,
frequency & distribution.
Find the mode, the most frequently occurring value(s), of any dataset. Paste comma or space-separated numbers to get instant results: mode classification (unimodal, bimodal, multimodal), a full frequency table with inline bars, a bar chart, and companion statistics.
Inputs
Dataset
Separate with commas, spaces, or new lines. Decimals and negatives accepted. Up to 1,000 values.
Examples
- Mode type
- Unimodal
- # of modes
- 1
- Max frequency
- 4×
- Unique values
- 5
- Total values
- 11
Statistical mode
n = 11
Appears 4 times , more than any other value.
Distribution
Unimodal
1 mode
Distribution
Frequency chart
Frequency table
All values & counts
| Value | Count | Rel. freq. | Distribution |
|---|---|---|---|
| 90mode | 4 | 36.4% | 4× |
| 78 | 2 | 18.2% | 2× |
| 85 | 2 | 18.2% | 2× |
| 92 | 2 | 18.2% | 2× |
| 88 | 1 | 9.1% | 1× |
Statistics guide
Understanding the mode and what it tells you.
In statistics, the mode is the value that appears most frequently in a dataset. Unlike the mean (which requires arithmetic) or the median (which requires sorting), the mode requires only counting, making it the simplest measure of central tendency to compute and the most immediately interpretable for categorical or discrete data.
How to find the mode step by step
- List all values in the dataset: 4, 7, 2, 4, 3, 7, 7, 4, 1, 7
- Count the frequency of each distinct value: 1→1, 2→1, 3→1, 4→3, 7→4
- Identify the maximum frequency: 4 (the value 7 appears 4 times)
- The mode is the value with that frequency: Mode = 7
If two values tie for the maximum frequency, both are modes (bimodal). If three or more values tie, the dataset is multimodal. If every value appears exactly once, the dataset has no mode.
Unimodal, bimodal, and multimodal distributions
| Type | Definition | Example | Mode(s) |
|---|---|---|---|
| No mode | All frequencies equal 1 | 1, 2, 3, 4, 5 | None |
| Unimodal | Exactly one most-frequent | 1, 2, 2, 3, 4 | 2 |
| Bimodal | Two tied at highest count | 1, 2, 2, 3, 3 | 2 and 3 |
| Multimodal | 3+ tied at highest count | 1, 1, 2, 2, 3, 3 | 1, 2, and 3 |
Mode vs. mean vs. median, when to use each
The three measures of central tendency each describe the "centre" of a dataset differently and suit different situations:
- Mode is ideal for categorical or discrete data — most popular product, most common shoe size, most frequent survey response. It is the only measure of central tendency that makes sense for non-numeric categories (e.g., "blue" is the modal eye colour).
- Mean works best for symmetric, continuous distributions with no extreme outliers — exam scores, physical measurements. One outlier (e.g., a billionaire in a salary survey) can drag the mean far from where most values lie.
- Median is robust to skewed data and outliers — home prices, income distributions, time series with rare spikes. If the mean and median differ substantially, the data is skewed.
| Measure | Best for | Affected by outliers? | Works for categories? |
|---|---|---|---|
| Mode | Categorical or discrete data | No | Yes |
| Median | Skewed numeric data | No | With ranks only |
| Mean | Symmetric numeric data | Yes | No |
Reading a frequency table
A frequency table lists each distinct value in the dataset alongside its absolute frequency (raw count) and relative frequency (count as a percentage of the total). It is the most direct way to see the distribution of discrete data:
| Value | Tally | Count | Relative freq. |
|---|---|---|---|
| 78 | II | 2 | 18.2% |
| 85 | III | 3 | 27.3% |
| 88 | I | 1 | 9.1% |
| 90 | IIII | 4 | 36.4% ★ |
| 92 | I | 1 | 9.1% |
| Total | 11 | 100% |
★ The mode is 90; it appears 4 times, more than any other score. The relative frequency (36.4%) tells you what share of the dataset that value represents.
Bimodal and multimodal distributions in practice
A bimodal distribution often signals that a dataset is a mixture of two distinct sub-populations. Classic examples:
- Height of adults: a dataset mixing male and female heights will show two peaks (one around the male average and one around the female average).
- Exam scores: a bimodal score distribution may reveal two groups: students who studied vs. those who did not.
- Customer purchase values: a retail dataset may show one peak for low-value everyday items and another for occasional high-value purchases.
When you encounter a bimodal or multimodal distribution, consider whether your data actually contains subgroups that should be analysed separately.
Limitations of the mode
Despite its simplicity, the mode has several drawbacks:
- Not always unique: A dataset can have no mode (all values appear once) or multiple modes — neither of which gives a single "centre."
- Ignores most of the data: The mode only considers frequencies, not the actual magnitudes of values. In the dataset {1, 1, 100, 200, 300}, the mode is 1 — despite most values being much larger.
- Sensitive to small samples: In small datasets, a value can appear twice by chance and become the mode without being "truly" more common in the underlying population.
- Continuous data: For truly continuous measurements (e.g., exact weight to 10 decimal places), every value will likely appear once, giving no mode. A kernel density estimator or frequency histogram with bins is more appropriate.
How to use this calculator
- Enter your data in the textarea. Values can be separated by commas, spaces, tabs, or new lines — paste directly from a spreadsheet, CSV, or hand-type them.
- Read the mode(s) in the results panel. A single large value means unimodal; multiple tiles mean bimodal or multimodal; a dash "—" means no mode.
- Check the frequency table to see each value's count and relative frequency. Mode rows are highlighted in indigo. Toggle between sorting by frequency (default) or by value.
- Study the bar chart: mode bars are highlighted in indigo. Multiple tall bars of equal height signal a multimodal distribution.