Mode Calculator Online
Find the mode, frequency distribution, unimodal/bimodal status, and companion mean/median.
Input Parameters
Live Result
Details
Steps
Count Total Observations: n = 14 numbers
Sort Observations Ascendingly: [3, 5, 7, 12, 13, 14, 20, 23, 23, 23, 23, 39, 40, 56]
Calculate Frequencies: Highest observed frequency is 4 times
Determine Mode: The value(s) with highest count (4) -> 23
Compare with Central Tendencies: Mean = 21.5, Median = 21.5
Quick Answer & Understanding Your Result
The Mode is the value that appears most frequently in a statistical dataset: In a discrete distribution, Mode = argmax(Frequency(x)). A dataset can have one mode (Unimodal), two modes (Bimodal), multiple modes (Multimodal), or No Mode if all values occur with equal frequency.
Mode Classification Types
- Unimodal Distribution: A single clear peak with one most frequent value (e.g., [2, 3, 3, 5] → Mode = 3).
- Bimodal Distribution: Exactly two values tying for the highest frequency (e.g., [1, 2, 2, 4, 4] → Modes: 2, 4).
- Multimodal Distribution: Three or more values sharing the peak frequency.
- No Mode (Uniform): All data values appear exactly the same number of times (e.g., [1, 2, 3, 4, 5]).
Companion Central Tendency Comparisons
- Mode vs Mean: The mode represents the most popular value, while the mean is the numerical average.
- Mode vs Median: The median divides the sample in half, resistant to extreme outliers.
- Categorical Suitability: The mode is the only measure of central tendency applicable to nominal categorical data.
Paste your numbers into the dataset box above to compute the mode, frequency distribution, and summary statistics instantly.
Formula & Calculation Logic
Mathematical FormulaThe mode is determined by counting occurrences of each unique value. The value with the highest tally is the mode.
Step-by-Step Guide
Enter Numbers
Paste numbers separated by commas, spaces, or newlines into the input box.
Generate Frequency Table
Click calculate to generate the frequency table and identify peak counts.
Identify Mode Classification
Determine the mode status: unimodal, bimodal, multimodal, or no mode.
Compare Summary Statistics
Review companion statistics: mean, median, range, and percentage distribution.
Worked Examples Table
| Example | Input Values | Calculated Result | Explanation |
|---|---|---|---|
| Unimodal Dataset: 1, 2, 2, 3, 4, 7, 9 | The number 2 appears twice while all other numbers appear once. | ||
| Bimodal Dataset: 10, 12, 12, 15, 18, 18, 20 | Both 12 and 18 appear twice, creating two distribution peaks. | ||
| No Mode Dataset: 4, 8, 15, 16, 23, 42 | All 6 numbers appear exactly once with equal frequency. |
Frequently Asked Questions
Evidence-Based Methodology & Authoritative References
NIST/SEMATECH e-Handbook of Statistical Methods
Wolfram MathWorld - Statistical Mode
Standard: ISO / W3C / IETF Authoritative Domain Standard
Formula: Mode = Value with max(Frequency)
Last Reviewed: August 21, 2026
Primary Source: NIST/SEMATECH e-Handbook of Statistical Methods
Reference Document: Wolfram MathWorld - Statistical Mode
Computation Privacy: 100% client-side 0ms computation, zero data retention
Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.
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Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.