STATISTICSDescriptive StatisticsStatistics Calculator
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Mode Calculator

Free mode calculator. Find mode, modal frequency, modal percentage. Raw data, frequency table, group

Run CalculatorExplore data analysis and statistical calculations

Why This Statistical Analysis Matters

Why: Statistical calculator for analysis.

How: Enter inputs and compute results.

M
STATISTICSDescriptive Statistics

Mode Calculator โ€” Unimodal, Bimodal, Multimodal

Find the most frequent value(s). Raw data, frequency table, grouped data. King's formula for grouped mode estimate.

Mean Median Mode โ†’Median โ†’

Real-World Scenarios โ€” Click to Load

mode_results.sh
CALCULATED
$ compute_mode --type="unimodal"
Type
unimodal
Mode(s)
4
Modal freq
3
Modal %
50.00%
Share:
Mode Result
Mode Calculator
UNIMODAL
Mode(s): 4Freq: 350.0%
numbervibe.com/calculators/statistics/mode-calculator

Frequency Bar Chart (mode highlighted in teal)

Your Result: unimodal

For educational and informational purposes only. Verify with a qualified professional.

Key Takeaways

  • โ€ข Mode: the value(s) that appear most frequently in a dataset
  • โ€ข Unimodal: one mode. Bimodal: two modes. Multimodal: three or more
  • โ€ข No mode: when all values occur with equal frequency (e.g., all unique)
  • โ€ข Grouped data: modal class = class with highest frequency. Mode estimate uses King's formula
  • โ€ข Modal frequency: count of the most frequent value(s). Modal %: (modal freq / n) ร— 100

Did You Know?

๐Ÿ“ŠThe mode is the only measure of central tendency that can be used with categorical data (e.g., favorite color).Source: Statistics textbooks
๐Ÿ“For grouped data, the mode is estimated because we don't know exact values within each class. King's formula interpolates within the modal class.Source: King, 1912
๐Ÿ“ˆBimodal distributions often indicate two distinct groups (e.g., men and women shoe sizes).Source: Exploratory data analysis
๐ŸŽฏA dataset can have no mode (all unique), one mode, or multiple modes. All are valid.Source: Descriptive statistics
๐Ÿ“‰The mode is robust to extreme outliers, unlike the mean.Source: Robust statistics
๐Ÿ”ขFor continuous data, the mode corresponds to the peak of the probability density function.Source: Probability theory

How It Works

1. Raw Data Mode

Count each value. The value(s) with the highest count are the mode(s).

2. Frequency Table

Each row is value, frequency. The value(s) with maximum frequency are the mode(s).

3. Grouped Data

Modal class = class with highest frequency. Mode estimate: L + (fโ‚โˆ’fโ‚€)/(2fโ‚โˆ’fโ‚€โˆ’fโ‚‚) ร— h (King's formula).

Mode Types Quick Reference

TypeDefinition
No modeAll values have equal frequency
UnimodalExactly one value has the highest frequency
BimodalExactly two values share the highest frequency
MultimodalThree or more values share the highest frequency

Expert Tips

Categorical Data

Use mode for nominal/ordinal data. Mean and median require numeric data.

Bimodal Check

If bimodal, consider splitting the data into subgroups for separate analysis.

Grouped Mode Estimate

The formula assumes frequencies decrease on both sides of the modal class. Works best for unimodal grouped data.

Mode vs Mean vs Median

Mode: most common. Mean: average. Median: middle. Use mode for categorical; median for skewed numeric.

Frequently Asked Questions

When is there no mode?

When every value appears the same number of times (e.g., all values unique, or a uniform distribution).

What is the modal class?

In grouped data, the class interval with the highest frequency. The mode lies somewhere within this class.

What is King's formula?

Mode โ‰ˆ L + (fโ‚โˆ’fโ‚€)/(2fโ‚โˆ’fโ‚€โˆ’fโ‚‚) ร— h. L = lower boundary of modal class, fโ‚ = modal frequency, fโ‚€ = frequency before, fโ‚‚ = frequency after, h = class width.

Can the mode be used for continuous data?

Yes. For raw continuous data, the mode is the most frequent value. For grouped data, we estimate it within the modal class.

What is modal frequency?

The count (frequency) of the most frequent value(s). For unimodal data, it is how many times the mode appears.

How do I enter a frequency table?

Use value,frequency per line. Example: 7, 3 and 8, 4 on separate lines. Leave raw data empty to use frequency table.

Formulas Reference

Mode = value(s) with maximum frequency

For raw data or frequency table

Grouped: Mode โ‰ˆ L + (fโ‚โˆ’fโ‚€)/(2fโ‚โˆ’fโ‚€โˆ’fโ‚‚) ร— h

King's formula for grouped data

Modal % = (modal freq / n) ร— 100

Percentage of observations in modal value(s)

Mode by the Numbers

1
Unimodal = one peak
2
Bimodal = two peaks
3+
Multimodal = many peaks
0
No mode = uniform

Applications

Survey Analysis

Most common response (e.g., favorite product, preferred size).

Retail

Best-selling item, most purchased size or color.

Quality Control

Most frequent defect type, typical measurement value.

Demographics

Most common age group, income bracket in a population.

Disclaimer: For grouped data, the mode estimate assumes a smooth unimodal distribution within the modal class. Results may vary with different class boundaries.

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