Histogram Generator
Create histograms and frequency distributions from your data. Visualize data distribution with automatic binning and detailed statistics.
What is a Histogram?
A histogram is a graphical representation of data distribution. It groups data into bins (intervals) and displays the frequency of values falling within each bin as bars.
How to Read a Histogram
- X-axis: Shows the range of values divided into bins
- Y-axis: Shows the frequency (count) of values in each bin
- Bar height: Represents how many values fall in that range
- Shape: Reveals the distribution pattern (symmetric, skewed, etc.)
Binning Methods
Sturges’ Formula (Auto)
k = 1 + 3.322 × log₁₀(n)
Good for normally distributed data with moderate sample sizes.
Square Root Rule
k = √n
Simple rule that works well for many distributions.
Custom Bins
Specify the exact number of bins based on your data and analysis needs.
Distribution Shapes
| Shape | Description | Example |
|---|---|---|
| Symmetric | Mirror image on both sides | Test scores |
| Right-skewed | Tail extends to the right | Income data |
| Left-skewed | Tail extends to the left | Age at retirement |
| Bimodal | Two distinct peaks | Mixed populations |
| Uniform | All bars similar height | Random numbers |
Statistics Provided
This tool calculates:
- Count: Total number of data points
- Min/Max: Range of values
- Mean: Average value
- Median: Middle value
- Range: Difference between max and min
Best Practices
- Choose appropriate bin count - Too few bins hide patterns; too many create noise
- Start with automatic binning - Adjust if needed
- Consider your audience - Simpler histograms for general audiences
- Label clearly - Include axis titles and units
Related Tools
- Mean Calculator - Calculate the average
- Standard Deviation Calculator - Measure spread
- Probability Calculator - Calculate probabilities
- Descriptive Statistics Calculator - Complete statistics
Frequently Asked Questions
What is a histogram used for?
A histogram visualizes the distribution of numerical data by grouping values into bins and showing the frequency of each bin. It helps you see patterns like symmetry, skewness, outliers, and whether data is normally distributed.
How is a histogram different from a bar chart?
Histograms display continuous data grouped into intervals (bins) with no gaps between bars. Bar charts display categorical data with gaps between bars. Histograms show frequency distributions; bar charts compare discrete categories.
How many bins should I use for a histogram?
A common rule is the square root of the number of data points (√n). Sturges’ formula (1 + 3.322 × log₁₀(n)) also works well. Start with automatic binning, then adjust: too few bins hide patterns, too many create noise.
What does histogram shape tell you about data?
Symmetric (bell-shaped) suggests normal distribution. Right-skewed (tail to right) means most values are low with some high outliers. Left-skewed (tail to left) means most values are high with some low outliers. Bimodal (two peaks) suggests two distinct groups.
How do I read a histogram?
The x-axis shows value ranges (bins), the y-axis shows frequency (count). Taller bars indicate more data points in that range. Look for the center (peak), spread (width), shape (symmetric vs skewed), and any gaps or outliers.
Want to learn the theory?
Our lessons explain the statistical concepts behind this calculator with clear examples.
Browse Lessons →