Visual Tool
BY: Statistics Fundamentals Team
Reviewed By: Minsa A (Senior Statistics Editor)

Histogram Maker

Create professional histograms from your data instantly. Paste values, choose bin width or let the tool calculate it automatically — get frequency, relative frequency, and cumulative distributions with optional normal curve overlay. Download as SVG or PNG.

Histogram Maker

Bin Width Auto (Sturges / Scott / FD) Modes Frequency · Relative · Density · Cumulative
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Bins—
Mean—
Std Dev—

Histogram

Descriptive Statistics

n (count)—
Mean—
Median—
Std deviation—
Variance—
Min / Max—
Skewness—

Bin Information

Number of bins—
Bin width—
Bin method used—
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Last bin end—
Modal bin—
Peak frequency—

Frequency Distribution Table

BinIntervalFrequencyRel. Freq.Cum. Freq.Cum. Rel. Freq.

Histogram Examples

Browse examples or create your own above

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What Is a Histogram?

A histogram is a graphical display of the distribution of continuous numerical data using adjacent rectangular bars. Each bar represents a bin (a range of values), and the bar's height corresponds to the frequency, relative frequency, or probability density of observations falling within that bin. Unlike bar charts, histogram bars touch each other because the underlying data is continuous — there are no gaps between bins.

Histograms were introduced by Karl Pearson in 1895 and remain one of the most fundamental tools in exploratory data analysis. According to the NIST Engineering Statistics Handbook, histograms are the first chart to draw when you receive a new dataset — they immediately reveal shape, center, spread, skewness, and potential outliers.

How to Choose Bin Width

Sturges' rule (default): k = ⌈log₂(n)⌉ + 1 bins. Works well for roughly normal distributions with n ≤ 200. Simple and widely used in textbooks and classroom settings.
Scott's rule: h = 3.49σ/n^(1/3). Optimal for normally distributed data, minimizing mean integrated squared error. Better than Sturges for larger datasets.
Freedman-Diaconis rule: h = 2·IQR/n^(1/3). Robust to outliers because it uses IQR instead of standard deviation. Best for skewed or heavy-tailed data.
Manual bin width: Use when you have domain-specific reasons for particular boundaries (e.g. grade ranges 60-70-80-90-100, age groups 0-10-20, salary brackets). Ensure bin width is consistent across all bins.

Histogram Shape Interpretation

ShapeDescriptionCommon Examples
Symmetric / Bell-shapedMirror-image left and right, single peak in centerIQ scores, measurement errors, heights
Right-skewed (positive)Long tail on the right, bulk of data on leftIncome, house prices, reaction times
Left-skewed (negative)Long tail on the left, bulk of data on rightExam scores with ceiling effect, age at retirement
BimodalTwo peaks; suggests two distinct subgroupsMixed populations, shift-work schedules
UniformRoughly equal frequency across all binsRandom number generators, uniform sampling
J-shapedMonotonically increasing or decreasingAge at first marriage, disease latency periods

Histogram vs Bar Chart

Histograms show the distribution of continuous quantitative data; bar charts compare discrete categories. In a histogram, bars touch because adjacent bins share a boundary — the data is continuous. In a bar chart, gaps between bars indicate the categories are separate and unordered. The key test: if your x-axis has numerical ranges, use a histogram. If it has named categories (departments, countries, products), use a bar chart.

Related Topics

Descriptive Statistics Box Plot Generator Bell Curve Generator Descriptive Stats Calculator Normal Distribution Guide Frequency Distribution Table

Sources & further reading:

  • NIST Engineering Statistics Handbook — Histograms
  • Pearson, K. (1895). Contributions to the mathematical theory of evolution. Philosophical Transactions of the Royal Society A. [First use of the histogram]
  • Freedman, D. & Diaconis, P. (1981). On the histogram as a density estimator. Zeitschrift für Wahrscheinlichkeitstheorie.

Frequently Asked Questions

There's no single answer — it depends on your data size and goals. Too few bins hide detail; too many bins make the chart noisy. Use Sturges' rule (k = log₂(n) + 1) as a starting point for normally distributed data with n ≤ 200. For larger samples or non-normal data, try Scott's or Freedman-Diaconis rules. Always inspect the result and adjust manually if needed.

Relative frequency is the proportion of observations in each bin: relative frequency = count / total × 100%. It allows comparison between histograms with different sample sizes. A relative frequency histogram has the same shape as a frequency histogram but shows percentages on the y-axis instead of counts.

A probability density histogram scales the y-axis so that the total area of all bars equals 1. The height of each bar is: density = relative frequency / bin width. This allows direct comparison with probability density functions (like the normal PDF). It's useful when overlaying a fitted curve and when bin widths are unequal.

Histograms display the distribution of continuous numerical data — bars touch because adjacent bins share a boundary. Bar charts compare discrete categories with gaps between bars to indicate separation. The x-axis test: ranges (0-10, 10-20) → histogram; names (Math, English, Science) → bar chart. Mixing them up is one of the most common mistakes in data visualization.

The normal curve overlay draws the theoretical normal distribution fitted to your data's mean and standard deviation. If your histogram bars closely follow the curve, the data is approximately normally distributed. Large deviations — especially skewness (asymmetry) or heavy tails — suggest non-normality, which matters for choosing appropriate statistical tests.