Generate histograms from raw data with 5 bin methods (Sturges, Square Root, Rice, Freedman-Diaconis, custom). SVG visualization, density, skewness, and bin comparison.
The histogram calculator groups raw numbers into equal-width bins and draws the result as a bar chart. It supports Sturges, Square Root, Rice, Freedman-Diaconis, and Custom binning, so you can compare a few different ways of summarizing the same dataset.
Histograms are useful when you want to see spread, skewness, clusters, and gaps at a glance. This calculator adds density values, cumulative frequencies, and a method comparison table so you can judge whether the bin choice is helping or hiding the pattern in the data.
Use it for continuous data such as ages, test scores, times, or measurements where the distribution shape matters more than the individual raw values.
Use a histogram when you need to see how values are clustered across a range. It is one of the fastest ways to spot skewed data, a long tail, a second peak, or a suspicious gap in the middle of the distribution.
The bin comparison in this calculator is especially helpful when you are not sure whether a narrow or wide bin width gives the clearest picture.
Sturges': k = 1 + 3.322 log₁₀(n). Freedman-Diaconis: width = 2 × IQR × n^(-1/3). Density = (relative frequency) / bin width. Pearson skewness = 3(mean − median) / SD.
Result: 5 bins, width 6.0, modal bin [73, 79) with frequency 5, near-symmetric skewness
Sturges' rule gives 5 bins for 15 data points. The histogram shows data concentrated in the middle bins with a slight left skew (Pearson skewness = −0.07). The red mean line at 81.5 sits slightly left of the tallest bar.
The method you choose changes the story the histogram tells. Sturges tends to give a smaller number of bins, which works well for small datasets. Freedman-Diaconis adapts to spread through the IQR and often works better for skewed data. Custom bins are useful when you need to match an existing reporting standard.
A symmetric histogram suggests values are balanced around the center. A right-skewed histogram has a long tail on the high end, while a left-skewed histogram has a tail on the low end. Multiple peaks can mean the data comes from more than one subgroup.
Histograms are common in quality control, survey analysis, and exploratory statistics because they give a quick visual summary before you move on to more formal measures such as variance, quantiles, or density curves.
Last updated:
Start with Sturges' rule for small/normal data or Freedman-Diaconis for larger or skewed data. Then adjust visually: too few bins create a flat, uninformative chart; too many make it spiky. The goal is to reveal the data's shape without noise. Most real datasets work well with 5–20 bins.
Histograms display continuous data grouped into bins — bars touch each other because the ranges are contiguous. Bar charts display categorical data — bars are separated because categories are distinct. Histograms show distributions; bar charts show comparisons.
A density histogram scales bar heights so that the total area of all bars equals 1. This makes it a probability distribution estimate and allows you to overlay theoretical PDFs (like the normal curve). The y-axis shows density (= relative frequency / bin width) instead of frequency.
Sturges' rule assumes normality and depends only on sample size n. Freedman-Diaconis uses the IQR (interquartile range) to adapt to the data's actual spread, making it more robust for skewed or heavy-tailed distributions. It typically produces narrower bins for tight data and wider bins for spread data.
Right-skewed: longer right tail, mean > median, more data clustered left. Left-skewed: longer left tail, mean < median, data clustered right. Symmetric: mirror image around center, mean ≈ median. The histogram's shape should match the numerical skewness measure.
Yes — outliers appear as isolated bars separated from the main body of the histogram by empty bins. However, histograms are less precise than box plots for outlier detection because the bin boundaries may obscure individual extreme values.