Histogram Generator
Paste or type numbers separated by commas or spaces, choose a bin count, and review the resulting frequency table alongside a quick summary.
Paste or type numbers separated by commas or spaces, choose a bin count, and review the resulting frequency table alongside a quick summary.
Histograms group continuous or discrete numeric data into consecutive intervals so you can quickly see where observations cluster. Suppose you have measurements represented by the set . After choosing a bin width , each bin counts the number of values that fall within its range. The frequency of bin is formally computed as , where denotes the left edge of the interval. Plotting these counts reveals the data’s shape—symmetry, skew, multimodality, or outliers.
Selecting an appropriate number of bins helps balance detail and readability. Too few bins hide structure; too many make the histogram noisy. A popular rule of thumb is the Freedman–Diaconis rule, which suggests a bin width of using the sample interquartile range. Try different bin counts with the calculator, then compare the results with tools such as the standard deviation calculator and the scatter plot generator to see complementary perspectives on the same data.
Consider the sample data set 4, 5, 5, 6, 6, 7, 9, 12, 12, 14. With four bins, the calculator produces intervals of equal width and the following table. Notice how the third bin captures the cluster around 12 while the first bin contains the lower values.
| Bin interval | Count |
|---|---|
| [4.00, 6.50) | 4 |
| [6.50, 9.00) | 3 |
| [9.00, 11.50) | 0 |
| [11.50, 14.00] | 3 |
If you change the bin count to eight, the tool reveals smaller fluctuations but also introduces empty bins that may distract from the main trends. Experimenting with different settings helps you decide which view best communicates your story.
Analysts often evaluate multiple rules when choosing a histogram layout. The comparison below illustrates how three common strategies behave for a sample of 1,000 observations drawn from a normal distribution. Each approach uses a different formula for bin width, leading to distinct levels of smoothing.
| Rule | Bin width | Resulting bins | Notes |
|---|---|---|---|
| Square-root choice | ≈0.63 | 32 | Simple heuristic that works for many classroom examples. |
| Sturges' rule | ≈0.82 | 24 | Prefers fewer bins and can oversmooth large data sets. |
| Freedman–Diaconis | ≈0.54 | 37 | Uses the interquartile range and adapts to outliers. |
After evaluating the histogram, consider pairing it with box plots or descriptive statistics to provide multiple views of the same distribution. AgentCalc offers tools such as the quartile calculator that complement histogram analysis.