Enter Data and Bin Options
Example Data Table
This sample shows how raw values can become grouped data.
| Sample Values | Rule | Data Count | Approximate Bins | Use Case |
|---|---|---|---|---|
| 12, 14, 17, 20, 21, 25, 28, 34, 39, 42 | Sturges | 10 | 5 | Small classroom dataset |
| 8, 9, 11, 12, 14, 18, 22, 30, 31, 37 | Square Root | 10 | 4 | Quick visual grouping |
| 5, 7, 8, 8, 9, 15, 16, 19, 24, 40 | Freedman-Diaconis | 10 | Depends on IQR | Data with possible outliers |
Formula Used
Sturges Rule: k = ceil(log₂(n) + 1)
Square Root Rule: k = ceil(√n)
Rice Rule: k = ceil(2 × n1/3)
Freedman-Diaconis Width: h = 2 × IQR / n1/3
Scott Width: h = 3.5 × s / n1/3
Relative Frequency: class frequency / total count
Density: frequency / (total count × bin width)
The calculator first sorts the values. It finds the minimum, maximum, range, mean, median, quartiles, variance, and standard deviation. Then it chooses the bin count or bin width from the selected rule. Each value is placed into its matching class interval. The last bin includes its upper endpoint, so maximum values are not missed.
How to Use This Calculator
- Paste numeric values into the data box.
- Separate values with commas, spaces, semicolons, or new lines.
- Select a bin rule for automatic grouping.
- Use manual bin count or width when required.
- Add optional lower and upper boundaries if needed.
- Choose decimal precision for cleaner output.
- Press the calculate button to view results.
- Download the frequency table as CSV or PDF.
Bins Statistics Guide
What Bins Mean
Bins are class intervals used to group numeric data. They help convert many raw values into a compact frequency table. This is useful when values are too detailed to read one by one. A good bin plan makes the distribution easier to understand. It can show center, spread, gaps, and skew. It also prepares data for a histogram.
Why Bin Choice Matters
A small number of bins can hide important movement. A very large number can create noise. The right choice depends on sample size, range, and variation. Sturges rule is simple and works well for many small datasets. The square root rule is fast and easy. Rice rule often gives more detail. Scott rule uses standard deviation. Freedman-Diaconis uses the interquartile range and handles outliers better.
Reading the Output
The frequency column shows how many values fall inside each class. Relative frequency shows the share of all values. Cumulative frequency adds classes from the bottom upward. Density adjusts frequency by bin width. This matters when comparing histograms with different class sizes. Midpoints are useful for grouped estimates and charts.
Advanced Use
Custom boundaries are helpful when reports need fixed class limits. Manual widths are useful for audit bands, score ranges, ages, prices, and lab measurements. Manual bin counts help when a chart must match a given style. Always check underflow and overflow counts. These show values outside your selected boundaries. If many values fall outside, widen the range or remove the custom limits.
Best Practice
Try more than one rule before final reporting. Compare the shape of the grouped table. Look for empty bins, extreme peaks, and long tails. Use the exported table in reports, dashboards, lessons, or quality checks. Keep the raw data saved, because grouped data loses detail.
FAQs
What is a bin in statistics?
A bin is a numeric interval. It groups values inside a lower and upper limit. Bins are commonly used to build histograms and frequency tables.
Which bin rule should I choose?
Use Sturges for small simple datasets. Use Freedman-Diaconis when outliers may exist. Use Scott when spread is important. Manual options work for fixed reporting ranges.
What is bin width?
Bin width is the size of each class interval. A width of 5 means each bin covers five units, such as 10 to 15.
What is relative frequency?
Relative frequency is the class frequency divided by the total number of values. It shows the proportion of data inside each bin.
Why is the upper boundary adjusted?
The calculator may extend the upper boundary so all bins have equal width. This keeps the frequency table consistent and easier to compare.
Can I use negative numbers?
Yes. The calculator accepts negative values, decimals, and whole numbers. Enter them with commas, spaces, semicolons, or line breaks.
What does density mean?
Density adjusts frequency by total count and bin width. It helps compare distributions when class widths or sample sizes differ.
Why do some values show as underflow or overflow?
Underflow values are below your chosen lower boundary. Overflow values are above the adjusted upper boundary. Review custom boundaries if these counts are high.