How this calculation works
Enter explicit outer edges and a whole bin count. Internal bins include their left edge and exclude the right; the final bin includes the final upper edge. Observations outside the outer range cause an error instead of being dropped.
bin width = (upper − lower)/bins; relative frequency = bin count/nA worked example
For 0,5,10,15,20 with edges 0 and 20 and two bins, [0,10) has 2 observations and [10,20] has 3. Relative frequencies are 40% and 60%.
Good to know
Unweighted descriptive calculations for up to 1,000 observations within ±1 trillion. Floating-point arithmetic and rounded display are used. No missing values are silently removed, no population distribution is inferred, and no confidence intervals are supplied.
Reference: NIST: histograms and frequency bins (opens in a new tab) ↗
Bin choices change the summary without changing the data
A grouped frequency table counts values within numerical intervals. Narrow bins show more local detail but may create many small counts; wide bins merge differences. A feature that appears under one binning choice should be checked against other reasonable widths.
The outer edges and bin count determine a common width. For edges 0 and 20 with two bins, the intervals are [0,10) and [10,20]. The internal edge 10 belongs to the second bin, while the final endpoint 20 is included in the last bin.
Every observation must lie within the stated outer edges. An out-of-range value causes an error instead of being silently excluded. This keeps the denominator for relative frequencies tied to the full supplied dataset.
Counts, proportions and densities have different units
Relative frequency is the bin count divided by the total count. Cumulative count sums through the current bin. The final cumulative count should equal the number of observations and all relative frequencies should sum to approximately 100% after display rounding.
A probability density histogram would divide relative frequency by bin width as well. This table reports counts and relative frequencies, not density heights. The distinction matters when comparing interval widths or interpreting a plotted area.
A stem-and-leaf plot preserves aligned individual observations, whereas a frequency table loses their positions inside each bin. Use the more detailed display when sample size and range make it readable; use grouped summaries when broad patterns are the question.
A few questions, answered
Which bin receives an exact internal-edge value?
The bin on its right. All bins are left inclusive and right exclusive, except the last bin also includes the final upper edge.
Are empty bins retained?
Yes. All requested equal-width intervals appear, including those with count zero.
Can I use unequal-width intervals?
Not here. This tool uses 1–50 equal-width bins with explicit outer edges.