Histogram Maker

Paste a list of numbers and get a clean, labeled histogram in one click — with a full frequency distribution table (frequency, relative frequency, and cumulative frequency) and a downloadable SVG for homework, reports, and slides.

Need to plan the classes by hand first? The class width calculator shows the arithmetic step by step.

How to Make a Histogram

  1. Find the smallest and largest values; their difference is the range.
  2. Choose a number of bins. Sturges' rule, k = ⌈log₂(n) + 1⌉, is a common starting point.
  3. Divide the range by k and round up to a convenient bin width.
  4. Start the first bin at or just below the minimum and add the width repeatedly.
  5. Count how many values land in each bin, then draw touching bars with heights equal to those counts.

Each bin includes its lower edge and excludes its upper edge — a value of exactly 70 goes in the 70–80 bin, not 60–70 — except the last bin, which also includes its upper edge so the maximum is never dropped.

Worked Example: 20 Exam Scores

Click Load example to use these scores: 62, 67, 71, 74, 75, 78, 79, 81, 82, 83, 84, 85, 86, 88, 89, 90, 91, 93, 95, 98.

  1. n = 20, minimum 62, maximum 98, range = 36.
  2. Sturges: ⌈log₂(20) + 1⌉ = ⌈5.32⌉ = 6 bins, so a raw width of 36 ÷ 6 = 6.
  3. Rounded up to a friendly width of 10, starting at 60: bins 60–70, 70–80, 80–90, 90–100.
  4. Frequencies: 2, 5, 8, 5 — relative frequencies 10%, 25%, 40%, 25%.

The histogram peaks in the 80s and has a longer tail on the left, a mild left (negative) skew. Confirm that numerically with the skewness calculator, or compare with the box plot of the same data.

Reading a Histogram's Shape

  • Symmetric / bell-shaped: mean ≈ median; the empirical rule may apply.
  • Right-skewed: a long tail toward large values (incomes, wait times); mean > median.
  • Left-skewed: a long tail toward small values (easy-exam scores); mean < median.
  • Bimodal: two peaks, often a sign that two different groups are mixed together.
  • Gaps and isolated bars: possible outliers — check them with the outlier calculator.

Histogram vs. Bar Chart

A histogram displays the distribution of one numerical variable, so its bars touch and the horizontal axis is a continuous number line. A bar chart compares categories — colors, brands, countries — so its bars are separated and can be reordered freely. If your data are labels rather than numbers, a bar chart is the right choice.

Frequently Asked Questions

How many bins should a histogram have?

There is no single correct number, but 5 to 20 bins suit most data sets. Sturges' rule, ⌈log₂(n) + 1⌉, gives 6 bins for 20 values and 11 for 1,000. Too few bins hide the shape; too many make it noisy. Try a few settings and choose the one that shows the pattern most clearly.

Which bin does a value on the boundary go into?

This maker uses left-closed bins, [lower, upper): a value equal to a boundary goes into the bin that starts there. The final bin is closed on both sides so the maximum is counted.

What is a relative frequency histogram?

It has the same bars as a frequency histogram, but the heights are proportions (frequency ÷ n) instead of counts. The relative column in the table gives those proportions, which always sum to 100%.

Can I use the histogram in Word or Google Docs?

Yes. Download SVG saves a vector image that scales without blurring. Word, PowerPoint, and Google Docs accept SVG directly; for other programs, open the SVG in a browser and take a screenshot or print it to PDF.

How do I make a histogram in Excel or on a TI-84?

In Excel 2016 or later, select the data and choose Insert → Statistic Chart → Histogram, then set the bin width under Format Axis. On a TI-84, enter data in L1, turn on STAT PLOT 1 with the histogram type, set Xscl to the bin width in WINDOW, and press GRAPH.

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