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Histogram Generator – Create Histograms Online Free

Create professional histograms from any dataset with our free online histogram generator. Customize bin sizes and view frequency distributions as visual bar charts instantly.

Leave empty for automatic (Sturges' formula)

Examples:

Understanding Histograms

A histogram is a graphical representation of data distribution. Unlike a bar chart that compares categories, a histogram shows how numerical data is distributed across continuous ranges called bins. The height of each bar represents how many data points fall within that range.

Histograms reveal patterns that raw numbers hide. You can quickly see if data is symmetric or skewed, identify outliers, spot gaps or clusters, and understand the overall shape of the distribution. They're essential tools in statistics, quality control, and data analysis.

How to Create a Histogram

  1. 1

    Collect and sort your data

    Gather all values and find the minimum and maximum to determine the range.

  2. 2

    Choose the number of bins

    Too few bins hide patterns; too many create noise. For most datasets, 5-15 bins work well.

  3. 3

    Calculate bin width

    Bin width = (max - min) / number of bins. Round to a convenient number if needed.

  4. 4

    Count frequencies

    Tally how many values fall into each bin. Each value goes into exactly one bin.

  5. 5

    Draw the histogram

    Draw bars with heights proportional to frequencies. Bars touch each other (no gaps).

Worked Examples

Example 1: Test Scores Histogram

Data: 65, 72, 78, 81, 85, 68, 73, 79, 82, 88, 70, 75, 80, 84, 90 (15 scores)

Min = 65, Max = 90, Range = 25
Using 5 bins: Width = 25/5 = 5
Bins: [65-70), [70-75), [75-80), [80-85), [85-90]
Count scores in each bin to create the histogram.

Example 2: Interpreting Histogram Shape

Symmetric (bell-shaped): Data clusters in the middle, tails off equally on both sides. Normal distribution.

Right-skewed: Long tail on the right. Common in income data, house prices.

Left-skewed: Long tail on the left. Common in test scores with a ceiling effect.

Bimodal: Two peaks. May indicate two different populations mixed together.

Example 3: Choosing Bin Numbers

Sturges' formula: bins = 1 + 3.322 × log₁₀(n)
For n = 100: bins ≈ 1 + 3.322 × 2 = 7.6 ≈ 8 bins
For n = 500: bins ≈ 1 + 3.322 × 2.7 = 10 bins
Square root rule: bins ≈ √n also works well.

Quick Fact

The histogram was introduced by Karl Pearson in 1895. Pearson, a founder of modern statistics, also developed the chi-squared test and correlation coefficient. He believed strongly in using data to understand the world – a revolutionary idea at the time.

Frequently Asked Questions

What's the difference between histogram and bar chart?

Histograms show distribution of continuous data – bars touch each other and represent ranges. Bar charts compare categorical data – bars are separated and represent distinct categories. Histograms have area proportional to frequency; bar charts have height proportional to value.

How do I choose the right number of bins?

Start with Sturges' formula or square root of sample size. Adjust based on what reveals patterns best. Too few bins oversimplify; too many create noise. Try different bin counts and see which tells the clearest story.

What if a value falls on a bin boundary?

By convention, the left boundary is inclusive and the right is exclusive. So [60-70) includes 60 but not 70. The value 70 goes in the next bin [70-80). This prevents double-counting.

Can histograms have unequal bin widths?

Yes, but then bar height should represent frequency density (frequency/width), not raw frequency. This ensures area is proportional to frequency. Equal-width bins are simpler and work for most purposes.

What does a gap in a histogram mean?

A gap (bin with zero frequency) suggests no data values in that range. This could indicate two separate populations, a natural break in the data, or simply random variation in small samples.

How do I compare two distributions?

Use the same bin boundaries for both histograms and overlay them (with transparency) or place them side by side. Alternatively, use frequency polygons (line graphs connecting bin midpoints) for cleaner comparison.

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