# What is Sturges’ Rule? (Definition & Example)

A histogram is a chart that helps us visualize the distribution of values in a dataset.

It turns out that the number of bins used in a histogram can have a huge impact on how we interpret the data.

If we use too few bins, the true underlying pattern in the data can be hidden: And if we use too many bins, we may just be visualizing the noise in a dataset: Fortunately, we can use a method known as Sturges’ Rule to determine the optimal number of bins to use in a histogram.

Sturges’ Rule uses the following formula to determine the optimal number of bins to use in a histogram:

Optimal Bins = ⌈log2n + 1⌉

where:

• n: The total number of observations in the dataset.
• ⌈ ⌉: Symbols that mean “ceiling” – i.e. round the answer up to the nearest integer.

### Example: Sturges’ Rule

Suppose we have the following dataset with n = 31 total observations: We can use Sturges’ Rule to determine the optimal number of bins to use to visualize these values in a histogram:

Optimal Bins = ⌈log2(31) + 1⌉ = ⌈4.954 + 1⌉ = ⌈5.954⌉ = 6.

According to Sturges’ Rule, we should use 6 bins in the histogram we use to visualize this distribution of values.

Here’s what a histogram with 6 bins would look like for this dataset: Notice how this seems to be enough bins to get a good idea of the underlying distribution of values without being too many that we’re just visualizing the noise in the data.

### Common Values for Sturges’ Rule

The following table shows the optimal number of bins to use in a histogram based on the total number of observations in a dataset, according to Sturges’ Rule: ### Alternatives to Sturges’ Rule

Sturges’ Rule is the most common method for determining the optimal number of bins to use in a histogram, but there are several alternative methods including:

The Square-root Rule: Number of bins = ⌈√n

The Rice Rule: Number of bins = ⌈2 * 3n

The Freedman-Diaconis’ Rule: Number of bins = (2*IQR) / 3n where IQR is the interquartile range.

### Bonus: Sturges’ Rule Calculator

Use this free online calculator to automatically apply Sturges’ Rule to determine the optimal number of bins to use for a histogram based on the size of a dataset.