*59*

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 = ⌈log _{2}n + 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** = ⌈log_{2}(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 * ^{3}√n⌉

**The Freedman-Diaconis’ Rule:** Number of bins = (2*IQR) / ^{3}√n 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.