(Not recommended) Histogram bin counts (2024)

FAQs

What is the recommended number of bins for a histogram? ›

Choose between 5 and 20 bins. The larger the data set, the more likely you'll want a large number of bins. For example, a set of 12 data pieces might warrant 5 bins but a set of 1000 numbers will probably be more useful with 20 bins. The exact number of bins is usually a judgment call.

Several rules of thumb exist for determining the number of bins, such as the belief that between 5 and 20 bins is usually adequate (for example, Matlab uses 10 bins as a default).

If you have too many bins, then the data distribution will look rough, and it will be difficult to discern the signal from the noise. On the other hand, with too few bins, the histogram will lack the details needed to discern any useful pattern from the data.

The default 'auto' algorithm chooses a bin width to cover the data range and reveal the shape of the underlying distribution. Scott's rule is optimal if the data is close to being normally distributed. This rule is appropriate for most other distributions, as well. It uses a bin width of 3.5*std(X(:))*numel(X)^(-1/3) .

A 'bin' for each sample point gives us no more information, but only stretches the width of the chart. A good bin width will usually show a recognizable normal probability distribution curve, unless the data is really multi-modal. Then there could be two or more distinct 'humps' in the histogram chart.

optBINS (optimal binning) determines the optimal number of bins in a uniform bin-width histogram by deriving the posterior probability for the number of bins in a piecewise-constant density model after assigning a multinomial likelihood and a non-informative prior.

Thus varying the bin width within a histogram can be beneficial. Nonetheless, equal-width bins are widely used. Several rules of thumb exist for determining the number of bins, such as the belief that between 5 and 20 bins is usually adequate.

There is no hard maximum for the number of bins in a histogram. If the variable being plotted is continuous, then an argument can be made for an infinite number of categories (and the histogram basically becomes a rug plot). The number of points in the data set is not an appropriate upper bound.

A histogram can be misleading if it has a deceptive scale and/or inappropriate starting and ending points on the y-axis. Watch the scale on the y-axis of a histogram. If it goes by large increments and has an ending point that's much higher than needed, you see a great deal of white space above the histogram.

Why would a histogram not be an appropriate? ›

A histogram would not be appropriate because histograms are used for continuous data and the data obtained is not continuous.

The Freedman-Diaconis rule is very robust and works well in practice. The bin-width is set to h=2×IQR×n−1/3. So the number of bins is (max−min)/h, where n is the number of observations, max is the maximum value and min is the minimum value.

We prefer the Rice rule, which is to set the number of intervals to twice the cube root of the number of observations. In the case of 1000 observations, the Rice rule yields 20 intervals instead of the 11 recommended by Sturges' rule.

Sturges' Rule Formula

The following formula is used to calculate the optimal number of bins in a histogram using sturges' rule. To calculate the optimal number of bins using sturges' rule, take the log base 2 of the number of observations in the data set, then add 1 to this result.

There is no strict rule on how many bins to use—we just avoid using too few or too many bins.

The Freedman-Diaconis rule is very robust and works well in practice. The bin-width is set to h=2×IQR×n−1/3. So the number of bins is (max−min)/h, where n is the number of observations, max is the maximum value and min is the minimum value.

Typically, no fewer than 5 and no more than 20 class intervals work best for a frequency histogram. Choose the first class interval to include your lowest (smallest value) data and make sure that no overlap exists so that one piece of data does not fall into two class intervals.