Adventures in Machine Learning

Creating Accurate Histograms: Choosing the Optimal Number of Bins

Histograms are an essential data visualization tool that shows the distribution of a set of continuous numerical data. A histogram is typically created by dividing the data range into intervals or bins and then plotting the frequency (or relative frequency) of the data points that fall within each bin.

Pandas, a popular data manipulation library in Python, provides an easy way to create histograms from pandas DataFrame. In this article, we’ll explore how to modify the number of bins in a pandas histogram and what the default number of bins is.

Using the bins argument to modify the number of bins in a pandas histogram

By default, pandas’ hist() method generates a histogram with ten bins. However, you can modify the number of bins to provide more granularity or simplicity in the visualization.

The hist() method accepts a bins argument that specifies the number of bins to use. For instance, hist(bins=20) will create a histogram with twenty bins, and hist(bins=5) will generate a histogram with five bins.

Multiple ways can be used to provide the number of bins. For example, you can specify the number of bins directly using the bins argument, as we’ve seen earlier.

Alternatively, you can also provide a range of values, and pandas will divide the range into equal-width bins. For instance, the code snippet below creates a histogram with five bins, where each bin represents a range of 10.

“`python

import pandas as pd

import numpy as np

data = pd.DataFrame({‘values’: np.random.normal(size=100)})

data.hist(column=’values’, bins=[-2, -1, 0, 1, 2])

“`

Changing the number of bins in a pandas histogram

Histograms can be incredibly informative, but setting the correct number of bins is crucial to avoid misleading interpretations. Too few bins make the distribution look too simple, while having too many bins can lead to overfitting and noise.

Finding the right number of bins is often more art than science and depends on the data and the context. One method for selecting the number of bins is to use the “square-root rule.” This rule suggests setting the number of bins to be the square root of the number of observations in the data set.

This heuristic rule creates a good balance between simplicity and information density, although it might not always be optimal for all cases. Another method for selecting the number of bins is the Freedman-Diaconis rule.

This rule suggests setting the bin width to 2 * IQR / n^(1/3), where the IQR is the interquartile range, and n is the number of data points. The ideal bin size is then the range of the data divided by the bin width.

Default number of bins in a pandas histogram

Pandas uses ten as the default number of bins in a histogram, but the number of bins can be changed using the bins argument. Ten may not always be the optimal number of bins, depending on the data’s nature and structure.

It’s also essential to note that the default number of bins can vary depending on the dataset’s size and nature. For example, if the data range is significantly smaller or larger than ten, pandas may adjust the number of bins accordingly to provide a better visualization.

Conclusion

Choosing the right number of bins is crucial to creating informative and accurate data visualizations. Pandas’ hist() method provides an easy way to create histograms from pandas DataFrame, and the number of bins can be customized using the bins argument.

While pandas defaults to ten bins, the number of bins can be changed using a range of techniques and methods like the square-root rule or Freedman-Diaconis rule. It’s essential to test multiple bin sizes to ensure that the resulting histogram provides meaningful insight into the data.

Choosing the optimal number of bins for a histogram is a critical step in creating an informative data visualization. The number of bins determines the granularity of the histogram and can affect how we interpret the distribution of the data.

Importance of choosing optimal number of bins for a histogram

If we choose too few bins, the histogram becomes too general and does not provide enough detail to understand the data correctly. On the other hand, if we choose too many bins, the histogram may become too detailed and show noise instead of patterns or trends.

The optimal number of bins varies depending on the data and the context. In general, we want to choose a number of bins that shows the underlying patterns in the data without creating false or misleading ones.

In this article, we will look at some tools and techniques that can help determine the optimal number of bins for a histogram. Sturges’ Rule for determining the optimal number of bins

Sturges’ Rule is a simple and commonly used formula for determining the optimal number of bins for a histogram.

Sturges proposed that the number of bins should be equal to ceil(log2(n+1)), where n is the number of observations in the dataset, and ceil is the ceiling function. Intuitively, Sturges’ Rule relies on the assumption that the optimal number of bins is a function of the number of observations in the dataset, with more observations requiring more bins to provide sufficient detail.

The plus one term accounts for the minimum required bin to include all observations. For example, suppose we have a dataset with 100 observations.

According to Sturges’ Rule, the optimal number of bins would be ceil(log2(100+1)) = 7. However, it is essential to note that Sturges’ Rule assumes that the data is normally distributed, and it may not provide the optimal number of bins for non-normal data.

In such a case, alternative methods, such as the Freedman-Diaconis rule, may provide a better estimation of the optimal number of bins.

Freedman-Diaconis rule for determining the optimal number of bins

The Freedman-Diaconis rule is an alternative method for determining the optimal number of bins for a histogram. This rule takes into account the interquartile range (IQR) of the data, which is a measure of the data’s spread, and the number of observations in the dataset.

The formula for the bin width is given by:

bin width = 2 * IQR / (n)^(1/3)

where n is the number of observations in the dataset. The optimal number of bins is then determined by taking the range of the data and dividing it by the bin width.

For example, suppose we have a dataset with 100 observations. The formula above for the bin width would be:

bin width = 2 * IQR / (100)^(1/3)

where IQR is the interquartile range of the dataset.

Once we have the bin width, we can divide the range of the data by the bin width to determine the number of bins. While the Freedman-Diaconis rule is widely recognized for being robust to outliers and non-normal data, it may also tend to overfit datasets with small sample sizes.

Visualization

In practice, it is a good idea to experiment with multiple bin sizes to determine the optimal one for the dataset at hand. Creating several histograms with differing numbers of bins can help determine which one is most informative and clearly shows the data’s patterns.

Conclusion

Determining the optimal number of bins for a histogram is an essential step in creating a data visualization that is informative and accurate. The choice of the number of bins affects the granularity of the histogram and can dramatically affect how we interpret the distribution of the data.

Several methods can be used to calculate the optimal number of bins for a histogram, such as Sturges’ Rule and the Freedman-Diaconis rule. By using appropriate and verified methods, we can ensure that the data visualization we create is informative and accurate.

In conclusion, choosing the right number of bins for a histogram is essential to create an informative data visualization that accurately represents the distribution of the data. Sturges’ Rule and the Freedman-Diaconis rule are popular methods to determine the optimal number of bins for a histogram, but it is essential to test multiple bin sizes to ensure that the resulting visualization provides meaningful insight into the data.

By applying appropriate techniques and selecting the optimal number of bins, we can create data visualizations that help us draw insights and make informed decisions.

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