Understanding Bins in Histograms

Histograms are a fundamental visualization tool for understanding data distribution. They display the frequency (or count) of data points that fall within specific ranges, providing a visual sense of how data is distributed. In Python, plt.hist() is commonly used to create these visualizations. The bars in a histogram represent these frequencies, with each bar corresponding to a specific range of values. These ranges are called bins. Imagine bins as containers lined up along a number line; each data point is placed into the container that matches its value. The height of a bar then indicates how many data points are held within that particular bin.

Understanding and controlling these bins is fundamental to creating informative histograms. The choice of bins can significantly alter the appearance and, consequently, the interpretation of the data's distribution.

The Role of Bins

Each bin covers a specific interval along the range of your data. For example, if your data ranges from 0 to 100, you might have bins covering 0-10, 10-20, 20-30, and so on. A data point with a value of 15 would fall into the 10-20 bin, increasing the count (and thus the height of the bar) for that specific bin.

By default, Matplotlib's plt.hist() function attempts to choose a reasonable number of bins for your data. However, this default isn't always optimal.

The Impact of the Number of Bins

Let's see how changing the number of bins affects the resulting histogram. We'll use some sample data drawn from a normal distribution.

import matplotlib.pyplot as plt
import numpy as np

# Generate some sample data
np.random.seed(42) # for reproducibility
data = np.random.randn(200) * 1.5 + 5 # 200 points, mean=5, std=1.5

# --- Plotting with different bin counts ---

plt.figure(figsize=(12, 4)) # Create a figure to hold the subplots

# Plot 1: Too few bins
plt.subplot(1, 3, 1) # (rows, columns, panel number)
plt.hist(data, bins=5, color='#228be6', edgecolor='white')
plt.title('Too Few Bins (bins=5)')
plt.xlabel('Value')
plt.ylabel('Frequency')

# Plot 2: Default number of bins (Matplotlib decides)
plt.subplot(1, 3, 2)
plt.hist(data, color='#15aabf', edgecolor='white') # Let Matplotlib choose bins
plt.title('Default Bins')
plt.xlabel('Value')
# plt.ylabel('Frequency') # Optionally hide y-label for middle plot

# Plot 3: Too many bins
plt.subplot(1, 3, 3)
plt.hist(data, bins=50, color='#40c057', edgecolor='white')
plt.title('Too Many Bins (bins=50)')
plt.xlabel('Value')
# plt.ylabel('Frequency') # Optionally hide y-label

plt.tight_layout() # Adjust layout to prevent overlap
plt.show()

As you can see from the plots generated by the code above:

1. Too Few Bins: Using only 5 bins creates a very coarse representation. We lose a lot of detail about the shape of the distribution. It looks blocky, and it's hard to tell if the data is truly bell-shaped.
2. Default Bins: Matplotlib's default choice (often around 10 bins for this amount of data) provides a better sense of the central tendency and spread. We can start to see the characteristic shape of the normal distribution.
3. Too Many Bins: Using 50 bins results in a very jagged histogram. Many bins have low counts (or even zero counts). This "spiky" appearance can be misleading, highlighting random fluctuations in the sample rather than the underlying distribution shape. It might suggest patterns or gaps that aren't really significant.

Let's visualize this comparison with interactive plots.

Histogram using 5 bins. The overall shape is captured, but details are lost.

Histogram using Matplotlib's default number of bins. This often provides a reasonable starting point.

Histogram using 50 bins. This shows excessive detail and noise, making the underlying pattern harder to discern.

How to Control Bins in Matplotlib

You can control the bins in plt.hist() using the bins argument:

1. Specify the Number of Bins: Pass an integer to the bins argument. Matplotlib will then create that many bins of equal width spanning the range of your data.

   # Create a histogram with exactly 20 bins
   plt.hist(data, bins=20, color='#845ef7', edgecolor='black')
   plt.title('Histogram with 20 Bins')
   plt.xlabel('Value')
   plt.ylabel('Frequency')
   plt.show()
   

2. Specify the Bin Edges: Pass a list or NumPy array defining the exact boundaries (edges) of each bin. This gives you precise control over where the bins start and end. If you provide $N$ edges, you will get $N-1$ bins.

   # Define specific bin edges
   bin_edges = [0, 2, 4, 6, 8, 10] # Creates bins: [0,2), [2,4), [4,6), [6,8), [8,10]
   
   plt.hist(data, bins=bin_edges, color='#f76707', edgecolor='black')
   plt.title('Histogram with Custom Bin Edges')
   plt.xlabel('Value')
   plt.ylabel('Frequency')
   plt.xticks(bin_edges) # Set x-ticks to match bin edges for clarity
   plt.show()
   

   Note: The notation [0, 2) means the bin includes 0 but excludes 2 (except for the last bin, which includes both edges).

Choosing the "Right" Number of Bins

So, how many bins should you use? Unfortunately, there's no single perfect answer. It often involves a degree of judgment and depends on:

• The amount of data: With more data, you can often support more bins without making the histogram too noisy.
• The shape of the distribution: Some distributions might require more bins to reveal specific features.
• The purpose of the visualization: Are you exploring the data or presenting a specific finding?

General Guidelines:

• Start with the default: Matplotlib's default is often a reasonable starting point.
• Experiment: Try a few different numbers of bins (e.g., half as many, twice as many as the default) to see how the appearance changes.
• Consider established rules (optional knowledge): Data scientists sometimes use formulas like Sturges' Rule or the Freedman-Diaconis rule to estimate an optimal bin width or number. Matplotlib and Seaborn often incorporate such rules in their default calculations. You don't usually need to calculate these yourself, but it's good to know that the defaults aren't arbitrary.
• Prioritize clarity: Choose a bin count that clearly communicates the main features of the distribution (central tendency, spread, skewness, modality) without being overly smooth or excessively noisy.

Selecting the right bins is a practical skill gained through experience. Don't be afraid to try different values until the histogram effectively represents your data's underlying pattern.