How to Use Histograms to Understand Data Distribution in EDA

Histograms are a fundamental visualization tool in Exploratory Data Analysis (EDA) used to understand the underlying distribution of numerical data. By displaying the frequency of data points within specified ranges or bins, histograms provide clear insights into the shape, central tendency, spread, and presence of outliers in the dataset. Understanding these elements is crucial for selecting appropriate modeling techniques and making informed decisions based on data characteristics.

Understanding Histograms

A histogram is a type of bar chart that groups continuous numerical data into intervals, known as bins. Each bin represents a range of values, and the height of the bar indicates the number of observations within that range. Unlike bar charts that represent categorical data, histograms are used exclusively for quantitative variables.

Key Components of a Histogram

• Bins: Intervals that divide the entire range of values. Choosing appropriate bin sizes is essential, as too few bins may oversimplify the data, while too many can overcomplicate and obscure patterns.

• Frequency: The number of data points that fall within each bin.

• Axes: The x-axis represents the range of values, while the y-axis shows the frequency of data points in each bin.

Why Use Histograms in EDA?

Histograms serve several important purposes in EDA:

• Visualizing Data Distribution: Easily identify the shape of the distribution (normal, skewed, bimodal, etc.).

• Detecting Skewness: Recognize if the data is left-skewed (long tail on the left) or right-skewed (long tail on the right).

• Spotting Outliers: Outliers appear as isolated bars far from the central distribution.

• Assessing Data Symmetry: Evaluate whether the data is symmetric around a central value.

• Understanding Spread and Variability: Get a sense of data dispersion.

Types of Data Distributions Visible Through Histograms

1. Normal Distribution

A symmetric, bell-shaped histogram indicates a normal distribution. This is often a desirable trait in datasets as many statistical tests assume normality.

2. Skewed Distribution

• Right-Skewed: The tail is longer on the right. Common in income data, where a few high values pull the average upward.

• Left-Skewed: The tail is longer on the left. Often seen in exam scores where most students score high, with a few low performers.

3. Bimodal or Multimodal Distribution

Multiple peaks in a histogram suggest the presence of more than one group or process in the data, potentially indicating a need for segmentation or clustering.

4. Uniform Distribution

All bins have roughly equal frequencies, suggesting no apparent pattern or central tendency.

5. Exponential Distribution

A rapid decrease in frequency from left to right is indicative of exponential decay, common in time-to-failure or survival data.

Creating Effective Histograms

Step 1: Choose the Right Variable

Use histograms for continuous variables. For categorical data, consider bar charts instead.

Step 2: Determine the Bin Size

• Fixed-width bins: Equal bin widths across the range.

• Adaptive bins: Variable widths to capture more nuanced data patterns.

Some common methods for automatic bin size determination include:

• Sturges’ rule: Suitable for normal distributions.

• Scott’s rule: Minimizes integrated mean squared error.

• Freedman-Diaconis rule: Robust to outliers and useful for skewed data.

Step 3: Interpret the Shape

Once plotted, examine the histogram’s shape to understand the distribution and identify potential issues in the data.

Practical Examples of Using Histograms in EDA

Example 1: Salary Analysis

Analyzing employee salaries using a histogram can reveal right-skewed data, where most employees earn within a certain range, but a few high earners increase the mean. This insight helps in choosing median instead of mean for reporting central tendency.

Example 2: Exam Scores

A histogram of exam scores can show whether the exam was too easy or too difficult. A left-skewed histogram may indicate most students scored high, suggesting an easy test.

Example 3: Web Traffic

Analyzing the number of daily visitors to a website might reveal a bimodal distribution if the site gets two peak traffic periods — for instance, during morning and evening hours.

Using Histograms with Python (Pandas and Matplotlib)

python
CopyEdit
import pandas as pd
import matplotlib.pyplot as plt

# Sample dataset
data = pd.DataFrame({'values': [10, 12, 14, 15, 15, 16, 17, 20, 22, 24, 24, 25, 27, 30]})

# Plotting histogram
plt.hist(data['values'], bins=5, edgecolor='black')
plt.title('Histogram of Values')
plt.xlabel('Value Range')
plt.ylabel('Frequency')
plt.show()

Histogram vs. Box Plot

While both histograms and box plots are used to explore distributions, histograms show the actual shape of the distribution and are better for detecting multiple modes and skewness. Box plots summarize data with five-number statistics and are more concise, but may miss subtle distribution details.

Best Practices for Using Histograms

• Choose appropriate bin sizes: Experiment with different settings to find the most informative view.

• Use density plots alongside: For smoother representation, especially with large datasets.

• Annotate histograms: Add labels, titles, and explanations to aid interpretation.

• Standardize axes: When comparing multiple histograms, use consistent scales.

• Avoid overfitting: Too many bins can create misleading patterns.

Advanced Variants

• Cumulative Histograms: Show cumulative frequencies; useful for percentile analysis.

• Stacked Histograms: Display distribution of subgroups within a dataset.

• Normalized Histograms: Show proportions instead of absolute frequencies.

Conclusion

Histograms are an essential tool in any data analyst’s toolkit for exploring and understanding numerical data. They provide immediate, intuitive insight into the shape, center, spread, and peculiarities of a dataset. Whether identifying skewness, detecting outliers, or revealing multimodal patterns, histograms offer a simple yet powerful means of initial data exploration. Used correctly, they lay the groundwork for deeper statistical analysis and more informed decision-making in data science workflows.