How to Use the Empirical Rule to Interpret Data in EDA

Exploratory Data Analysis (EDA) is a crucial step in understanding the characteristics of a dataset before applying more complex statistical or machine learning models. One of the fundamental tools for interpreting data during EDA is the Empirical Rule, also known as the 68-95-99.7 rule. This rule helps to quickly assess the distribution and spread of data when it follows a normal (bell-shaped) distribution.

Understanding the Empirical Rule

The Empirical Rule applies to data sets that approximate a normal distribution. It states that:

• About 68% of the data points lie within one standard deviation (σ) of the mean (μ).

• About 95% of the data points lie within two standard deviations (2σ) of the mean.

• About 99.7% of the data points lie within three standard deviations (3σ) of the mean.

This rule provides a quick way to evaluate the dispersion of data and detect outliers.

Applying the Empirical Rule in EDA

1. Check for Normality

   Before applying the Empirical Rule, it’s important to verify that the dataset is roughly normally distributed. This can be done through:

   • Visualizations such as histograms, Q-Q plots, or box plots.

   • Statistical tests like the Shapiro-Wilk test or Kolmogorov-Smirnov test.

2. Calculate Mean and Standard Deviation

   Compute the mean (μ) and standard deviation (σ) of the dataset or the variable of interest. These values serve as the reference points for applying the Empirical Rule.

3. Interpret Data Spread

   Using the mean and standard deviation, determine the ranges:

   • μ ± 1σ: Range where approximately 68% of data points fall.

   • μ ± 2σ: Range where approximately 95% of data points fall.

   • μ ± 3σ: Range where approximately 99.7% of data points fall.

   These intervals help understand the concentration of data points around the mean.

4. Identify Outliers

   Data points that fall outside the μ ± 3σ range can be considered outliers or extreme values. This identification aids in further investigation or data cleaning.

5. Summarize Data Characteristics

   By quantifying how data clusters around the mean, analysts can gain insights about the variability and consistency within the dataset.

Practical Example

Suppose you have a dataset of student test scores that are normally distributed with a mean score of 75 and a standard deviation of 10.

• About 68% of students scored between 65 and 85 (75 ± 10).

• About 95% scored between 55 and 95 (75 ± 20).

• About 99.7% scored between 45 and 105 (75 ± 30).

If a student scored 110, this would be an outlier according to the Empirical Rule.

Benefits of Using the Empirical Rule in EDA

• Quick Insights: Offers immediate understanding of data variability.

• Outlier Detection: Facilitates identification of unusual data points.

• Data Quality Checks: Helps in validating assumptions about data distribution.

• Basis for Further Analysis: Informs subsequent modeling decisions.

Limitations to Consider

• The Empirical Rule strictly applies to normally distributed data. For skewed or non-normal data, alternative approaches like percentile-based methods or other distribution-specific rules should be considered.

• Real-world data often deviates from perfect normality, so the rule provides an approximation rather than an exact measure.

Conclusion

Using the Empirical Rule in exploratory data analysis enables analysts to summarize data distribution effectively, detect anomalies, and make informed decisions early in the data processing pipeline. It serves as a foundational step in understanding the data’s structure, helping to guide more detailed statistical or machine learning analysis.