Percentiles and Quantiles | Fera Analytics

Introduction

Percentiles and quantiles are statistical measures that divide a dataset into equal parts, providing insights into the distribution and spread of data values. They are essential for understanding how data points are distributed relative to each other and are widely used in various fields, including finance, healthcare, and data analysis. This lesson covers definitions, calculations, interpretations, and applications of percentiles and quantiles in data analysis.

Percentiles

Percentiles divide a dataset into 100 equal parts, where each part represents a percentage of the data.

import numpy as np

# Example data
data = [10, 20, 30, 40, 50]

# Calculating the 25th percentile (Q1)
percentile_25 = np.percentile(data, 25)
print(f"25th Percentile (Q1): {percentile_25}")

# Calculating the median (50th percentile)
median = np.percentile(data, 50)
print(f"Median (50th Percentile): {median}")

# Calculating the 75th percentile (Q3)
percentile_75 = np.percentile(data, 75)
print(f"75th Percentile (Q3): {percentile_75}")

Interpretation:

25th percentile (Q1): 25% of the data values are less than or equal to this value.
Median (50th percentile): 50% of the data values are less than or equal to this value.
75th percentile (Q3): 75% of the data values are less than or equal to this value.

Quantiles

Quantiles generalize percentiles by dividing a dataset into any number of equal parts.

# Calculating quartiles (Q1, Q2, Q3) using numpy
quartiles = np.quantile(data, [0.25, 0.5, 0.75])
print(f"Quartiles (Q1, Q2, Q3): {quartiles}")

# Calculating the 90th percentile
percentile_90 = np.percentile(data, 90)
print(f"90th Percentile: {percentile_90}")

Interpretation:

Quartiles (Q1, Q2, Q3): Divide the data into four equal parts, representing 25%, 50%, and 75% of the data, respectively.
90th percentile: 90% of the data values are less than or equal to this value.

Applications of Percentiles and Quantiles

Data Analysis: Analyze data distribution and variability.
Performance Metrics: Evaluate rankings and distributions in various fields, such as education or healthcare.
Risk Assessment: Assess financial risks based on percentile ranks in investment portfolios.

Considerations

Interpolation Methods: Different methods (e.g., linear, lower, higher) for calculating percentiles and quantiles may yield slightly different results.
Outliers: Percentiles and quantiles are robust to outliers, making them suitable for analyzing skewed datasets.

Conclusion

Percentiles and quantiles are fundamental tools for analyzing data distributions and understanding the relative positioning of data points within a dataset. By calculating and interpreting percentiles and quantiles, analysts can effectively describe data variability, make comparisons, and derive insights for decision-making purposes. Mastering these concepts enhances the ability to interpret data distributional characteristics and supports evidence-based decision-making processes across various domains and applications in data science, finance, healthcare, and beyond.