How to Explore Data with Summary Statistics and Percentiles

Exploring data using summary statistics and percentiles is a foundational step in any data analysis process. These tools help in understanding the distribution, central tendency, and variability of a dataset, which are crucial for making informed decisions, detecting anomalies, and choosing appropriate modeling techniques. This article provides a comprehensive guide on how to explore data using summary statistics and percentiles, including practical steps and interpretations.

Understanding Summary Statistics

Summary statistics are numerical values that describe and summarize features of a dataset. The most commonly used summary statistics include measures of central tendency (mean, median, mode), measures of dispersion (range, variance, standard deviation), and shape (skewness, kurtosis).

1. Measures of Central Tendency

These metrics indicate the center of a data distribution:

• Mean (Average): Sum of all values divided by the number of values. It is sensitive to outliers.

• Median: The middle value when the data is sorted. It is robust against outliers and skewed distributions.

• Mode: The most frequently occurring value in the dataset. Useful for categorical data.

Each measure offers different insights. For example, in a right-skewed distribution, the mean will be greater than the median, indicating that a few high values are pulling the average upward.

2. Measures of Dispersion

These help understand the spread or variability of data:

• Range: Difference between the maximum and minimum values. It’s easy to compute but can be overly influenced by outliers.

• Variance: The average of the squared differences from the mean. It gives a sense of how much the data varies.

• Standard Deviation: The square root of variance. It is in the same unit as the data and is more interpretable than variance.

High dispersion indicates that data points are spread out widely, while low dispersion suggests they are close to the mean.

3. Shape of Distribution

• Skewness: Measures the asymmetry of the data distribution. A skewness of zero indicates a symmetric distribution.

• Kurtosis: Indicates the “tailedness” of the distribution. High kurtosis means more data in the tails, while low kurtosis means less data in the tails.

Understanding the shape helps in identifying whether the data meets assumptions for certain statistical tests or models.

Using Percentiles for Deeper Insights

Percentiles divide the dataset into 100 equal parts, providing a granular view of the data distribution.

• 25th Percentile (Q1): Marks the first quartile, where 25% of data lies below this value.

• 50th Percentile (Median/Q2): Indicates the midpoint of the data.

• 75th Percentile (Q3): Denotes the third quartile, where 75% of the data lies below this value.

The Interquartile Range (IQR), calculated as Q3 – Q1, measures the middle 50% of the data. It is particularly useful in detecting outliers, which typically lie below Q1 – 1.5×IQR or above Q3 + 1.5×IQR.

Exploratory Steps Using Summary Statistics and Percentiles

Step 1: Load and Inspect the Data

Begin with loading your dataset and performing a preliminary inspection. This includes checking the number of rows and columns, column types, and missing values.

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import pandas as pd

df = pd.read_csv('data.csv')
print(df.info())
print(df.head())

Step 2: Generate Descriptive Statistics

Use the .describe() method in pandas to quickly generate summary statistics.

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print(df.describe())

This output includes count, mean, standard deviation, min, 25%, 50%, 75%, and max values for each numeric column.

Step 3: Calculate Additional Statistics

For a more detailed analysis, compute skewness and kurtosis:

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print(df.skew())
print(df.kurtosis())

These values will help in understanding the distribution shape, which affects model selection and assumptions.

Step 4: Analyze Percentiles for Specific Insights

To understand specific thresholds, calculate custom percentiles:

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percentiles = [0.01, 0.05, 0.95, 0.99]
print(df.quantile(percentiles))

These are helpful in fields like finance or healthcare, where outliers may carry critical meaning (e.g., extreme risk or patient vitals).

Step 5: Visualize Summary Statistics and Percentiles

Visualization enhances interpretation. Use boxplots and histograms to visualize spread and distribution.

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import seaborn as sns
import matplotlib.pyplot as plt

sns.boxplot(data=df['target_column'])
plt.show()

sns.histplot(df['target_column'], bins=30, kde=True)
plt.show()

• Boxplot: Highlights the median, quartiles, and potential outliers.

• Histogram: Displays the frequency distribution of values, allowing you to see skewness and modality.

Handling Outliers and Skewed Distributions

Summary statistics and percentiles often expose data quality issues such as outliers or heavily skewed distributions. These issues can be addressed in several ways:

• Outliers: Use IQR-based filtering or z-score methods to identify and optionally remove or transform outliers.

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  Q1 = df['target_column'].quantile(0.25)
  Q3 = df['target_column'].quantile(0.75)
  IQR = Q3 - Q1
  
  filtered_df = df[(df['target_column'] >= Q1 - 1.5 * IQR) & 
                   (df['target_column'] <= Q3 + 1.5 * IQR)]
  

• Skewness: Apply transformations such as log, square root, or Box-Cox to reduce skewness.

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  import numpy as np
  df['target_column_log'] = np.log1p(df['target_column'])
  

Summary Statistics in Categorical Data

While percentiles and many summary statistics apply to numerical data, categorical data also benefits from summarization:

• Frequency Counts: Use .value_counts() to identify the most common categories.

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  print(df['category_column'].value_counts())
  

• Mode: Useful for identifying the most frequent category.

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  print(df['category_column'].mode())
  

• Cross-tabulation: For exploring relationships between categorical variables.

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  pd.crosstab(df['category1'], df['category2'])
  

Importance in Real-World Applications

• Finance: Percentiles are used in Value at Risk (VaR) calculations to estimate potential losses.

• Healthcare: Summary statistics help in understanding patient data distributions and identifying abnormal cases.

• Marketing: Analyzing purchase behavior using median and percentiles helps segment customers effectively.

Best Practices in Data Exploration

1. Always start with visualization alongside summary statistics to catch patterns or anomalies missed in numerical summaries.

2. Use both median and mean to understand the central tendency, especially with skewed data.

3. Calculate percentiles for a deeper dive into data behavior, especially in large datasets with wide distributions.

4. Interpret statistics in context—numbers only make sense when tied to domain knowledge and business goals.

5. Automate with tools like Python or R for repeatability and scalability in your data analysis workflow.

Exploring data through summary statistics and percentiles provides critical insights that drive decision-making, modeling choices, and data cleaning strategies. It allows analysts and data scientists to transform raw data into actionable knowledge with clarity and precision.