Descriptive Statistics › Introduction

Before moving far into modeling or inference, it is good practice to examine the basic properties of your data. Descriptive statistics provide this early view by showing where distributions are centered, how widely values vary, and what shape they take. These summaries help us assess data quality, spot potential issues such as outliers or skewness, and communicate findings to readers who may not need the underlying technical detail.

Descriptive statistics provide different types of summary information about data, organized into several key categories:

• Measures of central tendency (e.g., mean, median, mode): Identify typical or representative values in a dataset.
• Measures of variability (e.g., variance, standard deviation, range, interquartile range): Quantify how spread out the data points are.
• Measures of distribution shape (e.g., skewness, kurtosis): Describe the asymmetry and tail behavior of the data.

Understanding these descriptive measures matters for exploratory data analysis and for diagnosing potential problems in modeling. For instance, high skewness might suggest the need for data transformation, while extreme kurtosis could indicate the presence of outliers that warrant investigation. This chapter explores each of these fundamental concepts, giving the statistical basics needed for effective data analysis and modeling.