Understanding Descriptive vs Inferential Statistics: A Complete Guide for Beginners

📗 Chapter 2: Descriptive Statistics – Summarizing the Data

Master the Art of Data Exploration with Central Tendency, Variability & Visualization

🧠 Introduction

Before we build models, make predictions, or test hypotheses, we must understand our data. Descriptive statistics give us the tools to do just that.

Descriptive statistics are the first step in any data analysis pipeline — used to summarize, simplify, and visualize the key features of a dataset.

Whether you're dealing with a spreadsheet of survey responses or a massive machine-generated dataset, descriptive statistics help answer questions like:

• What does the data look like?
• Are there any outliers?
• What’s typical or average?
• How spread out is the data?

In this chapter, we’ll explore:

• Measures of central tendency
• Measures of dispersion
• Frequency distribution
• Data shape and visualization
• Python code for hands-on practice

📘 Section 1: What Are Descriptive Statistics?

Descriptive statistics refers to methods for summarizing raw data into meaningful information — either numerically or graphically.

Two Primary Goals:

1. Describe central values (What is typical?)
2. Describe spread or variability (How consistent or dispersed is the data?)

📊 Section 2: Measures of Central Tendency

These are values that represent the “center” or “average” of a dataset.

1. Mean (Arithmetic Average)

python

import pandas as pd

df = pd.DataFrame({'Marks': [50, 60, 70, 80, 90]})

mean_val = df['Marks'].mean()

print("Mean:", mean_val)

2. Median

The middle value when data is sorted.

python

median_val = df['Marks'].median()

print("Median:", median_val)

3. Mode

The most frequently occurring value.

python

mode_val = df['Marks'].mode()[0]

print("Mode:", mode_val)

🎯 Section 3: Measures of Dispersion

These help us understand how spread out the data is around the center.

1. Range

python

range_val = df['Marks'].max() - df['Marks'].min()

print("Range:", range_val)

Simple but highly sensitive to outliers.

2. Variance and Standard Deviation

• Variance: The average of squared differences from the mean
• Standard Deviation: Square root of variance

python

variance = df['Marks'].var()

std_dev = df['Marks'].std()

print("Variance:", variance)

print("Standard Deviation:", std_dev)

3. Interquartile Range (IQR)

python

Q1 = df['Marks'].quantile(0.25)

Q3 = df['Marks'].quantile(0.75)

IQR = Q3 - Q1

print("IQR:", IQR)

📊 Section 4: Frequency Distributions

A frequency distribution is a summary of how often each value (or range) occurs.

python

df['Marks'].value_counts().sort_index()

Example Table: Frequency Table of Scores

📈 Section 5: Visualizing Data

1. Histogram

python

import matplotlib.pyplot as plt

df['Marks'].hist(bins=5)

plt.title("Histogram of Marks")

plt.show()

Shows frequency of value ranges.

2. Box Plot

python

import seaborn as sns

sns.boxplot(df['Marks'])

plt.title("Boxplot of Marks")

plt.show()

• Highlights median, quartiles, and outliers

3. Bar Chart & Pie Chart (Categorical Data)

python

df_cat = pd.DataFrame({'Gender': ['M', 'F', 'M', 'F', 'M']})

df_cat['Gender'].value_counts().plot(kind='bar')

🧠 Section 6: Data Shape and Distribution

Understanding distribution shape helps you choose the right statistical methods.

python

sns.histplot(df['Marks'], kde=True)

📋 Section 7: Summary Table – Descriptive Statistics Techniques