Statistics for Data Science β Introduction
Understand core statistics concepts used in data science: descriptive stats, probability, distributions, sampling, and hypothesis testing.
π What is Statistics?
Definition
Statistics is the science of collecting, organizing, analyzing, and interpreting data to make decisions.
Key Functions
- Understand data behavior
- Identify patterns & trends
- Handle uncertainty
- Support business decisions
Statistics Process Flow
Without statistics, data science models cannot be validated or trusted. Statistics provides the mathematical foundation for ML algorithms.
π― Why Statistics is Important in Data Science?
EDA
Exploratory Data Analysis
Outlier Detection
Identify anomalies
Feature Understanding
Variable relationships
Model Validation
Performance metrics
π Real World Example
E-commerce Sales Analysis:
- Before predicting future sales, analyze historical average sales and variation
- Identify seasonal patterns using time series analysis
- Detect unusual spikes/drops using statistical process control
- Calculate confidence intervals for revenue forecasts
ποΈ What is Data?
Definition
Data is a collection of raw facts, values, observations, or measurements that can be processed to yield information.
Data Examples
Data Transformation Journey
β Why Do We Classify Data?
β Correct Analysis
Choose appropriate statistical methods and formulas
π Proper Visualization
Select suitable charts and graphs for each data type
π€ ML Model Selection
Build correct machine learning models based on data type
π« Avoid Errors
Prevent wrong conclusions and statistical mistakes
β οΈ Common Mistake Example
Wrong Approach: Calculating mean of Gender values (Male, Female) β
Why Wrong: Gender is categorical/nominal data. Mean requires numerical data.
Correct Approach: Use mode (most frequent category) or frequency tables β
π§ Types of Data
Data Classification Tree
(Categorical)
(Numerical)
This classification determines which statistical techniques are appropriate for analysis.
πΉ Qualitative (Categorical) Data
Nominal Data
- No inherent order or ranking
- Categories are mutually exclusive
- Only labels/names
- Cannot perform mathematical operations
Ordinal Data
- Natural order or ranking exists
- Differences between values not meaningful
- Relative position matters
- Can be sorted/ranked
π Statistical Operations for Qualitative Data
πΉ Quantitative (Numerical) Data
Discrete Data
- Countable whole numbers
- Finite number of values
- Cannot be subdivided
- Gaps between values
Continuous Data
- Infinitely divisible
- Decimal values possible
- Measured on a continuum
- No gaps between values
π Discrete vs Continuous Comparison
| Aspect | Discrete Data | Continuous Data |
|---|---|---|
| Nature | Countable | Measurable |
| Values | Whole numbers | Decimals possible |
| Visualization | Bar charts | Histograms |
| Examples | # of customers | Customer height |
π Essential Statistical Formulas
Mean (Average)
Where:
Ξ£xα΅’ = Sum of all values
n = Number of values
Variance
Where:
xα΅’ = Individual value
ΞΌ = Mean
n = Number of values
Standard Deviation
Where:
ΟΒ² = Variance
β = Square root
High Ο = Data spread out from mean
β οΈ Important Note: These formulas are applicable ONLY to Quantitative Data
Attempting to calculate mean/variance of categorical data leads to meaningless results!
π Practical Applications in Data Science
Descriptive Statistics
Summarize and describe data features using mean, median, mode, variance, etc.
Inferential Statistics
Make predictions about populations based on sample data using hypothesis testing.
Probability Distributions
Model uncertainty and randomness using Normal, Binomial, Poisson distributions.
ML Foundations
Statistical learning theory underpins regression, classification, clustering algorithms.
π’ Case Study: E-commerce Analytics
β Chapter Summary
Foundation
Statistics is essential for data-driven decision making in data science.
Classification
Correct data classification (Qualitative vs Quantitative) is crucial.
Formulas
Statistical formulas apply only to numerical (quantitative) data.
Applications
Strong statistical foundation leads to better ML models and insights.