FOUNDATIONS OF STATISTICS & PROBABILITY
FSP — Complete Notes
Prof. Dr. Rajlaxmi Chouhan
Weeks 1–13
WEEK 1 — Introduction to Statistics & Probability
All things in Data Science & AI → Stats & Probability play a vital role!
Module 1 — Basics
Flow of Statistics:
• Collection of Data → Description of Data (Descriptive Statistics) → Analysis of Data → Inferential
Statistics
• Random Selection: Division should be equally likely
• Scores / Average used in Description of Data
• Population: Total collection of elements
• Sample: Subgroup of population used
Applications:
• Most apps run on Data → Statistics & Probability
• How good is any player? → Find Average (Statistical Answer)
• One tool for Generating Data, One tool for Analyzing Data → Judging AI
WEEK 2 — Descriptive Statistics
1. Organizing The Data
• Data को Accumulate करना
• Frequency Table → Number of Occurrences
2. Visualizing The Data
• Line Graph, Bar Graph, Frequency Polygon, Histogram
• Relative Frequency Table → Frequency of Data / Total No. of Candidates (can be % also)
• Pie Chart
Histogram
• Lower Bound (35) and Upper Bound (40)
• Left End Inclusion: [35, 40) → e.g., 35 to 39, 40 to 44
Cumulative Frequency
• Total पर होते है → Last वाला Total Items के ऊपर होता है
• Relative Cumulative Frequency
, 📝 Note: अगर ये रट रहे हो तो ऊपर Upper Boundary of Class लगा दो। Eg: 500-600 की 600, 600-700 की 700
Cumulative Frequency Distribution = CDF = Ogive
• Class Interval v/s Cumulative Frequency
• Upper Boundary v/s Relative Cumulative Frequency
WEEK 3 — Measures of Central Tendency & Chebychev
Measures of Central Tendency
Tools to summarize a dataset
1. Mean (μ) — Average Value
Mean = Sum of Individual Items / Total No. of Items
• Outliers can affect the data!
2. Median
• Arrange Data in ascending order, Find middle values
• Even: (N/2 + N/2+1) / 2
• If odd → ((N+1)/2)th value
• Unaffected by High Outliers
3. Mode
• Most frequently occurring value
• If there is a tie between two → both are mode values → Bimodal Distribution
• Somewhat most useful! → Uses & Misleading
Uses of Mean:
• Evaluating Overall Usage
• Comparing Groups
• Budgeting Resources
• Individual Level Insights
• Decision making for popular plans
WEEK 4 — Measures of Dispersion
Variance & Standard Deviation
• Variance = σ² | Standard Deviation = √Variance = σ → Spread of Data
Population Variance (σ)
σ² = Σ(xᵢ - μ)² / N where μ = mean of entire population, N = entire
population
Sample Variance (s)
s² = Σ(xᵢ - μ)² / (n-1) where n = no. of samples (not entire population)
FSP — Complete Notes
Prof. Dr. Rajlaxmi Chouhan
Weeks 1–13
WEEK 1 — Introduction to Statistics & Probability
All things in Data Science & AI → Stats & Probability play a vital role!
Module 1 — Basics
Flow of Statistics:
• Collection of Data → Description of Data (Descriptive Statistics) → Analysis of Data → Inferential
Statistics
• Random Selection: Division should be equally likely
• Scores / Average used in Description of Data
• Population: Total collection of elements
• Sample: Subgroup of population used
Applications:
• Most apps run on Data → Statistics & Probability
• How good is any player? → Find Average (Statistical Answer)
• One tool for Generating Data, One tool for Analyzing Data → Judging AI
WEEK 2 — Descriptive Statistics
1. Organizing The Data
• Data को Accumulate करना
• Frequency Table → Number of Occurrences
2. Visualizing The Data
• Line Graph, Bar Graph, Frequency Polygon, Histogram
• Relative Frequency Table → Frequency of Data / Total No. of Candidates (can be % also)
• Pie Chart
Histogram
• Lower Bound (35) and Upper Bound (40)
• Left End Inclusion: [35, 40) → e.g., 35 to 39, 40 to 44
Cumulative Frequency
• Total पर होते है → Last वाला Total Items के ऊपर होता है
• Relative Cumulative Frequency
, 📝 Note: अगर ये रट रहे हो तो ऊपर Upper Boundary of Class लगा दो। Eg: 500-600 की 600, 600-700 की 700
Cumulative Frequency Distribution = CDF = Ogive
• Class Interval v/s Cumulative Frequency
• Upper Boundary v/s Relative Cumulative Frequency
WEEK 3 — Measures of Central Tendency & Chebychev
Measures of Central Tendency
Tools to summarize a dataset
1. Mean (μ) — Average Value
Mean = Sum of Individual Items / Total No. of Items
• Outliers can affect the data!
2. Median
• Arrange Data in ascending order, Find middle values
• Even: (N/2 + N/2+1) / 2
• If odd → ((N+1)/2)th value
• Unaffected by High Outliers
3. Mode
• Most frequently occurring value
• If there is a tie between two → both are mode values → Bimodal Distribution
• Somewhat most useful! → Uses & Misleading
Uses of Mean:
• Evaluating Overall Usage
• Comparing Groups
• Budgeting Resources
• Individual Level Insights
• Decision making for popular plans
WEEK 4 — Measures of Dispersion
Variance & Standard Deviation
• Variance = σ² | Standard Deviation = √Variance = σ → Spread of Data
Population Variance (σ)
σ² = Σ(xᵢ - μ)² / N where μ = mean of entire population, N = entire
population
Sample Variance (s)
s² = Σ(xᵢ - μ)² / (n-1) where n = no. of samples (not entire population)
