📊 Applied Statistics Portfolio (Statistics 1 & 2)

A structured portfolio of extra activities, empirical practice problems, and Python mini-projects for:

• Statistics 1: Descriptive & Foundational Methods
• Statistics 2: Inferential & Probability Models

Explore how theoretical statistics are brought to life in spreadsheets and Python—from hand-calculated frequency tables to advanced algorithmic simulations.

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🎯 Portfolio Core Focus

• Descriptive Statistics: Modeling of mean, median, mode, variance, and frequency distributions
• Probability & Simulations: Custom Monte Carlo frameworks—algorithmic dice rolls & randomness
• Theoretical Probability Models: Normal distribution fits on real datasets, empirical rule checks
• Central Limit Theorem (CLT): Sampling engine proving asymptotic normality
• Bivariate Relationships: Covariance matrix & scatter analysis on financial ratios

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🛠 Analytical Tech Stack

• Spreadsheet Modeling: Microsoft Excel (advanced formulas, Data Analysis Toolpak)
• Python/Notebooks: Google Colab, Jupyter (.ipynb)
• Core Libraries: numpy, pandas, matplotlib, scipy.stats, openpyxl

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📂 Repository Architecture

basic-statistics-projects/
├── Statistics 1 — Descriptive Foundations/
│   ├── STATISTICS-1-EXTRA_ACTIVITY_2/   # Frequency distributions
│   ├── STATISTICS-1-EXTRA_ACTIVITY_3/   # Central tendency
│   └── STATISTICS-1-EXTRA_ACTIVITY_4/   # Categorical/continuous plotting
│
└── Statistics 2 — Probability & Inference/
    ├── STATISTICS-2-EXTRA_ACTIVITY_1/   # Netflix dataset exploration
    ├── STATISTICS-2-EXTRA_ACTIVITY_2/   # Monte Carlo Dice Simulation
    ├── STATISTICS-2-EXTRA_ACTIVITY_3/   # Corporate Ratio Covariance
    ├── STATISTICS-2-EXTRA_ACTIVITY_4/   # Normal Curve Profit Analysis
    └── STATISTICS-2-EXTRA_ACTIVITY_5/   # Central Limit Theorem (CLT)

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🚀 Deep Dive: Statistical Experiments

🎲 Monte Carlo Dice Simulation

• Concept: Law of Large Numbers (LLN)
• Implementation: Python .ipynb, stochastic dice-rolls, live distribution plots

📉 Corporate Ratio Covariance

• Concept: Correlation & Covariance ($r$, $\sigma_{XY}$)
• Implementation: Balance-sheet ratios (Current, Quick, Cash), scatter-matrix viz

🔔 Normal Model on Google Profits

• Concept: Gaussian fit, Z-scores
  $$f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}$$
• Implementation: Google quarterly profits fit to Normal, probability densities of future returns

⚖️ Central Limit Theorem (CLT)

• Concept: Sampling means, limit theorem
• Implementation: Python engine simulating non-normal populations; batch sampling proves readout is normal as size $n\uparrow$

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🎮 How to Run / Interact

A. Excel Workspace

1. Open relevant STATISTICS-* activity folder, download .xlsx, and explore formulas.

B. Python & Jupyter

pip install numpy pandas matplotlib scipy openpyxl notebook
jupyter notebook

Alternatively: Drop .ipynb into Google Colab for instant cloud execution.

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📈 Learning Outcomes

• Hands-on descriptive and inferential stats via spreadsheet & code
• Real financial & business data translation to statistical models
• Visualization, reporting, and result interpretation for research portfolios

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👩‍💻 Author

Saloni Tiwari
🎓 IIT Madras BS Data Science
🎓 B.Sc Mathematics

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⭐️

If you found this portfolio useful, please ⭐ on GitHub!