📈 Data Science Statistics

📄 Project Overview

This repository contains a collection of statistical exercises designed for Data Science learning and practice.
It demonstrates core statistical concepts through interactive Jupyter Notebooks, using Python libraries for data manipulation, visualization, and statistical modeling.

📚 Examples

📊 Central Limit Theorem - Sampling Animation (CTL.ipynb)

This example demonstrates the Central Limit Theorem through a simple animated visualization.
It shows how the distribution of sample means tends toward a normal distribution as more samples are drawn from an original uniform distribution.

Key features:

• Animated histogram of sample means evolving over time
• Saved as an animated GIF for easy viewing
• Educational visualization of the Central Limit Theorem process

Generated output preview:

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📈 Central Limit Theorem - Interactive Animation (CTL_for_web_.ipynb)

This example generates an interactive animated visualization illustrating the Central Limit Theorem.
We repeatedly draw samples from a uniform distribution, calculate their means, and show how the distribution of these means becomes approximately normal as more samples are collected.

Key features:

• Three synchronized plots:
  • Distribution of sample means (top left)
  • Current sample distribution (top right)
  • Original population distribution (bottom)
• Animated frames updating dynamically with each new sample
• Interactive controls (start button) for running the animation
• Saved as an HTML file for easy sharing and embedding in web projects

Generated output preview:

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🎻 Bimodal Distribution Visualization (workshop/bimodal_dist.ipynb)

This exercise focuses on visualizing a bimodal distribution using multiple types of statistical plots:

• Boxplot: Showing distribution spread with the mean highlighted.
• Violin plot: Displaying the probability density function.
• Histogram: Representing frequency of occurrences.

Key features:

• Combined mosaic layout for side-by-side comparison
• Customized styles like dashed mean lines and dotted median bars
• Clear axis labels for better interpretation
• Useful for exploratory data analysis (EDA)

Generated output preview:

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🛠️ Libraries Used

• numpy
• pandas
• scipy
• seaborn
• matplotlib
• statsmodels
• plotly
• bokeh
• ipympl
• ipython
• jupyterlab

📂 Project Structure

Data_Science_Statistics/
├── assets/                        ← Images and GIFs
├── datasets/                      ← CSV datasets
├── html/                          ← HTML documents
├── workshop/                      ← Workshop practice notebooks
│   └── bimodal_dist.ipynb          ← Bimodal distribution visualization
├── CTL.ipynb                      ← Central Limit Theorem sampling animation
├── CTL_for_web_.ipynb              ← Central Limit Theorem interactive animation
├── descriptive_visualisation.ipynb← Descriptive statistics visualizations
├── intro.ipynb                    ← Introduction notebook
├── pebble_world.ipynb              ← Toy example for sampling exercises
├── pyproject.toml                  ← Project dependencies
├── README.md                       ← Project documentation
└── uv.lock                         ← Lock file for uv

🚀 How to Run

1. Clone the repository:

   git clone [email protected]:Kinetics20/Data_Science_Statistics.git
   cd Data_Science_Statistics

2. Install dependencies using uv:

   uv sync

3. Launch JupyterLab:

   jupyter lab

4. Open and explore the .ipynb notebooks.

📊 Topics Covered

• Central Limit Theorem
• Data Visualization
• Descriptive Statistics
• Distribution Analysis
• Sampling Techniques
• Exploratory Data Analysis (EDA)

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💬 Feedback

Contributions and suggestions are welcome!

👤 Author: Piotr Lipiński
🗓 Date: May 2025