Statistical Engine & Monte Carlo Simulation

Project Overview

This project implements a pure-Python statistical engine (StatEngine) that calculates mean, median, variance, standard deviation, and detects outliers from raw numerical data. It also includes a Monte Carlo simulation to model a startup server's daily crash probability and demonstrate the Law of Large Numbers.

Mathematical Logic

• Variance: Measures how spread out the data is.

  • Population variance: σ² = Σ(xᵢ - μ)² / N
  • Sample variance: s² = Σ(xᵢ - x̄)² / (N - 1) (Bessel's correction)

• Median Calculation:

  • If the number of data points is odd, the median is the middle value of the sorted dataset.
  • If even, the median is the average of the two middle values.

Setup and Run Instructions

Run the following commands in your terminal:

git clone https://github.com/nigussiemebatsion-sys/statistical_engine.git
cd statistical_engine
python main.py
python -m unittest discover tests

Acceptance Criteria Checklist

• Handles empty data lists without errors
• Cleans non-numerical elements from input data
• Accurately calculates mean, median, variance, standard deviation
• Differentiates between population vs sample variance
• Correctly identifies outliers
• Monte Carlo simulation approximates server crash probability
• Demonstrates Law of Large Numbers