Makindo Medical Notes

📊 The normal distribution shows that data near the mean are more frequent in occurrence than data far from the mean. It underpins much of probability theory and statistical inference.

🔔 The Classical Bell-shaped Curve

📖 Overview

The Normal Distribution (Gaussian distribution) is a continuous probability distribution that is symmetrical around its mean. It is characterised by the iconic bell-shaped curve and is one of the most important distributions in medicine, biology, and social sciences.

✨ Key Characteristics

• ⚖️ Symmetry: The curve is perfectly symmetrical around the mean.
• 🔔 Bell-Shaped: Peak at the mean with tails extending indefinitely.
• 📍 Mean = Median = Mode: All measures of central tendency align at the centre.
• 📏 Standard Deviation (σ): Controls spread → small σ = narrow & tall curve, large σ = wide & flat curve.

📐 Properties

• 📊 68–95–99.7 Rule (Empirical Rule):
  • ~68% of data within ±1σ
  • ~95% within ±2σ
  • ~99.7% within ±3σ
• ➗ Total Probability = 1: Area under curve = 100% of all outcomes.

🧮 Standard Normal Distribution

• Defined with μ = 0 and σ = 1.
• Values converted with Z-score: z = (X – μ) / σ
• 📌 Z-scores = "How many SDs away from the mean" → allows comparison across datasets.

📊 Applications

• 📈 Statistical Inference: Confidence intervals, hypothesis testing.
• 📚 Central Limit Theorem: Sampling means approximate normality when n is large.
• ⚙️ Quality Control: Control charts use normal distribution to detect abnormalities.
• 🧬 Natural & Social Sciences: Human height, IQ, lab measurements often approximate a normal curve.

🔍 Checking for Normality

• 👀 Visual Methods: Histogram (bell curve shape), Q–Q plots (linear trend).
• 📊 Statistical Tests: Shapiro–Wilk test, Kolmogorov–Smirnov test.

📝 Summary

✅ The Normal Distribution is fundamental in statistics. It is bell-shaped, symmetrical, and defined by its mean (μ) and standard deviation (σ). The 68–95–99.7 rule is a cornerstone concept, and Z-scores allow comparison across distributions. Understanding it is crucial for interpreting lab values, designing studies, and applying evidence-based medicine.