Course Progress
Part of 10 Chapters
Chapter 2
Probability Distributions: The Shapes of Data
#Probability Distribution#Normal Distribution#Standard Deviation#Skewness
Probability Distributions: How Data Behaves
In statistics, we don’t just look at single numbers; we look at their distribution. A probability distribution tells us which values are likely to occur and which are not.
1. The Normal Distribution (The Bell Curve)
The Normal Distribution is symmetrical, with most observations clustering around the central peak. It is governed by two parameters: the Mean (μ) and the Standard Deviation (σ).
The Normal Distribution Gradient
Most values fall within 1 standard deviation of the mean (the center).
2. The 68-95-99.7 Rule
- 68% of data falls within 1 standard deviation.
- 95% of data falls within 2 standard deviations.
- 99.7% of data falls within 3 standard deviations.
3. Other Distributions
While the Normal distribution is gold, real-world data can be skewed.
- Poisson: Used for counting events in a fixed interval.
- Exponential: Used for modeling the time between events.
💡 Professor’s Tip
The Central Limit Theorem states that if you take enough samples, their distribution will look normal, regardless of the original population’s shape. This is why the Normal Distribution is everywhere!