Fundementals of Statistics

Statistics is the study of learning things from what you observed, data you gathered.

Main Pillars of statistics

1. Descriptive Statistics

This is the study of telling things from the data you have. organizing, summarizing, and presenting data clearly.

• Measures of Central Tendency: Where does the middle of the data sit?

  • Mean: The average (sum of all values divided by the count).
  • Median: The exact middle value when the data is lined up from smallest to largest.
  • Mode: The value that appears most frequently.

• Measures of Dispersion (Spread): How spread out are the numbers?

  • Range: The difference between the highest and lowest values.
  • Variance & Standard Deviation: Measures of how much the data points typically deviate from the mean.

2. Inferential Statistics

This is the study where we make educated guesses about the big picture using smaller set of data.

• Population: The entire group you care about
• Sample: The subset of the population you actually measure

Probability & Distributions

In almost all cases, data follow patterns. In statistics, we use probability and these patterns (distributions) to come to conclusions.

• The Normal Distribution (The Bell Curve): In nature and human behavior, many things cluster around a central average and taper off symmetrically on both sides.

• Central Limit Theorem: A foundational rule in stats that says if you take large enough random samples from any population, the distribution of those sample means will look like a normal distribution (a bell curve). This is what makes inferential statistics possible.

Hypothesis testing

The scientific method of statistics. This is how to test something like a change we introduced, actually made the difference, or is it just the pure luck not the change.

Relationships b/w Variables

Statistics also helps us see how different data points interact with each other.

• Correlation: A measure of how strongly two variables change together. A correlation of +1 means they move in perfect lockstep; -1 means they move in perfect opposite directions; 0 means no relation.

  • Golden Rule: Correlation does not equal causation. Just because ice cream sales and shark attacks both rise in July doesn't mean ice cream causes shark attacks (the hidden variable is summer heat).

• Regression: Going a step beyond correlation to actually predict a future outcome. For example, using a house's square footage to predict its selling price.