Statistics and Probability Cheatsheet

Cheat Codes & Shortcuts

• Population: Entire group from which data are drawn.
• Sample: Subset of population used to gather information.
• Mean (Average): \( \bar{x} = \frac{1}{n} \sum_{i=1}^n x_i \)
• Median: Middle value of a sorted data set.
• Mode: Most frequent value(s) in a data set.
• Variance: \( \sigma^2 = \frac{1}{n} \sum (x_i - \bar{x})^2 \)
• Standard Deviation: \( \sigma = \sqrt{\text{variance}} \)
• Probability: Likelihood of an event, \( P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} \)
• Addition Rule: \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \)
• Multiplication Rule: For independent events, \( P(A \cap B) = P(A) \cdot P(B) \)

Quick Reference Table

Concept	Formula/Definition	Description
Mean	\( \bar{x} = \frac{1}{n} \sum_{i=1}^n x_i \)	Average of data values
Variance	\( \sigma^2 = \frac{1}{n} \sum (x_i - \bar{x})^2 \)	Measure of spread around mean
Standard Deviation	\( \sigma = \sqrt{\text{variance}} \)	Spread measure in same units as data
Probability	\( P(E) = \frac{\text{favorable outcomes}}{\text{total outcomes}} \)	Likelihood of event
Addition Rule	\( P(A \cup B) = P(A) + P(B) - P(A \cap B) \)	Probability of either event
Multiplication Rule	\( P(A \cap B) = P(A) \times P(B) \) (if independent)	Probability of both events

Advice

Statistics and Probability Quick Tips

• Know your terms: Population, sample, event, outcome.
• Probability Rules: Addition for "or", multiplication for "and" (if independent).
• Central tendency: Mean best for symmetric data, median for skewed data.
• Variance vs Standard Deviation: Std dev is easier to interpret as same units as data.
• Conditional Probability: Learn \( P(A|B) = \frac{P(A \cap B)}{P(B)} \).

Statistics and Probability Speed Quiz

Test your speed with 5 questions! You have 30 seconds per question.