Data Analysis & Statistics

Measures of Spread

• Range: max − min
• IQR: Q3 − Q1 (middle 50%)
• Mean Absolute Deviation: average distance of each value from the mean

A larger spread means the data is more variable; a smaller spread means more consistent.

Counting Principles

• Multiplication principle: if event A has m outcomes and event B has n, there are m × n combined outcomes.
• Permutations (order matters): P(n,r) = n!/(n−r)!
• Combinations (order doesn't matter): C(n,r) = n!/[r!(n−r)!]

Probability

• P(A or B) = P(A) + P(B) − P(A and B) [for non-mutually exclusive events]
• Conditional probability: P(A|B) = P(A and B)/P(B)
• Expected value: sum of (each outcome × its probability)