Statistics Formulas
Mean, median, variance, standard deviation, probability and more
Mean (Average)
x̄ = (Σx) / n
Where n = number of values
Median
Odd n: middle value
Even n: average of two middle values
Sort data first
Variance
σ² = Σ(x - x̄)² / n (population)
s² = Σ(x - x̄)² / (n-1) (sample)
Standard Deviation
σ = √(Σ(x - x̄)² / n)
s = √(Σ(x - x̄)² / (n-1))
Probability
P(A) = favorable / total
P(A or B) = P(A) + P(B) - P(A and B)
P(A and B) = P(A) × P(B) if independent
Normal Distribution
68% within 1σ
95% within 2σ
99.7% within 3σ (Empirical Rule)
Correlation
r = Σ[(x-x̄)(y-ȳ)] / (n·σx·σy)
-1 ≤ r ≤ 1
r=1 perfect positive, r=-1 perfect negative
Permutations & Combinations
P(n,r) = n! / (n-r)!
C(n,r) = n! / (r!(n-r)!)