Statistics Formula Cheat Sheet Guide for Data and Probability

Statistics formula cheat sheet explains mean, median, mode, probability, variance, and standard deviation, helping users analyze data, understand trends, and make better decisions using numbers.

Statistics Formula Cheat Sheet

Topic	Formula	Description
Mean (Average)	(Σx)/n	Sum of values divided by count
Weighted Mean	(Σwx)/(Σw)	Mean with weights
Median	Middle value	Central value in ordered data
Mode	Most frequent value	Highest frequency
Range	Max − Min	Spread of data
Population Variance	σ² = Σ(x−μ)² / N	Spread of population
Sample Variance	s² = Σ(x−x̄)² / (n−1)	Spread of sample
Standard Deviation	σ = √Variance	Dispersion measure
Z Score	z = (x−μ)/σ	Standardized value
Percentile	(Number below / Total) × 100	Position measure
Quartiles	Q1, Q2, Q3	Data division
Interquartile Range	IQR = Q3 − Q1	Middle spread
Outlier Rule	< Q1−1.5IQR or > Q3+1.5IQR	Detect outliers
Empirical Rule	68%–95%–99.7%	Normal distribution
Probability	P(A) = Favorable/Total	Basic probability
Complement Rule	P(A′) = 1 − P(A)	Opposite event
Addition Rule	P(A∪B) = P(A)+P(B)−P(A∩B)	Combined events
Multiplication Rule	P(A∩B) = P(A)P(B	A)
Conditional Probability	P(A	B) = P(A∩B)/P(B)
Bayes Theorem	P(A	B) = [P(B
Permutation	nPr = n!/(n−r)!	Ordered selection
Combination	nCr = n!/[r!(n−r)!]	Unordered selection
Expected Value	E(X) = ΣxP(x)	Mean outcome
Variance (Discrete)	Σ(x−μ)²P(x)	Spread measure
Binomial Probability	nCr pʳ (1−p)ⁿ⁻ʳ	Success probability
Normal Distribution	f(x)=1/(σ√2π)e^(-(x−μ)²/2σ²)	Bell curve
Standard Normal	z = (x−μ)/σ	Normalized value
Standard Error	σ/√n	Sampling variability
Confidence Interval	x̄ ± Z(σ/√n)	Estimate range
Margin of Error	Z(σ/√n)	Error range
Correlation Coefficient	r	Strength of relation
Regression Line	y = mx + c	Best fit line
Slope (Regression)	m = r(σy/σx)	Rate of change
Coefficient of Determination	R² = r²	Explained variance
Chi-Square	Σ(O−E)²/E	Test statistic
t-Test	(x̄−μ)/(s/√n)	Hypothesis test
F-Test	Variance₁/Variance₂	Compare variances

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