Sample mean: x-bar = (sum of x) / n
Population mean: mu = (sum of x) / N
Median of an odd count: The middle value when sorted
Median of an even count: The average of the two middle values
Range: Maximum minus minimum
Interquartile range: IQR = Q3 - Q1
Upper outlier fence: Q3 + 1.5 x IQR
Lower outlier fence: Q1 - 1.5 x IQR
Sample variance: s^2 = sum of (x - x-bar)^2 / (n - 1)
Population variance: sigma^2 = sum of (x - mu)^2 / N
Sample standard deviation: s = square root of sample variance
Z-score: z = (x - mean) / standard deviation
Standard error of the mean: s / sqrt(n)
Standard error of a proportion: sqrt(p(1 - p) / n)
Coefficient of variation: (standard deviation / mean) x 100 percent
Percentile rank: (number of values below x / total values) x 100
Probability of an event: Favorable outcomes / total outcomes
Complement rule: P(A') = 1 - P(A)
Addition rule: P(A or B) = P(A) + P(B) - P(A and B)
Multiplication rule, independent: P(A and B) = P(A) x P(B)
Conditional probability: P(A|B) = P(A and B) / P(B)
Bayes' theorem: P(A|B) = P(B|A) x P(A) / P(B)
Permutations: nPr = n! / (n - r)!
Combinations: nCr = n! / (r!(n - r)!)
Factorial: n! = n x (n-1) x ... x 1
Expected value: E(X) = sum of x x P(x)
Variance of a random variable: sum of (x - mu)^2 x P(x)
Binomial probability: P(X = k) = nCk x p^k x (1 - p)^(n - k)
Binomial mean: mu = np
Binomial standard deviation: sigma = sqrt(np(1 - p))
Geometric probability: P(first success on trial k) = (1 - p)^(k - 1) x p
Poisson probability: P(X = k) = e^(-lambda) x lambda^k / k!
Normal approx. to binomial condition: np >= 10 and n(1 - p) >= 10
Empirical rule: 68, 95, 99.7 percent within 1, 2, 3 standard deviations
Chebyshev's inequality: At least 1 - 1/k^2 of data lie within k standard deviations
Confidence interval for a mean: x-bar +/- t* x s/sqrt(n)
Confidence interval for a proportion: p-hat +/- z* x sqrt(p-hat(1 - p-hat)/n)
Margin of error (proportion): z* x sqrt(p-hat(1 - p-hat)/n)
Sample size for a proportion: n = (z*/E)^2 x p(1 - p)
One-sample t statistic: t = (x-bar - mu0) / (s / sqrt(n))
One-sample z statistic for proportion: z = (p-hat - p0) / sqrt(p0(1 - p0)/n)
Two-sample t statistic: t = (x1-bar - x2-bar) / sqrt(s1^2/n1 + s2^2/n2)
Degrees of freedom, one sample: n - 1
Chi-square statistic: sum of (observed - expected)^2 / expected
Expected count in a table: (row total x column total) / grand total
Degrees of freedom, chi-square table: (rows - 1)(columns - 1)
Pearson correlation: r = (1/(n-1)) x sum of (z_x x z_y)
Regression line: y-hat = a + bx
Slope of the regression line: b = r x (s_y / s_x)
Intercept of the regression line: a = y-bar - b x x-bar
Residual: observed y - predicted y
Coefficient of determination: r^2
Sum of squares total: sum of (y - y-bar)^2
ANOVA F statistic: F = mean square between / mean square within
Effect size, Cohen's d: (mean1 - mean2) / pooled standard deviation
Type I error probability: Alpha, the significance level
Power: 1 - beta
Odds: p / (1 - p)
Odds ratio: (a/b) / (c/d) for a 2 by 2 table
Relative risk: Risk in exposed group / risk in unexposed group
Percent change: (new - old) / old x 100
Weighted mean: sum of (w x x) / sum of w
Geometric mean: nth root of the product of n values
Harmonic mean: n / sum of (1/x)
Mode: The most frequent value
Skewness direction: Mean greater than median suggests right skew
Mean absolute deviation: sum of |x - mean| / n
Law of total probability: P(B) = sum of P(B|A_i) x P(A_i)
Hypergeometric probability: P(X = k) = [C(K,k) x C(N-K, n-k)] / C(N,n)
Central limit theorem standard deviation: sigma / sqrt(n)
Finite population correction: sqrt((N - n)/(N - 1))
Pooled proportion: (x1 + x2) / (n1 + n2)
Z critical value 95%: 1.96
Z critical value 99%: 2.576
Z critical value 90%: 1.645
Cumulative relative frequency: Running total of relative frequencies
Class width: (max - min) / number of classes
Sturges' rule: Number of classes is about 1 + log2(n)
Standard score for sample mean: z = (x-bar - mu) / (sigma / sqrt(n))
Tukey fences: Boundaries for outliers based on the IQR
Lower quartile position: (n + 1) / 4
Rule for sample variance denominator: Use n - 1 for samples to correct bias
Joint probability, dependent: P(A and B) = P(A) x P(B|A)
Mutually exclusive events: P(A and B) = 0

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