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