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IT 403 -- Formulas for Final Exam
Interquartile Range: IQR = Q3 - Q1
Inner fences for boxplot: Q1 - 1.5 × IQR; Q3 + 1.5 × IQR
Outer fences for boxplot: Q1 - 3.0 × IQR; Q3 + 3.0 × IQR
z-score for individual observations: z = (x - x) / SD+
Standard error of the average: SEave = SD+ / √n
z-score for sample average: z = (x - μ) / SEave
Ideal measurement model: xi = μ + ei
Linear regression model: yi = axi + b + ei
Estimated Linear regression model: yi - y = (r SDy / SDy) (xi - x)
Root mean squared error for regression: RMSE = (SD+) √(1 - r2)
Addition Rule: if A and B are disjoint events, P(A ∪ B) = P(A) + P(B).
Multiplication Rule: if A and B are independent events, P(A ∩ B) = P(A)P(B)
Probability of at Least One Success, of Bernoulli trials: 1 - (1 - p)n
Expected Value of a random variable: E(x) = x1P(x1) + ... + xmP(xm)
Ways to choose k items from n: nCk = n! / k! (n – k)!
Binomial Formula: P(k successes out of n) = nCk pk (1 – p)n-k
Theoretical Variance of a random variable: Var(x) =
(x1 - E(x))2 P(x1) + ... + (xm - E(x))2 P(xm)
Theoretical SD of a random variable: σx= sqrt(Var(x))
Expected Value of a Sum: E(S) = nE(x1)
Theoretical SD of a sum: σS= sqrt(n) σx
Expected Value Bernoulli Random Variable: E(x) = p
Theoretical Standard Deviation of Bernoulli Random Variable: σx= sqrt(np(1 – p))
Standard Error of a Sum, where the random variables x1, ... , xn are independent:
σS = sqrt(n) σx
Test Statistic for a z-test: z = (x - μ) / SEave, SEave = SD+ / sqrt(n)
Test Statistic for a t-test: t = (x - μ) / SEave, SEave = SD+ / sqrt(n)
Test Statistic for a Chi-squared test: χ2 = (O1 - E1)2 / E1 + ... + (Ok - Ek)2 / Ek