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Preparing your Lab
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Descriptive Statistics
Measures of Central Tendency
Mean (x̄)
Σxᵢ / n
Median
Middle value (sorted)
Mode
Most frequent value
Measures of Dispersion
Variance (s²)
Σ(xᵢ - x̄)² / (n-1)
Std Dev (s)
√s²
Range
Max - Min
Probability & Combinatorics
Permutation (Order matters)
nPr = n! / (n-r)!
Combination (Order doesn't matter)
nCr = n! / [r!(n-r)!]
P(A or B)
P(A) + P(B) - P(A and B)
P(A and B) [Independent]
P(A) · P(B)
P(A|B) [Conditional]
P(A and B) / P(B)
Distributions
Binomial
P(x) = nCx pˣ(1-p)ⁿ⁻ˣ
Normal
z = (x - μ) / σ
Poisson
P(x) = (e⁻ᵎ · λˣ) / x!
Inference & Regression
Confidence Intervals
Mean (Known σ):
x̄ ± Z(σ/√n)
Mean (Unknown σ):
x̄ ± t(s/√n)
Linear Regression
ŷ = b₀ + b₁x
b₁ = r(sy/sx) (Slope)
b₀ = ȳ - b₁x̄ (Intercept)
Chi-Square Statistic:
χ² = Σ (O - E)² / E