Descriptive Statistics
Mean (Arithmetic Average)
x̄ = (Σx) / n
Where Σx is the sum of all values, and n is the number of values.
ExploreStandard Deviation
σ = √[(Σ(x - μ)²) / N]
Where μ is the population mean, and N is the population size.
ExploreProbability
Conditional Probability
P(A|B) = P(A∩B) / P(B)
The probability of event A occurring, given that event B has occurred.
ExploreBayes' Theorem
P(A|B) = [P(B|A) × P(A)] / P(B)
Calculates the probability of a hypothesis given observed evidence.
ExploreDistributions
Normal Distribution PDF
f(x) = (1/σ√2π) × e^(-(x-μ)²/2σ²)
Describes the probability density function of a normal distribution.
ExploreBinomial Probability
P(X=k) = C(n,k) × p^k × (1-p)^(n-k)
Gives the probability of k successes in n trials.
ExploreStatistical Inference
Confidence Interval
x̄ ± (z × σ/√n)
Provides a range within which a population parameter is likely to fall.
ExploreSample Size Determination
n = (z²σ²) / E²
Calculates the necessary sample size for a desired margin of error.
ExploreRegression
Linear Regression Equation
ŷ = β₀ + β₁x
Models the relationship between a dependent and independent variable.
ExploreLeast Squares Regression Line
b₁ = r(Sy/Sx)
Determines the line of best fit for a set of data points.
ExploreCorrelation
Pearson Correlation Coefficient
r = Σ((x-x̄)(y-ȳ)) / √[Σ(x-x̄)²Σ(y-ȳ)²]
Measures the strength and direction of a linear relationship.
ExploreSpearman's Rank Correlation
ρ = 1 - (6Σd²) / (n(n² - 1))
Measures the monotonic relationship between two ranked variables.
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