Statistics is the science of collecting, organizing, analyzing, and interpreting numerical data.
Mean (μ) = Σx / N
Given the numbers: 5, 10, 15, 20, 25
Mean = (5 + 10 + 15 + 20 + 25) / 5 = 15
Measures of dispersion describe the spread of data points in a dataset.
Variance (σ²) = Σ(x - μ)² / N
Given the numbers: 5, 10, 15, 20, 25
Variance = ((5-15)² + (10-15)² + (15-15)² + (20-15)² + (25-15)²) / 5 = 50
The coefficient of variation (CV) is a measure of relative variability.
CV = (σ / μ) * 100%
Given the numbers: 5, 10, 15, 20, 25
CV = (7.071 / 15) * 100% ≈ 47.14%
Probability is the measure of the likelihood that an event will occur.
P(A) = Number of favorable outcomes / Total number of outcomes
Probability of rolling a 6 on a fair die:
P(6) = 1 / 6 ≈ 0.1667
The algebra of events deals with the union, intersection, and complement of events in probability.
Union: P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Intersection: P(A ∩ B) = P(A) * P(B|A)
Complement: P(A') = 1 - P(A)
Given P(A) = 0.5, P(B) = 0.4, and P(A ∩ B) = 0.2:
P(A ∪ B) = 0.5 + 0.4 - 0.2 = 0.7
The addition theorem states that the probability of the union of two events is the sum of their individual probabilities minus the probability of their intersection.
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Given P(A) = 0.6, P(B) = 0.3, and P(A ∩ B) = 0.1:
P(A ∪ B) = 0.6 + 0.3 - 0.1 = 0.8