Statistics Foundations
Visual guide to core statistical concepts · 통계학 기초 시각 가이드
1. Mean (Average)
The mean is the sum of all values divided by the count: x̄ = Σxᵢ / n. It represents the "center" of a dataset.
The mean is sensitive to outliers. A single extreme value can shift it significantly. For skewed data, the median is often more representative. Always check both when analyzing datasets.
평균은 이상치에 민감합니다. 하나의 극단값이 평균을 크게 이동시킬 수 있습니다. 치우친 데이터에서는 중앙값이 더 대표적인 경우가 많으므로, 데이터 분석 시 항상 둘 다 확인하세요.
2. Variance & Standard Deviation
Variance measures spread: σ² = Σ(xᵢ − x̄)² / n. Standard deviation σ = √(variance) gives spread in original units.
Standard deviation is more intuitive than variance because it's in the same units as the data. In a normal distribution, about 68% of data falls within ±1σ of the mean, and 95% within ±2σ. This is the foundation of quality control and confidence intervals.
표준편차는 데이터와 같은 단위이므로 분산보다 직관적입니다. 정규분포에서 데이터의 약 68%가 평균 ±1σ 이내, 95%가 ±2σ 이내에 있습니다.
3. Permutations & Combinations
Permutations (order matters): P(n,r) = n!/(n−r)!. Combinations (order doesn't matter): C(n,r) = n!/[r!(n−r)!].
Quick way to remember: "Does the order of selection matter?" If choosing a team captain and vice-captain from 10 people, order matters (permutation: 10×9=90). If just picking 2 people for a committee, order doesn't matter (combination: 90/2=45).
"선택 순서가 중요한가?"를 기억하세요. 10명 중 회장과 부회장을 뽑으면 순열(10×9=90), 단순히 2명을 뽑으면 조합(90/2=45)입니다.
4. Correlation
Correlation (r) measures linear relationship between two variables. Range: −1 (negative) to +1 (positive). r=0 means no linear relation.
Correlation does NOT imply causation. Ice cream sales and drowning deaths are correlated (both increase in summer), but one doesn't cause the other. Always look for confounding variables before drawing conclusions from correlation data.
상관관계는 인과관계를 의미하지 않습니다. 아이스크림 판매량과 익사 사고는 상관관계가 있지만(둘 다 여름에 증가), 하나가 다른 것을 유발하지 않습니다.