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Central Tendency (Mean / Median / Mode)
conceptedited by Cairni · 방금 · AIv1
핵심 개념
Central tendency describes where the centre of a data set sits. There are three main measures, each with different strengths. Lecture notes.md
| Measure | Definition | Best used when… | Weakness |
|---|---|---|---|
| Mean | Sum of all values ÷ count | Data is symmetric, no extreme outliers | Strongly pulled by outliers |
| Median | Middle value after sorting | Data is skewed (e.g. income, house prices) | Ignores the actual magnitude of values |
| Mode | Most frequently occurring value | Categorical or discrete data | May not be unique; can be meaningless for continuous data |
How outliers affect the mean
A single extreme value — like one billionaire in an income dataset — can drag the mean far above what most people actually earn. In that case, the median gives a more realistic picture of the "typical" value. Lecture notes.md
Key link: In a Normal Distribution, all three measures coincide — mean = median = mode — because the distribution is perfectly symmetric. Lecture notes.md
Relationship to other topics
- Spread is the natural next step: once you know the centre, Spread (Variance & Standard Deviation) measures how far values scatter around it.
- Skew and outliers feed directly into the Correlation vs Causation discussion — confounded or skewed data can mislead correlations too.
- Practice all cue questions together on the Review & Spaced Repetition page.
큐 질문 (능동적 회상)
Work through these *before* looking back at the notes above.
- 1.What is the formula for the mean, and why is it sensitive to outliers?
- 2.When should you prefer the median over the mean? Give a real-world example.
- 3.Which measure of central tendency is most appropriate for categorical data, and why?
- 4.In a perfectly symmetric (normal) distribution, what is the relationship between mean, median, and mode?
- 5.A dataset of seven salaries has one CEO earning 100× the others. Sketch how the mean and median would compare — which is higher, and why?
*(Answers are in the notes above and in Lecture notes.md.)*
요약
The mean is the arithmetic centre but bends toward extremes; the median is the robust middle; the mode is the crowd favourite — pick the one that honestly represents your data.