← Statistics — Data Analysis
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Statistics — Data Analysis

Chapter 1 · Describing Data

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Mean
xˉ=∑xn\bar{x} = \frac{\sum x}{n}
Sensitive to outliers.
Median / mode
Median = middle value (robust); mode = most frequent.
Range / IQR
IQR=Q3−Q1\text{IQR} = Q_3 - Q_1
IQR is outlier-robust spread.
Standard deviation
σ=1n∑(xi−xˉ)2\sigma = \sqrt{\tfrac{1}{n}\sum (x_i - \bar{x})^2}
Mean / median / mode
Mean sensitive to outliers; median robust; mode = most frequent.
Spread
IQR=Q3−Q1,    σ=∑(x−xˉ)2n\text{IQR} = Q_3 - Q_1,\;\; \sigma = \sqrt{\tfrac{\sum(x-\bar x)^2}{n}}
Outliers
x<Q1−1.5 IQR  or  x>Q3+1.5 IQRx < Q_1 - 1.5\,\text{IQR}\;\text{or}\;x > Q_3 + 1.5\,\text{IQR}
Common trap
Adding a constant shifts the mean but NOT the spread; scaling changes both.