← Statistics — Data Analysis
Mathematics · Topic Cheatsheet

Statistics — Data Analysis

16 key results accumulated across 2 chapters.

Mean
Ch 1
xˉ=∑xn\bar{x} = \frac{\sum x}{n}
Sensitive to outliers.
Median / mode
Ch 1
Median = middle value (robust); mode = most frequent.
Range / IQR
Ch 1
IQR=Q3−Q1\text{IQR} = Q_3 - Q_1
IQR is outlier-robust spread.
Standard deviation
Ch 1
σ=1n∑(xi−xˉ)2\sigma = \sqrt{\tfrac{1}{n}\sum (x_i - \bar{x})^2}
Mean / median / mode
Ch 1
Mean sensitive to outliers; median robust; mode = most frequent.
Spread
Ch 1
IQR=Q3−Q1,    σ=∑(x−xˉ)2n\text{IQR} = Q_3 - Q_1,\;\; \sigma = \sqrt{\tfrac{\sum(x-\bar x)^2}{n}}
Outliers
Ch 1
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
Ch 1
Adding a constant shifts the mean but NOT the spread; scaling changes both.
Correlation coefficient
Ch 2
−1≤r≤1-1 \le r \le 1
Sign = direction; ∣r∣|r| = strength. Near ±1 strong, near 0 weak.
Correlation ≠ causation
Ch 2
A relationship in data doesn't prove one variable causes the other (watch for confounders).
Regression line
Ch 2
y=a+bxy = a + bx
Least-squares: minimises Σ(residuals)².
Passes through
Ch 2
(xˉ,yˉ)(\bar{x}, \bar{y})
The mean point always lies on the regression line.
Prediction caution
Ch 2
Interpolation (within data) is reliable; extrapolation far beyond it is risky.
Correlation r
Ch 2
−1 ≤ r ≤ 1; near ±1 strong linear; r ≈ 0 no LINEAR link (may still be related).
Regression line
Ch 2
y−yˉ=b(x−xˉ)y - \bar y = b(x - \bar x)
Passes through (x̄, ȳ); use to predict y from x only.
Common trap
Ch 2
Correlation ≠ causation; do not extrapolate far outside the data range.