Revision sheet

Variables

• Cases: who or what. Variables: what is recorded.
• Categorical: groups. Quantitative: meaningful numbers.

Watch out: numeric codes (ZIP, ID) are categorical.

Describing a distribution

Shape, center, spread, outliers, in context.

Watch out: skewed right means mean > median (usually).

Center

• Mean: sum ÷ n; pulled by extremes.
• Median: middle value; resistant.

Watch out: even count: average the two middle values.

Spread

• Range, IQR (resistant), standard deviation.
• $s$ divides by $n - 1$; $s^2$ is the variance.

Watch out: the SD is the square root of the variance.

Outliers and boxplots

• Fences: $Q_1 - 1.5\,\text{IQR}$ and $Q_3 + 1.5\,\text{IQR}$.
• Boxplot: five-number summary plus outliers.

Watch out: 1.5 × IQR, not 1 × IQR.

Transforming data

$a + bx$: center → $a + b\cdot$center; spread → $|b|\cdot$spread.

Watch out: adding a constant never changes the spread.

z-scores and the normal model

• $z = (x - \mu)/\sigma$; $x = \mu + z\sigma$.
• 68–95–99.7 within 1, 2, 3 SDs.

Watch out: the percentages are for both sides together.