Stats 1: Quick Refresher Formulas

TIP

How to use: Review this sheet 15 minutes before any quiz.

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Week 1-2: Data & Viz

• Relative Frequency: $r{f}_i=\frac{f_i}{N}$
• Pie Chart Angle: $\theta =r{f}_i\times 360^{\circ }$
• Class Width: $\text{Upper Limit}-\text{Lower Limit}$

Week 3: Central Tendency

• Sample Mean ($\bar{x}$): $\frac{\sum x_i}{n}$
• Median:
  • Odd $n$: $(\frac{n+1}{2})$-th term.
  • Even $n$: Average of $(\frac{n}{2})$-th and $(\frac{n}{2}+1)$-th terms.
• Percentile Rank ($i$): $i=\frac{k}{100}\times n$
  • If decimal $\to$ Round UP.
  • If integer $\to$ Avg of $i$ and $i+1$.

Week 4: Dispersion

• Range: $\text{Max}-\text{Min}$
• IQR: $Q3-Q1$
• Outlier Fences: $[Q1-1.5(\text{IQR}),Q3+1.5(\text{IQR})]$
• Sample Variance ($s^2$): $\frac{\sum (x_i-\bar{x}{)}^2}{n-1}$
• Sample SD ($s$): $\sqrt{s^2}$
• Coefficient of Variation (CV): $\frac{s}{\bar{x}}\times 100$

Week 5-6: Counting

• Permutation: ${}^n{P}_r=\frac{n!}{(n-r)!}$
• Combination: ${}^n{C}_r=\frac{n!}{r!(n-r)!}$
• Circular Permutation: $(n-1)!$
• Pascal: ${}^n{C}_r{+}^n{C}_{r-1}{=}^{n+1}{C}_r$

Week 7-8: Probability

• Union: $P(A\cup B)=P(A)+P(B)-P(A\cap B)$
• Conditional: $P(A|B)=\frac{P(A\cap B)}{P(B)}$
• Independence: $P(A\cap B)=P(A)\cdot P(B)$
• Bayes: $P(A|B)=\frac{P(B|A)P(A)}{P(B)}$