square-roots

A quick refresher on the math you’ll need in this book.

Order of Operations (PEMDAS)

• Parentheses → Exponents → Multiplication/Division → Addition/Subtraction
• Example:
  $$3 + 2 \times (4^2) = 3 + 2 \times 16 = 35$$

Fractions and Division

• Example:
  $$\frac{24}{6} = 4$$

Square Roots

• Example:
  $$\sqrt{9} = 3$$
• Example:
  $$\sqrt{\frac{16}{4}} = \sqrt{4} = 2$$

Summation Notation (Σ)

• Means “add them up.”
• Example:
  $$\Sigma X = 2+5+7 = 14$$
• Example:
  $$\Sigma (X-\bar{X})^2 = (2-4)^2 + (5-4)^2 + (7-4)^2 = 4+1+9 = 14$$

Exponents and Squares

• $$x^2 = x \times x$$
• Example:
  $$5^2 = 25$$

Mini Example: Variance and Standard Deviation

Data: 6, 8, 10

1. Mean:
   $$\bar{X} = \frac{6+8+10}{3} = 8$$
2. Deviations: –2, 0, +2
3. Squared deviations: 4, 0, 4
4. Variance:
   $$\frac{8}{2} = 4$$
5. Standard deviation:
   $$\sqrt{4} = 2$$

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