AP® Biology Equations and Formulas

Statistical Analysis and Probability

  • Mean

    • Formula: \bar{x} = \frac{{\sum{i=1}^{n} xi}}{{n}}
    • \bar{x}: sample mean
    • n: size of the sample

  • Standard Error of the Mean

    • Formula: SE_{\bar{x}} = \frac{s}{{\sqrt{n}}}
    • s: sample standard deviation (i.e., the sample-based estimate of the standard deviation of the population)

  • Standard Deviation

    • Formula: s = \sqrt{\frac{{\sum (x - \bar{x})^2}}{{n-1}}}

  • Chi-Square

    • Formula: \chi^2 = \sum \frac{{(o-e)^2}}{{e}}
    • o: observed results
    • e: expected results
    • Degrees of freedom are equal to the number of distinct possible outcomes minus one.

  • Chi-Square Table

    • Provides critical values for different degrees of freedom and p-values (0.05 and 0.01 are common significance levels).
    • Degrees of Freedom: 1, 2, 3, 4, 5, 6, 7 ,8
    • P Value 0.05: 3.84, 5.99, 7.82, 9.49, 11.07, 12.59, 14.07, 15.51
    • P Value 0.01: 6.64, 9.21, 11.34, 13.28, 15.09, 16.81, 18.48, 20.09

Laws of Probability

  • If A and B are mutually exclusive, then: P(A \text{ or } B) = P(A) + P(B)
  • If A and B are independent, then: P(A \text{ and } B) = P(A) \times P(B)

Hardy-Weinberg Equations

  • p^2 + 2pq + q^2 = 1
  • p + q = 1
    • p: frequency of the dominant allele in a population
    • q: frequency of the recessive allele in a population

Metric Prefixes

  • $10^9$: giga (G)
  • $10^6$: mega (M)
  • $10^3$: kilo (k)
  • $10^{-2}$: centi (c)
  • $10^{-3}$: milli (m)
  • $10^{-6}$: micro ($\mu$)
  • $10^{-9}$: nano (n)
  • $10^{-12}$: pico (p)

Descriptive Statistics

  • Mode: Value that occurs most frequently in a data set
  • Median: Middle value that separates the greater and lesser halves of a data set
  • Mean: Sum of all data points divided by the number of data points
  • Range: Value obtained by subtracting the smallest observation (sample minimum) from the greatest (sample maximum)