Statistics Cheat Sheet: Formulas, Definitions & Excel Functions

Posted on Apr 30, 2024 in Mathematics

Statistics Cheat Sheet

Key Concepts and Definitions

Data Types

  • Categorical Data: Data that can be grouped into categories.
    • Numeric: Represented by numbers (e.g., zip codes).
    • Non-numeric: Represented by words (e.g., colors).
  • Quantitative Data: Numerical data that represents measurements or counts.
    • Interval: Differences between values are meaningful (e.g., temperature).
    • Ratio: Has a true zero point (e.g., height).

Descriptive Statistics

  • Mean (x̄): The average of a data set. Excel: =AVERAGE(data)
  • Median: The middle value of a sorted data set. Excel: =MEDIAN(data)
  • Mode: The most frequent value in a data set. Excel: =MODE(data)
  • Range: The difference between the highest and lowest values. Excel: =MAX(data) – MIN(data)
  • Variance (s²): Measures how spread out the data is from the mean. Excel: =VAR.S(data)
  • Standard Deviation (s): The square root of the variance. Excel: =STDEV.S(data)

Probability

  • Discrete Probability Distribution: Describes the probability of each value of a discrete random variable.
    • Requirements: f(x) ≥ 0, Σf(x) = 1
  • Binomial Probability Distribution: Models the probability of successes in a fixed number of independent trials.
    • Parameters: n (number of trials), p (probability of success)
    • Excel: =BINOM.DIST(x, n, p, FALSE)
  • Normal Probability Distribution: A continuous probability distribution with a bell-shaped curve.
    • Z-Score: Measures how many standard deviations a data point is from the mean. Formula: (x – μ) / σ
    • Excel Functions: NORM.S.DIST(z, TRUE), NORM.S.INV(probability)

Other Important Concepts

  • Population Parameters: Measurements from an entire population (e.g., population mean: μ, population standard deviation: σ).
  • Sample Statistics: Measurements from a sample of a population (e.g., sample mean: x̄, sample standard deviation: s).
  • Correlation: Measures the linear relationship between two variables. Excel: =CORREL(array1, array2)
  • Covariance: Measures how two variables change together. Excel: =COVARIANCE.S(array1, array2)

Excel Formulas Quick Reference

  • Quartiles: =QUARTILE.INC(array, k)
  • Interquartile Range: =QUARTILE.INC(array, 3) – QUARTILE.INC(array, 1)
  • Percentile: =PERCENTILE.INC(array, k)

Additional Notes

  • This cheat sheet provides a summary of key statistical concepts and formulas. Refer to your textbook or other resources for more detailed information.
  • Always ensure you understand the assumptions and limitations of the statistical methods you use.