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Statistics

Introduction to Statistics

  • Types of Data: Qualitative vs. Quantitative

  • Levels of Measurement: Nominal, Ordinal, Interval, Ratio

  • Populations vs. Samples

  • Types of Studies: Observational vs. Experimental

  • Sampling Methods: Random, Stratified, Cluster, Systematic

Organizing Data

  • Frequency Tables and Histograms

  • Stem-and-Leaf Plots

  • Dot Plots and Box-and-Whisker Plots

  • Bar Graphs and Pie Charts

  • Misleading Graphs and Bias

Descriptive Statistics

  • Measures of Central Tendency: Mean, Median, Mode

  • Measures of Dispersion: Range, Variance, Standard Deviation

  • Interquartile Range (IQR)

  • Percentiles and Z-Scores

  • Identifying Outliers

Probability

  • Basic Probability Rules

  • Theoretical vs. Experimental Probability

  • Compound Events: Independent and Dependent

  • Conditional Probability

  • Counting Principles: Permutations and Combinations

Probability Distributions

  • Discrete vs. Continuous Distributions

  • Binomial Distribution

  • Normal Distribution and the Empirical Rule (68-95-99.7)

  • Standard Normal Distribution and Z-Tables

  • Approximating Binomial with Normal

Inferential Statistics

  • Sampling Distributions

  • Central Limit Theorem

  • Confidence Intervals for Means and Proportions

  • Margin of Error and Interpretation

  • Determining Sample Size

Hypothesis Testing

  • Null and Alternative Hypotheses

  • Type I and Type II Errors

  • P-Values and Significance Levels

  • One-Tailed vs. Two-Tailed Tests

  • Hypothesis Tests for Means, Proportions, and Variances

Correlation & Regression

  • Scatterplots and Correlation Coefficients (r)

  • Line of Best Fit and Least Squares Regression

  • Interpreting Slope and y-Intercept

  • Coefficient of Determination (r²)

  • Making Predictions and Identifying Outliers

Chi-Square & Other Tests (Optional/Advanced)

  • Chi-Square Goodness-of-Fit Test

  • Chi-Square Test for Independence

  • t-Tests: One-Sample, Two-Sample, and Paired

  • ANOVA (Analysis of Variance) Basics

Cumulative Review & Applications

  • Connecting Concepts Across Units

  • Interpreting Statistical Results

  • Common Mistakes and Misconceptions

  • Real-World Data and Case Studies