Basics of Statistics

Author

Instructor Name

1. Populations vs. Samples

  • Population: Entire group of interest (e.g., all SU undergraduate students, all cars in a parking lot).
  • Sample: Subset of the population used for analysis.
  • Key criteria for a good sample:
    • Random: Every experimental unit has an equal chance of being selected.
    • Representative: Reflects the population’s diversity (e.g., includes all genders, majors).

Example: To study SU students’ sleep habits, randomly select 200 students across all majors/years.

2. Variables & Data Types

Variables describe experimental units (e.g., age, major, car color).

Numerical (Quantitative) Data

  • Expressed as numbers with units.
  • Examples: Height (cm), exam scores, years of education.

Categorical (Qualitative) Data

  • Non-numeric labels or categories.

    • Nominal: No inherent order (e.g., gender, car color).
    • Ordinal: Ordered categories (e.g., product ratings: Poor, Fair, Good).

3. Summarizing Data

Numerical Data

  • Mean: Average value:
    x‾=1n∑i=1nxi\bar{x} = \frac{1}{n}\sum_{i=1}^n x_i
  • Variance: Spread around the mean:
    s2=1n−1∑i=1n(xi−x‾)2s^2 = \frac{1}{n-1}\sum_{i=1}^n (x_i - \bar{x})^2

Categorical Data

  • Use frequency counts or percentages (e.g., 30% Biology majors, 70% Engineering).

4. Visualizing Data

Choose graphs based on data type:

  • Numerical Data:

    • Histograms: Show distribution shape.
    • Boxplots: Highlight median, quartiles, outliers.

  • Categorical Data:

    • Bar charts: Compare category frequencies.
    • Pie charts: Show proportions (use sparingly!). ## Lab Prep Connection

Before starting Lab 0 and Lab 1, review how to classify variables and choose an appropriate summary or graph. Practice using mean(), median(), table(), and ggplot2 histograms, boxplots, and bar charts on the lab datasets.