Variables and Graphs in Statistics

Variable and Data

• A variable is a characteristic or attribute that can take on different values.
• Data refers to the collected values of a variable, classified into two main types: categorical and quantitative.

Types of Variables

• Categorical Variables: Represent categories or groups (e.g., gender, color).

  • Nominal: No natural order (e.g., types of fruit).
  • Ordinal: Natural order but no uniform differences (e.g., rankings).

• Quantitative Variables: Represent measurable quantities (e.g., height, age).

  • Discrete: Can take specific values (e.g., number of children).
  • Continuous: Can take any value within a range (e.g., weight).

Graphs for Categorical Data

• Bar Charts: Represent the frequency of each category with rectangular bars; height corresponds to the number of occurrences.
• Pie Charts: Show proportions of categories as slices of a pie; helpful for displaying percentage relationships.

Graphs for Quantitative Data

• Line Charts: Display data points connected by straight lines; useful for showing trends over time.
• Dot Plots: Represent data points as dots along a number line; effective for small datasets and to visualize distributions.
• Stem and Leaf Plots: Present quantitative data by separating values into stems (leading digits) and leaves (final digits); enables quick visual data insights.

Relative Frequency Histograms

• Histograms display the distribution of quantitative data by representing the frequency of data within specified intervals (bins).
• Relative frequency histograms show proportions of each bin relative to the total number of observations, enhancing interpretability of distribution shapes.