graphical displays of data

Introduction

• Overview of the lesson on graphical displays of data.

• Topics covered include pie charts, bar graphs, histograms, relative histograms, stem and leaf plots, dot plots, heat maps, and line graphs.

Definition of Graph

• A graph is a visual representation of data that allows for quick understanding.

• A legend describes how different data categories are represented in the graph.

Types of Graphs

Pie Charts

• Pie Chart: Circular graph used for qualitative data.

  • Depicts parts of a whole.

  • Shows how large each category is in relation to the whole.

Bar Graphs

• Bar Graph: Represents the amount of data in each category using bars.

  • Pareto Chart: A bar graph ordered in descending order; used for nominal data only.

  • Side by Side Bar Graph: Displays multiple samples of data side by side within the same graph.

  • Stacked Bar Graph: Combines multiple samples of data stacked on top of each other for each category in one graph.

Histograms

• Histogram: A bar graph displaying frequency distribution of quantitative data.

  • Frequency Histogram: Heights of bars represent frequencies of each class.

  • Relative Frequency Histogram: Heights of bars represent relative frequencies for each class.

Stem and Leaf Plots

• Stem and Leaf Plot: Graphs quantitative data by splitting each data value into two parts: a stem and a leaf.

  • Last significant digit is the leaf; remaining digits are the stem.

  • Ordered Stem and Leaf Plot: Leaves are arranged in numerical order to clarify the dataset features.

Procedure for Constructing a Stem and Leaf Plot

1. Create two columns: one for stems and one for leaves.

2. List each stem in numerical order, typically listed only once unless clarity warrants repeating.

3. List each leaf next to its corresponding stem; should match the count of original data values.

4. Create a key for interpretation of the stem and leaf plot.

5. Optionally, sort the leaves in numerical order for an ordered representation.

Dot Plots

• Dot Plot: Graphical depiction where each data value is represented by dots above the corresponding value on a number line.

Heat Maps

• Heat Map: Graph that uses color to indicate the value of a category or area, providing a visual understanding of data density or intensity.

Line Graphs

• Line Graph: Displays data points representing values at particular times, connected by line segments.

  • Illustrates changes in a quantitative variable over time.

Conclusion

• Overview of the multiple graphical displays discussed and their respective utilities in data representation.