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Analyzing Graphs for Misleading Characteristics and Proper Labeling

Understand the types of graphs (time-series, cross-sectional, and pictographs), identify misleading characteristics, ensure proper scaling, and recognize different shapes of graphs. Learn to detect errors and correct them by following examples and solutions.

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Analyzing Graphs for Misleading Characteristics and Proper Labeling

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  1. Section 2.3 Analyzing Graphs

  2. Objectives Identify misleading characteristics of a graph.

  3. Title, Axes, Source How to Properly Label a Graph

  4. Appropriateness of the Graph A time-series graphis a line graph that is used to display a variable whose values change over time. A cross-sectional graph displays information collected at only one point in time. A pictograph is a bar graph that uses pictures of objects instead of bars.

  5. Appropriateness of the Graph Pictographs can be deceiving.

  6. Scaling of Graphs Another important feature to look out for is that the graph is scaled properly. • If you stretch or shrink the scale on the y-axis, the shape of the graph may change dramatically. • A line that rises gently on one scale might look very steep with a different scale. When analyzing a graph, check to make sure that the scale represents the data well.

  7. Example 2.18: Scaling of Graphs Consider the graph below on US federal minimum hourly wage rates, unadjusted for inflation. What errors can you find in the graph? How should they be fixed? Source: US Department of Labor, Wage and Hour Division (WHD). “History of Federal Minimum Wage Rates Under the Fair Labor Standards Act, 1938-2009.” http:// www.dol.gov/whd/minwage/chart.htm (24 Jan. 2012).

  8. Example 2.18: Scaling of Graphs (cont.) Solution Notice that the x-axis does not have a consistent scale. The years are as few asone year apart and as many as nineyears apart, so the shape of the graph is distorted. To correct this graph, the x-axis needs to be changed to use a consistent scale. The corrected graph can be found in Exercise 10 in the Chapter 2 Exercises.

  9. Shapes of Graphs Uniform Symmetric Skewed to the Right Skewed to the Left An outlier is a data value that falls outside the normal shape of the graph.

  10. Shapes of Graphs Uniform – the frequency of each class is relatively the same.

  11. Shapes of Graphs Symmetrical – the data lie evenly on both sides of the distribution.

  12. Shapes of Graphs Skewed to the Right – the majority of the data fall on the left side of the distribution. The “tail” of the distribution is on the right.

  13. Shapes of Graphs Skewed to the Left – the majority of the data fall on the right side of the distribution. The “tail” of the distribution ison the left.

  14. Example 2.19: Shapes of Graphs Describe the overall shape of the following distribution.

  15. Example 2.19: Shapes of Graphs (cont.) Solution Notice that if we draw a smooth curve skimming the top of the histogram, we begin to see a curve similar to the shape of the symmetric curve. To be symmetric, the left and right sides of the graph should be close to mirror images. Drawing a line down the center of the graph, we can see that both sides of the graph are indeed mirror images of each other.

  16. Example 2.19: Shapes of Graphs (cont.) Thus, this histogram has a symmetric shape.

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