HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 2.3 Analyzing Graphs

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Objectives o Identify misleading characteristics of a graph. o ALSO – identify shape of a distribution.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Appropriateness of the Graph A time-series graph is 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.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. 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, ” hart.htm (24 Jan. 2012).

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.18: Scaling of Graphs (cont.) Solution Notice that the x-axis does not have a consistent scale. The years are sometimes one year apart and sometimes even ten years 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.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Look at the two graphs shown below depicting the same data on people’s satisfaction level with their local shopping mall. Which graph is more accurate and why? Graphical Descriptions of Data 2.3 Analyzing Graphs HAWKES LEARNING SYSTEMS math courseware specialists

Side-by-Side but Different Scales

Note the pies’ sizes are different, and for the right reason, too

Shapes of Distributions Change of topic now – next: What shape does this distribution have? The configuration is like this: Quantities (or relative quantity) along the vertical axis What’s the shape of the graph of the data in here in the chart? Number values or classes along the horizontal axis

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Graphical Descriptions of Data 2.3 Analyzing Graphs HAWKES LEARNING SYSTEMS math courseware specialists 1.Uniform – the frequency of each class is relatively the same. 2.Symmetrical – the data lies evenly on both sides of the distribution. 3.Skewed to the Right – the majority of the data falls on the left of the distribution. 4.Skewed to the Left – the majority of the data falls on the right of the distribution. Shapes of Distribution:

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.19: Shapes of Graphs Describe the overall shape of the following distribution.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. 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.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.19: Shapes of Graphs (cont.) Thus, this histogram has a symmetric shape.