Section 4-1 Graphs, Good and Bad Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Statistics is the science of planning studies and experiments obtaining data organizing, summarizing, presenting, analyzing, and interpreting data drawing conclusions based on the data Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Data collections of observations (such as measurements, genders, survey responses) Review Two types of Data – 1. Categorical 2. Quantitative (or Numeric) Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Categorical (qualitative) Data consists of names or labels (representing categories) Example: The genders (male/female) of professional athletes Example: Shirt numbers on professional athletes uniforms - substitutes for names. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Where Does the Information Come From? A question is asked. What kind of ice cream does everyone like in our class? Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

How Is the Information Gathered? A survey is made. Chocolate 1111 1 Vanilla 111 Strawberry 1111 Mint & Chip 1111 11 Rocky Road 11 Bubble Gum 1 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

How Is the Information Presented? Pie chart is made to describe the data. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

How Is the Information Presented? A bar graph is made to display the data. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Bar Graph Uses bars of equal width to show frequencies of categories of qualitative data. Vertical scale represents frequencies or relative frequencies. Horizontal scale identifies the different categories of qualitative data. A multiple bar graph has two or more sets of bars, and is used to compare two or more data sets. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Median Income of Males and Females Multiple Bar Graph Median Income of Males and Females Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

“Stacked” Bar Graphs Another way to merge bar graphs is to “stack” all the bars of an ordinary bar graph on top of one another to form a single bar representing 100% of the (valid) cases. We can then combine nine such stacked bars to “tell the story” of the changing perceived importance of different types of issues in Presidential elections over the last 33 years. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. 11

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Bar graphs, unlike pie charts, CAN add to more (or less) than 100%. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Line Graph Never use line graphs to display qualitative (categorical) data ….only use pie charts or bar graphs Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Bad Graphs Some graphs are bad in the sense that they contain errors. Some are bad because they are technically correct…but misleading. Some are simply too complicated to understand!!! It is important to develop the ability to recognize bad graphs and identify exactly how they are misleading. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

But pie charts are not helpful if there are many unordered categories Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Nonzero Axis Misleading because one or both of the axes begin at some value other than zero, so that differences are exaggerated. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Pictographs Drawings of objects. Example: three-dimensional objects such as money bags, stacks of coins, army tanks (for army expenditures), people (for population sizes), barrels (for oil production), and houses (for home construction) are commonly used to depict data. These drawings can create false impressions that distort the data. Pictographs using areas and volumes can therefore be very misleading. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Annual Incomes of Groups with Different Education Levels Bars need to have the same width This is too busy, too difficult to interpret and understand. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Annual Incomes of Groups with Different Education Levels Misleading because it depicts one-dimensional data with three-dimensional boxes. Last box is 64 times as large as first box, but income is only 4 times as large. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Annual Incomes of Groups with Different Education Levels Fair, objective, unencumbered by distracting features. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Graphs To correctly interpret a graph, you must analyze the numerical information given in the graph, so as not to be misled by the shape of the graph. READ labels and units on the axes! Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.

Pictographs Diagram b is designed to exaggerate the difference by increasing each dimension in proportion to the actual amounts of oil consumption. Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved.