Section 8.3 Enhancement, Distraction, and Distortion Misleading graphs Misleading graphs Scales and axis manipulationScales and axis manipulation Line graphs and croppingLine graphs and cropping 3D effects3D effects PictographsPictographs Graphical mapsGraphical maps

Scaling and Axis Manipulation To emphasize differences among the bars of a bar graph, you can leave off part of the vertical axis.To emphasize differences among the bars of a bar graph, you can leave off part of the vertical axis. Reversing the axes is another way to create a misleading graph.Reversing the axes is another way to create a misleading graph.

Example 1 The graph appears to show that Beary Sticks has a lot less sugar than other cereals.The graph appears to show that Beary Sticks has a lot less sugar than other cereals.

Example 1, cont’d The first graph was misleading because:The first graph was misleading because: There was no scale. There was no scale. The axis began at 8, not at 0.The axis began at 8, not at 0.

Example 2 3 brands of baked beans3 brands of baked beans Brand X: $0.79 Brand X: $0.79 Brand Y: $0.89 Brand Y: $0.89 Brand Z: $0.99 Brand Z: $0.99 Create a bar graph that emphasizes the differences in the prices.Create a bar graph that emphasizes the differences in the prices.

Example 2, cont’d Start the vertical scale at 75 cents instead of at 0.Start the vertical scale at 75 cents instead of at 0.

Example 3 This bar graph shows that a company’s profits decline over time.This bar graph shows that a company’s profits decline over time.

Example 3, cont’d Switch the axes and put the years in reverse order, and the graph has a more positive feel and may be misleading.Switch the axes and put the years in reverse order, and the graph has a more positive feel and may be misleading.

Example 4 Create a graph that gives the impression that things are getting better rather than worse.Create a graph that gives the impression that things are getting better rather than worse.

Example 4, cont’d The years are in reverse order. The years are in reverse order. The vertical scale starts at 20. The vertical scale starts at 20. The graph is tall and narrow. The graph is tall and narrow.

Line Graphs and Cropping Cropping:Cropping: A viewing window is chosen to make a trend look more or less impressive. A viewing window is chosen to make a trend look more or less impressive.

Cropping, cont’d

Example 5 Draw two line graphs that give different impressions.Draw two line graphs that give different impressions.

Example 5, cont’d Start one vertical axis at 0 and the other at 24.Start one vertical axis at 0 and the other at 24.

Example 6 The price of a stock from April 25 through May 5 seems to have a large increase.The price of a stock from April 25 through May 5 seems to have a large increase. Notice the vertical axis begins at 98. Notice the vertical axis begins at 98.

Example 6, cont’d The same stock over a longer time shows a gradual decline overall.The same stock over a longer time shows a gradual decline overall. Notice the vertical axis begins at 0. Notice the vertical axis begins at 0.

Example 6, cont’d This graph has the same information as the last graph, but a different vertical scale.This graph has the same information as the last graph, but a different vertical scale. The decrease is more dramatic because the vertical axis starts at 100. The decrease is more dramatic because the vertical axis starts at 100.

Three-Dimensional Effects Three-dimensional effects:Three-dimensional effects: Often used in newspapers and magazines. Often used in newspapers and magazines. Can make a graph more attractive. Can make a graph more attractive. Can obscure a true picture of the data. Can obscure a true picture of the data.

Example 7 It can be difficult to read exact values from a 3-D graph.It can be difficult to read exact values from a 3-D graph. The profits were almost $100,000 in 2003 but it looks lower on this graph. The profits were almost $100,000 in 2003 but it looks lower on this graph.

Example 8 It is also hard to read exact values from this 3-D line graph.It is also hard to read exact values from this 3-D line graph.

Example 9 In a 3-D pie chart, the exploded sector appears larger than it really is.In a 3-D pie chart, the exploded sector appears larger than it really is.

Pictographs Pictograph: pictures, symbols, or icons represent quantities.Pictograph: pictures, symbols, or icons represent quantities. Can represent data in interesting ways, but can also be misleading. Can represent data in interesting ways, but can also be misleading.

Example 10 This pictograph predicts the world population.This pictograph predicts the world population. Each person icon represents 1 billion people. Each person icon represents 1 billion people.

Example 11 Each hotdog represents 10% of campers.Each hotdog represents 10% of campers.

Example 12 This pictograph compares amounts spent on different holiday gifts.This pictograph compares amounts spent on different holiday gifts.

Example 13 Why is this pictograph misleading?Why is this pictograph misleading?

Example 13, cont’d The bars are not proportional in height to the amounts they represent.The bars are not proportional in height to the amounts they represent. There were 4 times as many students in grades 1-8 as there were in pre-elementary. There were 4 times as many students in grades 1-8 as there were in pre-elementary. The grades 1-8 bar is only about 3 times as tall as the pre-elementary bar. The grades 1-8 bar is only about 3 times as tall as the pre-elementary bar. This makes the difference look smaller than it is. This makes the difference look smaller than it is.

Example 14 Why is this pictograph misleading?Why is this pictograph misleading?

Example 14, cont’d The bars are not proportional to the amounts they represent.The bars are not proportional to the amounts they represent. The bars are also slanted, making the top bar look longer and the bottom bar look shorter.The bars are also slanted, making the top bar look longer and the bottom bar look shorter.

Example 15 Why is this pictograph misleading?Why is this pictograph misleading?

Example 15, cont’d The amount of milk sold in 2003 was twice the amount in The amount of milk sold in 2003 was twice the amount in It is not clear whether the volume or the height of the carton represents the milk quantity. It is not clear whether the volume or the height of the carton represents the milk quantity. The volume of the second carton is 8 times larger than the first carton. The volume of the second carton is 8 times larger than the first carton.

Example 16 Why is this pictograph misleading?Why is this pictograph misleading?

Example 16, cont’d The number of bottles in each stack is not proportional to the dollar amounts.The number of bottles in each stack is not proportional to the dollar amounts. The heights of the stacks are proportional.The heights of the stacks are proportional. It is not clear whether it should be viewed as a bar graph or as a pictograph. It is not clear whether it should be viewed as a bar graph or as a pictograph.

Customized Pie Charts Pie charts can be embedded in another picture, or include other content.Pie charts can be embedded in another picture, or include other content.

Example 18 This pie chart distorts the data.This pie chart distorts the data.