### Student Page 2.2.5 What's Wrong with this Picture? Critiquing Graphs

News articles and ads are sometimes accompanied by graphs. Sometimes these graphs are deceiving. Complete What's Wrong with this Picture? Critiquing Graphs, in light of what you have learned about scale. In each graph check to see if the \(\)- and \(y-\)scales are correct. Are the distances between each of the \(x\)-values to scale? Are the distances between each of the \(y\)-values to scale? How can you tell?

Plot each graph using an electronic tool. Set the \(x\) and \(y\) scales to be the same as those used in each graph. Compare the appearance of the graph you created with the designed graph.

#### 1.

Study the graphs in Figure 2.2.5.1. Some are accurate, some are not. For each graph:

##### (a)

Determine if it is drawn accurately. Recreate the graph electronically to help you decide.

##### (b)

Which graphs are good representations of the data?

##### (c)

Which graphs still need work to make them more accurate? What parts of these graphs need work? Describe any changes needed to help the viewer accurately interpret the information provided.

#### 2.

Consider Table 2.2.5.2.

Speeding on Interstate | FINE |
---|---|

71-75 mph | 115.00 |

76-80 mph | 125.00 |

81-85 mph | 135.00 |

86-95 mph | 145.00 |

96 mph or above | 155.00 |

##### (a)

The independent variable is the variable that changes independent of any other variable. Either you must manipulate this variable yourself, or it changes on its own; it does not rely on the other variable. In the table, what is the independent variable? Why do you think so?

##### (b)

The *depend*ent variable is the variable that *depend*s on another variable. What is the dependent variable in the table? Why do you think so?

##### (c)

Use Figure 2.2.5.3 to display the data in Table 2.2.5.2. In mathematics, the horizontal axis *always* represents the independent variable. The vertical axis *always* represents the dependent variable.

#### 3.

What are important features of an accurate, informative graph?

#### 4.

Read a data analytics co-founder's point of view of how graphs can distort the facts^{ 19 }, retrieved April 21, 2020.

##### (a)

The author indicates three of the most common ways graphs can be designed to cause data to be misleading. Are any of these ways used to create misleading graphs in Student Page Exercise 2.2.5.1.

##### (b)

Find or create a graph (if you create the graph use real data) that misleads the public. Explain what is misleading about the graph.

Data sources for graphs, retrieved April 20, 2020:

Amount Needed to Equal the Buying Power of $15,000 in 1953

^{ 20 }.Consumption of Sugar Drinks by Age: U.S. Department of Health and Human Services, Centers for Disease Control and Prevention, National Center for Health Statistics, NCHS Data Brief No. 71, August 2011.