Chapter 7 Project

Misleading Graphs

An activity to demonstrate the use of bar graphs in real life.

Unfortunately, we can be intentionally or unintentionally misled by statistics, particularly when graphs are used to convey findings. In this project, you'll learn how to spot when this occurs with a bar graph and how to fix the representation.

Suppose the following table reported education levels among all young adults (18–24 years old) within the United States for a specific year.

1. The percent value in the first category is lower than all the others. For the other three categories, calculate how many times bigger the percents are compared to the percent value in the first category.

2. Suppose a graphic designer presents the information in the following bar graph. For each of the four categories, calculate the area of the bar shown. (Recall that the area of a square is $A=s^2$.)

   

   A misleading bar graph titled "Highest Education Level Attained". the vertical axis is labeled "Percent ($\%$)" and ranges from $0$ to $80$ in units of $10$. The horizontal axis is labeled "Category" and has the following labels, given from left to right: "Neither a High School Diploma nor a G.E.D.", "High School Diploma or G.E.D", "Bachelor's Degree", "Beyond Bachelor's Degree". The bars for each category are drawn as squares, instead of the usual rectangles used in bar graphs. The bar for "Neither a High School Diploma nor a G.E.D." rises to $5$ percent. The bar for "High School Diploma or G.E.D." rises to $65$ percent. The bar for "Bachelor's Degree" rises to $20$ percent. The bar for "Beyond Bachelor's Degree" rises to $10$ percent.

3. Similar to Problem 1, the area in the first category is smaller than the areas for all the other categories. Calculate how many times bigger the area of each of the other three are compared to the area in the first category.

4. There is a relationship between the area comparisons in Problem 3 to the percent comparisons in Problem 1. What is it? (Hint: What type of geometric figures are shown in the graph and what calculation does this suggest?)

5. Review Section 7.3. Which step of constructing a vertical bar graph was skipped, whether intentional or not? How could this alter the perceptions of those reading the graph in Problem 2?

6. Construct a vertical bar graph that follows all the steps shown in Section 7.3.

7. Although we are able to do the calculations and make the comparisons to spot the misrepresentation, why do you think the skipped step mentioned in Problem 5 is important? (Note: Whether for short reading or a deep dive, look into the works of psychologist Jean Piaget.)

8. Suppose that one year later the information was updated and presented in the following table. While it may be understandable that the information was presented this way, it cannot be used to construct a bar graph for educational levels of young adults in the US. Why?

   Highest Education Level Attained	Percent ($\%$)
   At Least a high School Diploma or G.E.D.	$96$
   At Least a Bachelor's Degree	$24$
   Beyond a Bachelor's Degree	$11$

9. Use the information from the table in Problem 8 to do the following.

   1. Construct a new table like the one from the beginning of the project. (Hint: Subtraction is required.)

   2. Explain why subtraction was required to construct the table in part a.

   3. Construct a vertical bar graph to go along with the table in part a.