2. Describing Data with Tables and Graphs

Visualizing Qualitative vs. Quantitative Data

2. Describing Data with Tables and Graphs

Visualizing Qualitative vs. Quantitative Data

4:19 minutes

Problem 2.3.12b

Textbook Question

Gas Hike The average per gallon price for regular unleaded gasoline in the United States rose from \$1.46 in 2001 to \$2.77 in 2018.

Source: U.S. Energy Information Administration

b. Construct a misleading graphic that makes it appear the average price roughly quadrupled between 2001 and 2018.

Verified step by step guidance

Understand that a misleading graphic can exaggerate the change by manipulating the y-axis scale or the visual representation of the data.

Start by plotting the average price per gallon for 2001 and 2018 on a vertical axis (y-axis). Normally, the y-axis should start at 0 to accurately reflect proportional changes.

To make the price increase appear roughly quadruple, adjust the y-axis to start at a value close to the 2001 price (for example, just below \$1.46) instead of 0. This reduces the visual baseline and exaggerates the height difference between the two points.

Plot the 2001 price at \$1.46 and the 2018 price at \$2.77 on this truncated y-axis. The visual difference will look much larger than the actual increase.

Optionally, use a bar chart or line graph with thick bars or lines to further emphasize the difference, making the increase appear about four times larger than it really is.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Scale Manipulation in Graphs

Scale manipulation involves adjusting the axes of a graph, especially the y-axis, to exaggerate or minimize changes in data. By truncating or expanding the scale, a graph can misleadingly amplify differences, making small changes appear large or vice versa. Understanding this helps identify when visuals distort the true data story.

Data Representation and Integrity

Data representation refers to how numerical information is visually or textually presented. Maintaining integrity means accurately reflecting the data without distortion. Misleading graphics violate this principle by presenting data in ways that deceive viewers, such as exaggerating trends or differences beyond what the numbers support.

Percentage Change vs. Absolute Change

Percentage change measures relative change between two values, while absolute change is the simple difference. Misleading graphics often confuse or exaggerate these concepts, for example, by implying a quadruple increase when the actual percentage increase is less. Understanding both helps interpret data changes correctly.

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Textbook Question

Oil Reserves The U.S. Strategic Oil Reserve is a government-owned stockpile of crude oil. It was established after the oil embargo in the mid-1970s and is meant to serve as a national defense fuel reserve, as well as to offset reductions in commercial oil supplies that would threaten the U.S. economy. The graphic depicts oil reserves in 1977 and 2018.

a. How many times larger should the graphic for 2018 be than the 1977 graphic (to the nearest whole number)?

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Textbook Question

The U.S. Strategic Oil Reserve is a government-owned stockpile of crude oil. It was established after the oil embargo in the mid-1970s and is meant to serve as a national defense fuel reserve, as well as to offset reductions in commercial oil supplies that would threaten the U.S. economy. The graphic depicts oil reserves in 1977 and 2018.

b. The United States imported approximately 10.14 million barrels of oil per day in 2018. At that rate, assuming no change in U.S. oil production, how long would the U.S. strategic oil reserve last if no oil were imported?

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Textbook Question

Energy Need during Pregnancy The total energy need during pregnancy is normally distributed, with mean μ = 2600 kcal/day and standard deviation σ = 50 kcal/day.

Source: American Dietetic Association.

a. Is total energy need during pregnancy qualitative or quantitative?

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Textbook Question

Gas Hike The average per gallon price for regular unleaded gasoline in the United States rose from \$1.46 in 2001 to \$2.77 in 2018.

Source: U.S. Energy Information Administration

a. Construct a graphic that is not misleading to depict this situation.

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Textbook Question

Ideal Family Size The following USA Today–type graphic illustrates the ideal family size (total children) based on a survey of adult Americans.

a. What type of graphic is being displayed?

b. Describe any problems with the graphic.

c. Construct a graphic that is not misleading and makes the data stand out.

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Textbook Question

Retain Your Knowledge: Decision Making and Hunger Does hunger improve strategic decision making? That is, if you are hungry are you more likely to make a favorable decision when the outcome of your decision is uncertain (as in business decisions)? To test this theory, researchers randomly divided 30 normal weight individuals into two groups. All subjects were asked to refrain from eating or drinking (except water) from 11 P.M. on the day prior to their 9 A.M. meeting. At 9 A.M., the subjects were randomly assigned to one of two groups. The subjects in Group 1 were fed breakfast while the subjects in Group 2 were not fed. All subjects were administered a computerized version of an exam that assesses complex decision making under uncertain conditions. The assessment consisted of subjects choosing cards from four decks marked A, B, C, and D. Cards in decks A and B had a point value of 100 while cards in decks C and D had point values of 50. However, deck A had penalty cards that deducted points between 150 and 300; deck B had one penalty card of 1250; deck C had penalty cards between 25 and 75 points; deck D had a single penalty card of 250 points. So, decks A and B had stiffer penalties over the long haul than decks C and D and in the long haul, decks C and D resolted in more points than decks A and B. In total, the subjects would select 100 cards. However, the response variable was the number of cards selected from decks C and D out of the last 60 cards selected. The thinking here is that after 40 card selections, the subjects would be aware of the advantage of decks C and D. The researchers administered a Barret Impulsivity Scale to be sure the two groups did not differ in terms of impolsivity (e.g., “I do things without thinking”). There was no difference in impulsivity, age, or body mass index between the two groups. Before the exam, subjects were asked to report their level of hunger and it was found that Group 2 was significantly more hungry than Group 1. After analysis of the data, it was determined that the mean number of advantageous cards (decks C and D) selected by the subjects in Group 2 was 33.36 cards while the mean was 25.86 for the subjects in Group 1. The researchers concluded that hunger improves advantageous decision making.

c. What is the response variable? Is it qualitative or quantitative? If quantitative, is it discrete or continuous?

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Textbook Question

f. What are the statistics in the study?

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Textbook Question

Platelet-Rich Plasma In a prospective cohort study, 20 patients with alopecia (hair loss) had platelet-rich plasma (PRP) injected in their scalps. After three months, the mean difference in hair density (after - before) was 170.70 hairs per square centimeter with a standard deviation of 37.81hairs/cm2. Source: Gkini MA, Kouskoukis AE, Tripsianis G, Rigopoulos D, Kouskoukis K., “Study of Platelet-Rich Plasma Injections in the Treatment of Androgenetic Alopecia through a One-Year Period”. J Cutan Aesthet Surg, 2014; 7:213–219.

b. What is the variable of interest in this study? Is it qualitative or quantitative?

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Gas Hike The average per gallon price for regular unleaded gasoline in the United States rose from \$1.46 in 2001 to \$2.77 in 2018.Source: U.S. Energy Information Administrationb. Construct a misleading graphic that makes it appear the average price roughly quadrupled between 2001 and 2018.

Key Concepts

Scale Manipulation in Graphs

Data Representation and Integrity

Percentage Change vs. Absolute Change

Watch next

Gas Hike The average per gallon price for regular unleaded gasoline in the United States rose from \$1.46 in 2001 to \$2.77 in 2018.

Source: U.S. Energy Information Administration

b. Construct a misleading graphic that makes it appear the average price roughly quadrupled between 2001 and 2018.