Question 1

Which of the following is a common way that graphs can misrepresent data by manipulating the vertical axis?

Accepted Answer

By starting the Y-axis at a value greater than zero, exaggerating differences between data points.

Question 2

A bar graph compares the percentage of burglaries in July-August (20.19%) to the average for other months (7.98%), but the July-August value is a sum for two months while the other is an average over ten months. What is misleading about this comparison?

Accepted Answer

It compares a sum to an average, making July-August appear disproportionately high.

Question 3

Why can three-dimensional pie charts be misleading when presenting categorical data?

Accepted Answer

They exaggerate the size of categories closer to the viewer, distorting their perceived importance.

Question 4

A graph shows world population growth with uneven time intervals on the horizontal axis. What is the main issue with this graph?

Accepted Answer

It creates the illusion of linear growth when the intervals are not uniform.

Question 5

In a misleading area graph, the area of a soccer ball representing participation in 2009 is four times larger than in 1991, but the actual increase is only 40%. What is the error in this representation?

Accepted Answer

The area exaggerates the increase, making it appear as a 300% increase instead of 40%.

Question 6

Which of the following best describes why truncating the Y-axis can be misleading in a bar graph comparing hospital performance?

Accepted Answer

It visually exaggerates small differences, making them appear more significant.

Question 7

A three-dimensional pie chart shows 'Violent Crime' as the most prominent category, but the actual percentage is only 20%. What graphical technique is being used to mislead the viewer?

Accepted Answer

Exploding and visually emphasizing a slice to distort perception.

Question 8

Suppose a graph uses bars of different widths to represent monthly sales. What is a potential problem with this approach?

Accepted Answer

It can mislead viewers by making some months appear more important due to wider bars.

Question 9

Which of the following is a best practice to avoid misrepresentation when creating a bar graph?

Accepted Answer

Start the Y-axis at zero to accurately reflect differences.

Question 10

A news article presents a graph where the vertical axis is labeled in increments of 0.1, starting at 99.5%. The graph shows a difference between two groups as dramatic, but the actual difference is only 0.5%. What is the main issue with this graph?

Accepted Answer

The scale exaggerates small differences, misleading the viewer.

Question 11

If a graph uses area (such as the size of a circle) to represent a one-dimensional increase (such as percentage growth), what mathematical error is likely being made?

Accepted Answer

The area increases with the square of the radius, exaggerating the actual growth.

Question 12

Which of the following equations correctly represents the area of a circle used in an area graph?

Accepted Answer

$$A = \pi r^2$

Question 13

A graph shows the number of graduates over time, but the time intervals on the X-axis are not equal. What is the likely effect on the interpretation of the data?

Accepted Answer

It can create a false impression of consistent growth or decline.

Question 14

Which of the following is NOT a common way that graphs can misrepresent data?

Accepted Answer

Using a consistent scale and starting axes at zero.

Question 15

A misleading graph shows a 40% increase in soccer participation by making the soccer ball's area four times larger. If the original area is $$A$$, what should the new area be to accurately represent a 40% increase?

Accepted Answer

$$A_{new} = 1.4A$$

Question 16

Which of the following best describes why using three-dimensional effects in pie charts can be misleading?

Accepted Answer

They distort the perceived size of slices, making some categories appear larger than they are.

Graphical Misrepresentations of Data in Statistics

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