Introductory Statistics Test 1 Review – Step-by-Step Study Guidance

Q13. The following graph shows the ratings (1-5 stars) on Yelp for Hot Doug’s Restaurant. Label the x and y axis.

Background

Topic: Interpreting and Labeling Graphs (Frequency Distributions)

This question tests your ability to read and interpret bar graphs (or histograms) and to correctly label the axes based on the data being presented. Understanding how to label axes is a fundamental skill in statistics, as it helps communicate what the graph is showing.

Key Terms:

• X-axis (Horizontal axis): Usually represents the categories or groups being measured (in this case, the number of stars in the Yelp rating).

• Y-axis (Vertical axis): Usually represents the frequency or count of observations in each category (in this case, the number of reviews for each rating).

Step-by-Step Guidance

1. Look at the graph and identify what each bar represents. Notice the numbers below each bar (1, 2, 3, 4, 5) and the heights of the bars.

2. Determine what the horizontal axis (x-axis) categories are. In this graph, each bar corresponds to a different Yelp star rating.

3. Examine the vertical axis (y-axis) and see what the numbers along this axis represent. The numbers increase in regular intervals and match the heights of the bars, which correspond to the number of reviews for each rating.

4. Think about appropriate labels for each axis based on what is being measured and counted.

Try labeling the axes on your own before revealing the answer!

Final Answer:

• X-axis label: Yelp Star Rating (1 to 5 stars)

• Y-axis label: Number of Reviews (Frequency)

The x-axis should be labeled with the rating categories (1, 2, 3, 4, 5 stars), and the y-axis should be labeled as the number of reviews, since the height of each bar shows how many people gave each rating.

Q14. The following is a USA Today-type graph. Do you think the graph is misleading? Why? If you think it is misleading, what might be done to improve the graph?

Background

Topic: Graphical Misrepresentation and Data Visualization

This question tests your ability to critically evaluate graphs for misleading features. In statistics, it is important to recognize when a graph may distort the data, either intentionally or unintentionally, and to suggest ways to improve the accuracy and clarity of data presentation.

Key Terms:

• Misleading graph: A graph that visually distorts the data, making differences appear larger or smaller than they really are.

• Pictogram: A graph that uses pictures or symbols to represent data, which can exaggerate differences if the area or volume of the symbols is not proportional to the data values.

• Proportionality: Ensuring that the visual representation accurately reflects the numerical differences in the data.

Step-by-Step Guidance

1. Examine the graph and note how the data is being represented. Notice the use of dollar signs and graduation caps of different sizes to represent different savings methods.

2. Compare the actual percentages listed (17%, 21%, 31%, 37%) to the sizes of the symbols. Ask yourself: Do the sizes of the symbols accurately reflect the differences in the data?

3. Consider whether the use of 3D images or pictograms could exaggerate the differences between categories. For example, does the largest symbol look much more than twice as big as the smallest, even though the percentage is only about twice as large?

4. Think about how the graph could be improved to more accurately represent the data. What type of graph would avoid this kind of distortion?

Try analyzing the graph and suggesting improvements before revealing the answer!

Final Answer:

Yes, the graph is misleading. The sizes of the dollar signs and graduation caps are not proportional to the actual percentages, making the differences between categories appear much larger than they really are. This is a common problem with pictograms, especially when the area or volume of the images increases faster than the data values.

To improve the graph, use a simple bar chart or column chart where the heights of the bars are directly proportional to the percentages. This would make it easier to accurately compare the values and avoid visual exaggeration.