Exercises 1B
1B.1 For the following situations, select the graph type (bar, line, pie, multiple bar, multiple line, stack) that is the most appropriate:
a. The proportion of lottery dollars given to four main categories - environmental, educational, medical and recreational causes.
The word proportion indicates that a pie chart is appropriate.
b. The proportion of each mortgage payment that is interest tracked over the 20 year mortgage period.
Proportion here implies a pie chart, but giving a pie chart for each of 20 years will not work. This is the setting for a stack plot. However since mortgage payments are often fixed rate, implying that monthly payments stay constant, the proportion asked for is a proportion of a fixed amount and so it is appropriate to compare dollars with dollars. A simple line graph is all that is requires.
c. Average (per-year) spending by the Governor’s Office compares to that of the previous Governor in a variety of categories.
This is definitely the setting for a stack plot. The stacking allows comparison of the proportions in the categories each year and also shows how the total amount changes over time.
d. Number of students receiving grades of A, B, C, D and F on a given test.
A simple bar graph is usually preferred although a pie chart is also fine.
e. The budgets of 6 different state agencies over the past 5 years.
A set of budgets are being tracked over time and so a multiple line graph is the preferred graph type. This is easier to interpret than a multiple bar graph.
f. A couple’s taxable income for each year since 1995.
A simple bar graph or line graph are both fine here; a line graph is better because of the time line.
1B.2 A survey is conducted among high school and college students about the students’ favorite activities. 50 high school students were surveyed and 100 college students were surveyed. The following results were found with the accompanying bar chart.
High School / CollegeSports / 15 / 20
Music / 10 / 10
Study / 5 / 35
Friends / 10 / 15
Other / 10 / 20
The two categories are displayed together as a form of comparison:
Do you agree with the way the data was displayed? Discuss your thoughts in a short paragraph.
The chart is comparing the favorite activities of students in high school with those in college. A multiple-bar graph has been preferred to multiple-line graph because there is no sense of order of the subjects along the horizontal axis. This is a good choice of graph to present the data.
The chart would be better given a label for the vertical axis and a heading for the chart itself. But there is a more serious flaw: By summing across the categories, it can be seen that each student surveyed has chosen just one category – the gray values sum to 50 while the maroon ones sum to 100. This is not going to give a meaningful comparison. It would be better to put both groups on the same scale – say using percentages which will double the height of the gray bars.
1B.3 The following stack plot (not a multiple line graph) shows sales of three models of automobiles in consecutive years (Labeled as Years 1, 2 and 3.)
How have sales of Model B changed over the three years? Explain your reasoning.
Sales of Model B have decreased from Year 1 to Year 3. Because this is a stack plot, the horizontal line above the words ‘Model B’ reflects combined sales of Models A and B. Together these have remained flat from year 1 to Year 3, but Model A’s sales have increased while Model B’s sales have decreased.
1B.4 Below is a graph depicting AIMS scores for Flagstaff, Arizona.
a) Do you think the type of graph used depicts the data in the best way? Explain your reasoning.
The chart is showing student success in the AIMS tests in comparison to the state as a whole. A multiple-bar graph has been preferred to multiple-line graph because there is no sense of order of the subjects along the horizontal axis. This is a good choice of graph to present the data.
b) Is there something missing that could have been added to the graph to make it more complete?
The chart is well labeled with a precise label along the vertical axis and a chart heading that makes it clear that it represents AIMS scores for 8th graders in 2009. There is no ambiguity. Again, this is an excellent chart.