07 Jan either a pie chart

MATH399 Applied Managerial Statistics

Week 2 Assignment Choose appropriate graphs to display data

QuestionFor which of the following sets of data is a pie chart appropriate? Assume that only the two given categories will be included.

the percentage of people that drive to work and the percentage of people that walk to work

the percentage of people that speak only one language and the percentage of people that speak multiple languages

the percentage of people who own cell phones and the percentage of people who own tablets

the percentage of people who like horror films and the percentage of people who like romantic dramas

QuestionVirginia polled a large sample of individuals to find the percentage of students with known food allergies and the percentage of students without known food allergies. Which of the following could sufficiently display the data if only the two given categories are to be included?

bar graph

pie chart

either a pie chart or a bar graph

neither a pie chart nor a bar graph

QuestionThe Terman Study of the Gifted followed children who scored above a certain level on an I.Q. test into adulthood. The study collected information on the same participants, including the average height of the group, approximately every five years. Which of the following could best display how the average height of participants changes over time?

Bar graph

Line graph

Pie chart

Either a bar graph or a pie chart

Appropriate Data Displays

Choosing Appropriate Data Displays

There are many different ways to displaying data, but choosing the most appropriate type of display is important. Each type of data display shows data in different ways, and certain ones are more accurate and useful depending on the type of data collected.

Bar Graphs

Bar graphs consist of bars that are separated from each other. The bars can be rectangles or they can be rectangular boxes (used in three-dimensional plots), and they can be vertical or horizontal. Bar graphs are appropriate for categorical data – data separated into qualitative categories, and when you want to show the absolute quantity of each category. They are useful for making comparisons between separate subcategories.

A bar graph has a horizontal axis labeled Type of Transport with groups Car, Walking, Bus, and Taxi and a vertical y-axis labeled Number of Learners from 0 to 25 in increments of 5. There are vertical bars, each of which is above one of the Group labels. The heights of the bars are as follows, with the horizontal axis label listed first and the bar height listed second: Car, 10; Walking, 20; Bus, 15; and Taxi, 5.

The bar graph above shows the type of transportation adult learners use to get to and from their night school classes. The categories of the types of transportation are represented on the x-axis, while the quantity, or number of learners, is shown on the y-axis.

Pie Charts

Pie charts are a type of graph where a circle is divided into sectors, or slices, which each show the proportion of that subcategory compared to the whole. Like bar graphs, pie charts are also good for representing categorical data, but unlike bar graphs, all of the data values in a pie chart must fall into just one category. (No data value can land in two different subcategories.) Pie charts are helpful for showing the relative quantity of categories and comparing the subcategories to the whole.

A pie chart titled Approximate Composition of the Air is divided into three sectors with labels and percentages as follows: Nitrogen, 79 percent; Oxygen, 20 percent; and Other gases, 1 percent. Text reads: N B “Other gases” includes carbon dioxide left-parenthesis 0.03 percent right-parenthesis and small proportions of other gases including argon and water vapor.

The pie chart above represents the composition of the air broken into three subcategories – found in the legend in the upper right corner. The slices show the proportion of each subcategory, in comparison with the total composition. (i.e. Nitrogen makes up approximately 79% of the total composition of the air.)

You could use a bar graph to show this information, however it would not have been as clear. The bar for Nitrogen would be 79 units in height, but those units would be percentages, which is a bit odd. A bar graph could not show the proportions of the composition of the air as easily as a pie chart.

Bar Graphs vs. Pie Charts

As long as there is no overlap of data values (i.e. a data value does not fall into two different categories), you may use either a bar graph or a pie chart. Keep in mind that a bar graph is more helpful when comparing categories to each other, whereas a pie chart is more helpful when showing a category’s proportion to the whole.

However, if any data value falls into two or more categories, then it is better to use a bar graph. (i.e. If you want to show the number of students on different sports teams, and there is a student who plays soccer and baseball.) A pie chart with overlapping data values can be misleading.

Line Graphs

Line graphs are useful for representing specific data values over time, with the x-axis as time and the y-axis as the changing quantity. (These are also known as a time series graphs.)

A line graph titled Total Population of Thoralby has a horizontal x-axis labeled from 1870 to 2010 in increments of 20 and a vertical y-axis labeled from 0 to 350 in increments of 50. The graph consists of 11 plotted points connected by line segments from left to right. The coordinates of the plotted points are at left-parenthesis 1870 comma 275 right-parenthesis, left-parenthesis 1880 comma 210 right-parenthesis, left-parenthesis 1890 comma 200 right-parenthesis, left-parenthesis 1900 comma 210 right-parenthesis, left-parenthesis 1910 comma 175 right-parenthesis, left-parenthesis 1920 comma 200 right-parenthesis, left-parenthesis 1930 comma 160 right-parenthesis, left-parenthesis 1950 comma 125 right-parenthesis, left-parenthesis 1960 comma 325 right-parenthesis, left-parenthesis 2000 comma 150 right-parenthesis, and left-parenthesis 2010 comma 150 right-parenthesis. All coordinates are approximated.

The line graph above shows the time (in years) on the x-axis, and the total population of a small town named Thoralby on the y-axis. The line graph is useful when comparing the changing population over time, as you read from left to right.

Unlike bar graphs and pie charts, line graphs should not be used for categorical data. Displaying categorical data in a line graph could be misleading, seemingly giving the categories a certain “order.”

Key Terms

• Bar graph: a graph to summarize and organize categorical data consisting of rectangular bars that are separated from each other and the length (or height) of the bar for each category is proportional to the number or percent of individuals in each category

A Bar graph may also be referred to as a Bar chart

• Categorical data: data separated into qualitative categories

• Pie chart: a type of graph where a circle is divided into sectors, or slices, which each show the proportion of that subcategory compared to the whole

A Pie chart may also be referred to as a Pie graph or a Circle graph

• Line graph: a bar graph with the tops of the bars represented by points joined by lines (with rest of the bar not shown) and are only appropriate for ordered (rather than qualitative) variables that show how a quantity changes over time

A Line graph may also be referred to as a Line chart or as a Time series graph

QuestionStephanie polled a large sample of individuals to find the percentage of people who like horror films and the percentage of people who like romantic dramas. Which of the following could sufficiently display the data if only the two given categories are to be included?

bar graph

pie chart

either a pie chart or a bar graph

neither a pie chart nor a bar graph

QuestionWhich of the following sets of data should not be displayed with a pie chart? Assume that only the two given categories will be included.

the percentage of people who like horror films and the percentage of people who like romantic dramas

the percentage of in-state students and the percentage of out-of-state students

the percentage of people that speak only one language and the percentage of people that speak multiple languages

the percentage of students that are full-time and the percentage of students that are part-time

QuestionDeborah conducted a survey in which she collected data on the percentage of workers with college degrees and the percentage of workers without college degrees. Which of the following could sufficiently display the data if only the two given categories are to be included?

pie chart

bar graph

neither a pie chart nor a bar graph

either a pie chart or a bar graph

QuestionFor which of the following sets of data is a pie chart appropriate? Assume that only the two given categories will be included.

the percentage of people who jog more than three times a week and the percentage of people who lift weights more than three times per week

the percentage of students that have science majors and the percentage of students that have humanities majors

the percentage of people that support a new speed limit law and the percentage of people who oppose the new speed limit law

the percentage of people who own cell phones and the percentage of people who own tablets