11.19: Data Display Choices
What is your bedtime? Have you ever tried to convince your parents to change it?
Kelly is wishing for a new bedtime. Her parents insist that she heads to bed at 9 pm each night and Kelly wants to go to bed at 9:30 pm. After a long argument, she decides to conduct a survey of the other kids in her class to figure out how many kids go to bed at 9 pm, 9:30 pm and 10 pm or later. She tells her penpal Justin about her plan and he decides to conduct the same survey in New Zealand.
Kelly is excited. Maybe with enough data from two different countries, her parents will allow her to change her bedtime. Kelly writes up the survey and asks the 25 students in her class to participate. She asks Justin to survey 25 students as well so that their data can be easily compared. If they survey different numbers of students, it will be more challenging to compare the data.
Here are Kelly’s results.
9 pm = 7 students
9:30 pm = 12 students
10 pm or later = 6 students
Justin conducts a survey and emails Kelly the results. Here is what he discovered.
9 pm = 2 students
9:30 pm = 7 students
10 pm or later = 16 students
Kelly is amazed that most of the students that Justin surveyed go to bed at 10 pm or later. She knows that will never fly with her parents, but she might have collected enough evidence to get to 9:30 pm.
Next, Kelly wants to create a display to show her parents. She wishes to create two different displays-one to show her data alone and one to show her data compared with Justin’s data. Kelly isn’t sure how to go about it. This is where you come in-learning about data displays is the focus of this Concept. With your help Kelly will be able to complete her task!
Guidance
A survey is a way of collecting data based on personal information given by individuals. Oftentimes, a survey can be taken to learn personal preferences. Surveys are done all the time. They are done at schools, by businesses, even by the government. Sometimes, television companies conduct surveys to figure out the television preferences of their viewers.
A survey is one method of working with statistics. Statistics involve collecting, analyzing and displaying data. In the introduction problem, Kelly and Justin conducted a real-world survey.
Let’s look at some of what they did to conduct the survey.
- They decided on a question. Their question had to do with bedtimes. They asked students “What time do you go to bed at night?”
- Next, they chose parameters. Parameters are boundaries. They chose three bedtimes for students to choose from. If the boundaries had been left open, Kelly and Justin might have had so many different responses that it would have been difficult to organize and analyze the data. They left the last category a bit more open-10 pm or later to cover anyone who did not specifically fit in one of the other spots.
- Then they conducted the survey and collected the data.
- After finishing the survey, it is time to select a way to display the data. There are many different ways to display data in a visual way. Each way has a different purpose. By becoming familiar with the different ways to display data, a person can choose the one that best serves his/her purpose.
Now that the survey has been conducted, it is time to choose a data display. When creating a display, there are different ways to show data.
As Kelly thinks about the different ways to display data, she thinks that she wants to create two different displays.
The first one will show only her data and will be a circle graph.
The second one will show her data and Justin’s and will be a double bar graph.
Are these good choices? Kelly isn’t sure. Let’s think about each type of data display and how Kelly can show her survey results.
1. Bar Graph – A bar graph displays the frequency of data or how often data occurs.
Kelly wants to show that many students have a later bedtime than she does. Given this information, a bar graph might be a possible way for Kelly to display her individual data without including Justin’s data.
2. Double Bar Graph – Compares the frequency of two sets of data.
When Kelly creates a display to show her data and Justin’s data, a double bar graph is a way to show both sets of data in the same spot. Given this, a double bar graph is a possible option.
3. Line Graph – shows how data changes over time.
Kelly did not conduct a survey to address how bedtimes changed over time. She conducted a survey to count the how many of her peers had each bedtime. She wants to prove that many students have a later bedtime than she does, so she should also have a later bedtime. Given her goal, a line graph is NOT a good option for Kelly.
4. Double Line Graph – compares how two sets of data change over time.
Given Kelly’s goal and the way that the survey was conducted, this is not an option for Kelly.
5. Circle Graph – shows a percentage out of a whole.
If Kelly was to change her data to show the percentage of students with each bedtime, she could probably prove to her parents that many students have a later bedtime than she does. This could be an excellent option for Kelly.
Kelly’s selections will work.
She can create a circle graph to show her survey alone and a double bar graph to show her survey data and Justin’s.
Now that Kelly has chosen her two displays, she needs to analyze and interpret her data. First, to create a circle graph, Kelly needs to write her data in terms of percentages. She will need to change each amount of the whole to a percentage for the work to make sense.
Let’s look at the survey results once again.
Kelly surveyed 25 students.
7 students have a 9 pm bedtime.
12 students have a 9:30 pm bedtime.
6 students have a bedtime that is 10 pm or later.
To convert this data to percentages, Kelly first needs to write a fraction for each bedtime.
\begin{align*}\frac{7}{25} =\end{align*}
\begin{align*}\frac{12}{25} =\end{align*}
\begin{align*}\frac{6}{25} =\end{align*}
Next, Kelly needs to change each fraction to a %. To do this, she can rewrite each fraction as an equal fraction out of 100.
\begin{align*}\frac{7}{25} &= \frac{28}{100} = 28 \%\\
\frac{12}{25} &= \frac{48}{100}=48 \%\\
\frac{6}{25} &= \frac{24}{100}=24 \%\end{align*}
Now Kelly has percentages, and she can create her circle graph.
What about the double bar graph?
To do this, she can create two axes. On the \begin{align*}x\end{align*}
With a double bar graph Kelly can use the actual numbers. She doesn’t need to convert any numbers to fractions or percentages.
Now let’s look at which data display would work best for each example.
Example A
If I wanted to show how often someone ate ice cream, which data display would make the most sense?
Solution: Bar Graph
Example B
If I wanted to show percentages out of a whole, which visual display would make the most sense?
Solution: Circle Graph
Example C
If I wanted to show how data changes over time, which display would make the most sense?
Solution: Line Graph
Now let's go back to Kelly and the survey.
Here are Kelly’s results.
9 pm = 7 students
9:30 pm = 12 students
10 pm or later = 6 students
Justin conducts a survey and emails Kelly the results. Here is what he discovered.
9 pm = 2 students
9:30 pm = 7 students
10 pm or later = 16 students
Kelly is amazed that most of the students that Justin surveyed go to bed at 10 pm or later. She knows that will never fly with her parents, but she might have collected enough evidence to get to 9:30 pm.
Based on this Concept, Kelly has decided to create two displays. First, she will create a circle graph to show her data in terms of percentages. Then, she will create a double bar graph to show her data in relationship to Justin’s data.
She hopes that her data will help her to prove to her parents that 9:30 is a reasonable bedtime.
Here is Kelly’s data for the circle graph.
\begin{align*}\frac{7}{25} &= \frac{28}{100} = 28\%\\
\frac{12}{25} &= \frac{48}{100}=48\%\\
\frac{6}{25} &= \frac{24}{100}=24\%\end{align*}
Next, she can use these percentages and draw them into a circle graph. Remember that a circle graph shows data out of 100%, so Kelly’s data is right on target.
Next, Kelly creates a double bar graph to show her data in comparison to Justin’s. Here is the double bar graph.
Vocabulary
Here are the vocabulary words in this Concept.
- Survey
- a method of collecting data where you ask a sample of people the same question. You create options for answers and then gather the data to create a display.
- Statistics
- the method of collecting, analyzing and displaying data.
Guided Practice
Here is one for you to try on your own.
Keith gathered the following data about bus fare.
1997 .35
1998 .35
1999 .40
2000 .40
2001 .45
Based on this data, which display would make the most sense to display the data accurately? Why?
Answer
This data shows how the price of bus fare has changed over time. A line graph is the best visual display for the data.
Video Review
Here are videos for review.
Khan Academy, Reading Pie Graphs
Khan Academy, Reading Bar Graphs
Practice
Directions: Select the best display for each description of data. Choose from circle graph, line graph, double line graph, bar graph or double bar graph.
- The percentages of people who enjoy ice cream
- How stamp prices have changed over time
- How stamp prices changed in 1996 and in 1998.
- The number of students who attended college in 1990, 1991, and 1992
- The percentages of people who prefer chocolate, vanilla or strawberry ice cream.
- The changes in prices at one movie theater over a period of three years.
- The changes in prices at two different movie theaters over a period of three years.
- A graph showing how sales had declined during the past month
- A graph showing the number of students with perfect attendance during the past three months.
- A graph showing the number of students with perfect attendance at two different schools during the past three months.
- The percentages of students who complete homework.
- The percentages of students who enjoy playing particular sports.
- How the percentages of students who attend college has changed over time.
- How the price of a hamburger has changed over time.
- The percentages of people who enjoy watching particular sports events.
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binning
Binning involves separating your data separated into separate classes or categories.continuous variables
A continuous variable is a variable that takes on any value within the limits of the variable.discrete random variables
Discrete random variables represent the number of distinct values that can be counted of an event.relative frequency table
A relative frequency table is specifically designed to display the ratio of each individual frequency to the total frequency of the data.Statistics
Statistics is a branch of mathematics that involves collecting, analyzing and displaying data.Survey
A survey is a method of collecting data where you ask a sample of people the same question.Image Attributions
Here you'll learn to create surveys and data displays.