For Alma's social studies class, she is creating a presentation on the number of homeless people in her city and two other nearby cities. She has collected data on the number of homeless people for the past 50 years in Lancaster, Columbus, and Starkville. Alma doesn't know the best way to display her data. How can she determine the best type of display?

In this concept, you will learn how to determine which kind of data display is best for a given set of data.

### Choosing Data Displays

**Data** is a set of numerical or non-numerical information. Data can be analyzed in many different ways. In this concept you will determine the best type of graphical display for different types of numerical data.

**Graphs** are visual representations of data. Different types of graph represent different types of data. For example, line graphs are best for representing data trends over time. Bar graphs are best for showing relationships between data.

A **stem-and-leaf plot** shows the distribution of the data. Data values in a stem-and-leaf plot are split into a stem and leaf, which require data values to share stems. This display is best used to list data.

A **box-and-whisker plot** illustrates the distribution of a data set in quartiles. Box-and-whisker plots are best used to display data in quartiles to analyze the distribution of data.

A **line graph** shows the relationship between independent and dependent variables over time. In the graph, each data value is represented by a point in the graph, which are connected by a line. Line graphs are best used when showing changes over time.

A **bar graph** shows the relationship between different values of data, with each value represented by a column in the graph. Bar graphs are best used when comparing between groups or changes over time.

A **histogram** is a vertical bar graph that illustrates the frequency of the data. Histograms are best used to show the distribution or frequency of data graphically.

When determining what type of display to use, consider what type of data is being represented.

Let's look at an example.

What kind of data display is best to represent the world population over time, from 1750 to 2000?

First, consider what type of data will be displayed. In this case, the data are numerical values over time.

Next, consider if the data best shown graphically or in another kind of display? In this case, the data are best represented graphically.

Next, since the data does not represent frequencies, either a bar or line graph is best. Since the data are showing a trend over time, the amount of population, a line graph is best.

The answer is the data should be displayed with a line graph.

### Examples

#### Example 1

Earlier, you were given a problem about Alma and her presentation on homelessness.

Alma has data on the number of homeless people in three cities for the past 50 years. She must decide what is the best way to display this data in a presentation.

First, Alma must consider what type of data she will display. In this case, the data are numerical values that compare different cities, or groups, over time.

Next, Alma must consider if the data best shown graphically or in another kind of display? In this case, the data are best represented graphically given the large number of data points.

Next, since Alma's data does not represent frequencies, either a bar or line graph is best. Since the data are comparing three groups over time, a multiple bar graph is best.

The answer is the data should be displayed with a multiple bar graph.

#### Example 2

Which of the following charts should be used to show the number of cholera cases in 2005? Explain your reasoning.

First, consider what type of data is being displayed. In this case, the data are the number of cholera cases by country.

Next, consider whether the data is best represented in columns or in a pie chart. In this case, the data is best represented in columns because it is comparing values.

The answer is the data should be displayed with the bar graph. Since the data compares the number of cholera cases between countries, this type of data is best displayed in a bar graph. In addition, the data does not represent the total number of cholera cases in the world, which would be best shown with a pie chart.

#### Example 3

The Emirate of Abu Dhabi wants to make a chart that compares the number of females to males born over the last 10 years. What is the best way to display this information?

First, consider what type of data will be displayed. In this case, the data are numerical values being compared over time.

Next, consider if the data best shown graphically or in another kind of display? In this case, the data are best represented graphically.

Next, since the data does not represent frequencies, either a bar or line graph is best. Since the data are comparing two groups over time, the number of females and males, a multiple bar graph is best.

The answer is the data should be displayed with a multiple bar graph.

#### Example 4

A hundred people were asked how much time they spend exercising daily. What is the best way to display this data?

First, consider what type of data will be displayed. In this case, the data are numerical values that represent the amount of time people spend exercising each day.

Next, consider if the data best shown graphically or in another kind of display? In this case, since there is a large number of data values, the data are best represented graphically.

Next, since the data can be used to show the frequency that people exercise, a histogram is the best type of graph.

The answer is the data should be displayed with a histogram.

#### Example 5

What is the best type of display to represent the distribution of English exam scores for all 7th graders?

First, consider what type of data will be displayed. In this case, the data are numerical values that represent grades on an exam.

Next, consider if the data is best shown graphically or in another kind of display? In this case, the data is best represented graphically.

Next, since the data should be displayed to shown the distribution of exam scores, a box-and-whisker plot is best.

The answer is the data should be displayed with a box-and-whisker plot.

### Review

The graph below depicts the quarterly sales for two competing computer companies. Use the information on the graph to answer the question below.

- True or false. Each company has increased its computer sales each quarter.
- True or false. One company has had a more significant increase in sales between quarters one and two, than the other.
- If number two is true, which company has had a more significant increase in sales?
- What were the average sales for Computer Company 1 in quarter 3?
- What were the average sales for Computer Company 2 in quarter 4?
- Which company did not show much of a change in profits from quarter 3 to quarter 4?
- What were those average earnings?

**The data table below depicts the final score for ten football games played this past season.**

\begin{align*}48 \quad 56 \quad 42 \quad 59 \quad 62 \quad 45 \quad 36 \quad 58 \quad 49 \quad 50\end{align*}

- What is the most appropriate display for the data?
- Create a display of that data.

**The data below depicts the number of hours students in seventh grade spent working on a science project.**

\begin{align*}& \# 1 \quad \# 2 \quad \# 3 \quad \# 4 \quad \# 5 \quad \# 6 \quad \# 7 \quad \# 8 \quad \# 9 \quad \# 10\\ & 12 \quad \ 14 \quad \ 11 \quad \ 15 \quad \ 16 \quad \ 13 \ \quad 10 \quad \ \ 9 \quad \ \ 16 \quad \ \ 8\end{align*}

- Create a bar graph of the data.
- Create a line graph of the data.

**The data table below depicts the amount of weekly allowance received by fifteen teenagers.**

\begin{align*}25 \quad 15 \quad 20 \quad 30 \quad 10 \quad 5 \quad 8 \quad 12 \quad 18 \quad 23 \quad 27 \quad 15 \quad 18 \quad 25 \quad 10\end{align*}

- Create a frequency table of the data.
- Create a histogram of the data.
- Create a box-and-whisker plot of the data.

**The data table below depicts the magnitude of the last ten earthquakes that occurred in Sacramento, California.**

\begin{align*}3.8 \quad 4.2 \quad 4.3 \quad 5.1 \quad 3.6 \quad 4.6 \quad 3.6 \quad 3.5 \quad 4.1 \quad 4.5\end{align*}

- Create a stem-and-leaf plot of the data.
- Create a histogram of the data.

### Review (Answers)

To see the Review answers, open this PDF file and look for section 11.14.