9.2 Encoding Data That Change Over Time

Line Charts and Trend Curves

A time series graph is used in many fields such as finance, health care, economics, etc. to visualize data measurements over time. To construct a time series graph, the horizontal axis is used to plot the time increments, and the vertical axis is used to plot the values of the variable that we are measuring, such as revenue, enrollment, inventory level, etc. By doing this, we make each point on the graph correspond to a point in time and a measured quantity. The points on the graph are typically connected by straight lines in the order in which they occur. Once the chart is created, a researcher can identify trends or patterns in the data to help guide decision-making.

Using Python for Times Series Data Visualization

Data visualization is a very important part of data science, and Python has many built-in graphing capabilities through a package called matplotlib. To import this package into a Python program, use the command:

import matplotlib.pyplot as plt

Matplotlib contains functions such as plot that can be used to generate time series graphs.

After defining the $(x,y)$ data to be graphed, the Python function plt.plot(x, y) can be used to generate the time series chart.

Example 9.6

Problem

Use the plot function in Python to create a time series graph for the dataset shown in Example 9.5.

Solution

In the following Python code, note that the plt.plot with marker specifies that points should be plotted at the various $(x,y)$ points. In addition, plt.ylim specifies the range for the y-axis.

Python Code

    # import the matplotlib library
    import matplotlib.pyplot as plt
    import matplotlib.ticker as ticker
    
    # Define the x-data
    x = [1, 2, 3, 4, 5, 6, 7, 8]
    
    # Define the y-data
    y = [8641, 9105, 9361, 9895, 9230, 8734, 8104, 7743]
    
    # Use the plot function to generate a time series graph
    plt.plot(x, y, marker='o', linestyle='-')
    
    # Set the scale for the y-axis
    plt.ylim(6000, 11000)  # This sets the y-axis range from 6000 to 11000
    
    # Define a function to format the ticks with commas as thousands separators
    def format_ticks(value, tick_number):
        return f'{value:,.0f}'
    
    # Apply the custom formatter to the y-axis
    plt.gca().yaxis.set_major_formatter(ticker.FuncFormatter(format_ticks))
    
    # Add labels to the x and y axes by using xlabel and ylabel functions
    plt.xlabel("Year")
    plt.ylabel("Enrollment")
    
    # Add a title using the title function
    plt.title("Enrollment at a Community College")
    
    # Show the plot
    plt.show()
    

The resulting output will look like this:

The graph indicates that the enrollment gradually increased over years 1 to 4 but then began to decrease from years 4 to 8.

Guidelines for Creating Effective Visualizations

You have likely come across poorly constructed graphs that are difficult to interpret or possibly misleading in some way. However, if you follow certain guidelines when creating your visualizations, you will be sure your visualizations are effective and represent the data fairly.

The first rule is to ensure your graph or chart is clear and easy to understand. You may be familiar with the type of data collected, but your audience may not be. Provide a title and label each axis, including units where appropriate. Provide a data source where appropriate. Use scales for the axes and avoid distortion (i.e., don’t intentionally adjust the scale to produce a desired effect in the graph).

The use of colors to differentiate data can be an important part of graphs and displays. Overall, the use of color can make the visualization more appealing and engaging for the viewer. However, there are some important things to keep in mind when using color. Be sure to apply color consistently to represent the same categories. Ensure that there is contrast between different colors to make them easily distinguishable. For example, if you used various shades of blue for the sectors in a pie chart, it might be difficult for the reader to distinguish among them.

Keep in mind that some viewers may be color-blind, so it’s a good rule of thumb to use color palettes that are accessible to color-blind individuals. The most basic rule for a color-blind palette is to avoid combining green and red.

You should also be aware that colors can have different meanings in different cultures. Keep the number of colors used in your visual to a minimum. One rule of thumb is to limit the number of colors to three to five to avoid a color palette that is too confusing.

Create the graph with your audience in mind. If the graph is intended for a general audience, then the graph should be as simple as possible and easy to interpret, perhaps with pie charts or bar charts. Don’t include too many categories in your pie chart; if you have more than about five or six categories, you may want to consider a different type of chart. Consider combining categories where appropriate for simplicity. (Sometimes an “other” category can be used to combine categories with very few counts.) If the graph is intended for a more technical audience or for more complicated types of analyses, then a more detailed display such as a scatterplot with regression line and confidence bounds may be appropriate. (Visualizing data with scatterplots is covered in Multivariate and Network Data Visualization Using Python.)

Selecting the Best Type of Visualization

When creating graphs and displays to visualize data, the data scientist must consider what type of graph will work best with the collected data and will best convey the message that the data reveals. This section provides some guidance on the optimal type of graph for different scenarios.

Before we discuss how to choose the best visualization, it is important to consider the type of data being presented. Recall that data can be divided into the broad categories of qualitative data (describes categories or groups) and quantitative data (numeric data) and that quantitative data is further classified as discrete (usually counts) and continuous (usually measurements that can take on any value within a range). You first need to be clear about the type of data being illustrated.

Then, carefully consider the goal of the visualization—that is, what are you trying to accomplish with the graph or display? What is your data telling you? How is it distributed, and what patterns or relationships do you want to highlight? You might be interested in comparing different groups of categories, or you may be interested in showing how data is distributed over some interval. Recall from the previous discussion of correlation and regression that we are often interested in showing correlations or relationships between quantitative variables. Table 9.4 offers some suggestions for picking the most appropriate graphing method based on your goals and type of data.