Arithmetic Line Graph

A graph representing the arithmetic values of variables (or events) is an Arithmetic Line Graph.

A line graph illustrates data points at successive intervals to present time-series data (such graphs are also referred to as Time-series graphs). The data points on the graph are connected by a simple arithmetic line to complete the picture. Each plotted point in the diagram simultaneously indicates the variable’s value against time or a specified independent variable.

Arithmetic or time-series graphs are of two types: a) with one variable b) with two or more variables.

Arithmetic Line Graph:

Uses

• Line graphs are primarily used to track changes in events over time.
• It would help if you remembered that line graphs are meaningful only when there is a correlation between the successive points in the graph.
• Typically, the Y-axis is used for plotting the value of whatever variable we are measuring.
• The X-axis is either time represented chronologically or based on some independent variable.
• The graphs usually have continuous data along both axes.
• It is not advisable to use line graphs to compare multiple categories for a single variable at a single point.

Characteristics

Now, a recap of some of the essential terms connected with line graphs:

Arithmetic Line Graph Notes: Parts of a Graph

• Coordinate axes: The horizontal line and vertical lines that intersect each other and are mutually perpendicular are the X-axis and the Y-axis.

• Origin: The origin is the point of intersection of the two coordinate axes (the X and the Y-axis). At this point, the value of both variables is zero.

• Scale: A scale is a set of numbers that help to measure the objects. The distance between two numbers indicates a uniform unit throughout a scale. Without a relevant scale, without a suitable scale, a graph will not project relevant information.  In arithmetic line graphs, only a linear scale is used, indicating that equal distances (in the diagram) represent similar values.

• Title: The title gives a brief description of the quantities or variables represented in the graph.

Arithmetic Line Graph: Remembering Variables

There are two types of variables:

• Dependent: Those variables in an experiment that are observed or studied under the supposition that they depend (or are regulated by some mathematical function) on the values of other variables are the Dependent variables. Dependent variables are described as the variable that depends on the value of some other number. For example, in the equation X = Y+4, X is a dependent variable as its value is linked to the value of Y.

• Independent: Independent variables do not depend on any other variable in the scope of the experiment in question.  Some common independent variables are time, space, density, mass, etc. In other words, the variable that the experimenter manipulates or modifies (like time) is an Independent variable. The dependent variable is the result that is expected to change when the independent variable is modified.

 Arithmetic Line Graph: Concept of False Baseline

• False  baseline is a technique relating to a graphical presentation: A false baseline is used when the data starts with high values. For example, a false baseline is used in an arithmetic line graph to break the continuity of the Y-axis with the origin and use another value as the starting point of the graph.

•  If we maintain the continuity of the value, plotting the values from the origin will mean a considerable blank space, giving a poor visual representation. When the difference between the smallest value of the Y-series and the zero is vast, a false line helps break that distance gap.

• The primary purpose of using a false baseline is to magnify particular sections of the graph to make it more visible to highlight trends like significant fluctuations in value. Like the Y-axis, false baselines are also used to economise space on the X-axis by drawing a kinked line. The purpose here is to improve the visual presentation.

Arithmetic Line Graph: Illustration of False Baseline

The following arithmetic line graph examples will illustrate the concept better.

Let us assume that a city car dealer wants to present the sales data of a car model to the company to gain some additional incentives. The dealer’s objective is to impress the company with the excellent work done to improve sales of the particular model.

There are two sets of values, a) the number of cars sold in a year and b) the period, in terms of years, say, over the last 10 Years.

One set of data is the period from 2011 to 2020.

The second set (of data) will indicate the yearly sales of the particular car model.

A quick look at the data indicates that the sales value starts from 900 and goes up to 1200.

 So, for the Y-axis, the minimum value is 900, and the maximum is 1200.

If you plot the sales data from the origin (0), a significant portion of the graph will be blank, giving a poor visual impression. Therefore, a false base is created with 800 for plotting the sales data. The dealer can now put up an impressive presentation with the help of an arithmetic line graph.

Arithmetic Line Graph: Summary of Points to Remember

1. Know your variables- look at both the paired data sets
2. Establish the variable range first –the difference between the highest and the lowest data value indicate the range
3. Use horizontal axis to plot data or time increments and vertical axis for plotting the values of variable you are measuring
4. Each point (on the graph) refers to a specific date and a measured quantity
5. Straight lines typically connect the points on the graph in order of occurrence
6. Once the data points are displayed graphically, interesting features appear and make trends easy to spot. In most scientific studies, trends are essential for future projections.