A graph is a visual representation of a relationship between, but not restricted to, two variables. A graph generally takes the form of a one- or two-dimensional figure such as a scatterplot. Although, there are three-dimensional graphs available, they are usually considered too complex to understand easily.
A graph commonly consists of two axes called the x-axis (horizontal) and y-axis (vertical). Each axis corresponds to one variable. The axes are labelled with different names, such as Price and Quantity.
The place where the two axes intersect is called the origin. The origin is also identified as the point (0,0).
A point on a graph represents a relationship. Each point is defined by a pair of numbers containing two co-ordinates (x and y). A co-ordinate is one of a set of numbers used to identify the location of a point on a graph.
In the following section, you will learn how to determine both co-ordinates for any given point, and to correctly label the co-ordinates of a point.
The x-co-ordinate of a point is the value that tells you how far the point is from the origin on the (horizontal) x-axis. In order to find the x-co-ordinate of a point on any graph, draw a straight line from the point to intersect at a right angle with the x-axis. The number where the line intersects with the x-axis is the value of the x-co-ordinate.
Figure 2 is a graph with two points, A and B. Identify the x-co-ordinate of points A and B.
Answer: The x-co-ordinate of point A is 50, and the x-co-ordinate of point B is 200.
The y-co-ordinate of a point is the value that tells you how far away the point is from the origin on the vertical or y-axis. To find the y-co-ordinate of a point on a graph, draw a straight line from the point to intersect at a right angle with the y-axis. The number where the line intersects the y-axis is the value of the y-co-ordinate.
Identify the y-co-ordinate for point A and point B on Figure 3.
Answer: The y-co-ordinate of point A is 200, and the y-co-ordinate of point B is 50.
Once you have determined the co-ordinates of a point, you can label the points using ordered pair notation. This notation is simple—points are identified by stating their co-ordinates in the form of (x, y). Note that you must plot the x-co-ordinate first as in Figure 2. The x- and y-co-ordinates for each of points A and B are identified in Figure 4 below.
If a point falls on an axis, you do not need to draw lines to determine the co-ordinates of the point. In Figure 5 below, point C lies on the y-axis and point D lies on the x-axis. When a point lies on an axis, one of its co-ordinates must be 0.
Answer the following questions using Figure 6 below.
Answers; 1. Point A 2. Point B 3. Point C
There are times when you will be given the coordinates of a point and will need to find its location on a graph. This process is often referred to as plotting a point. The process for plotting a point is shown below.
Plot the point (200, 150) using the following step-by-step approach.
First, draw a perpendicular line extending out from the x-axis at the x-co-ordinate of the point. In the example, the x-co-ordinate is at 200.
Then, draw a perpendicular line extending out from the y-axis at the y-co-ordinate of the point, the y-co-ordinate is at 150.
Finally, draw a dot where the two lines intersect. This is the point we are plotting (200, 150).
The scale of a graph is very important. It is determined by the data for each axis, and should be measured accordingly.
A survey was conducted of the Grade 9 students at Elm High. The students were asked which of the following four team sports they preferred.
The results were:
In Figure 10, these four preference categories have been placed on the x-axis, each representing the grouped data collected. Because the categories are nominal (names, not numbers) and describe qualitative (not quantitative) distinctions, the groups can be placed in any order on the axis.
On the y-axis, the data values range from 0 to 80 students. As mentioned earlier, your origin should be located at 0 where the x-axis and y-axis meet. Since the largest group of students by sport preference is 75, then it would be appropriate to end the scale at 80, resulting in a scale that ranges from 0 to 80. Depending on how the scale is arranged, the graph will not change, but its visual appearance might be altered.
The interval of the scale is the amount of space along the axis from one mark to the next. If the range of the scale is small, the general rule is to take the range of the scale and divide it by 10. Make this your interval. For ranges that are larger, the interval is typically 5, 10, 100, 500, 1,000, etc. Use numbers that divide evenly into 100, 1,000 or their multiples in order to provide a graph that is easy to understand.
In this case, if you take 80 and divide it by 5, you will get 16. However, it might be better to use 10 because it is easier to analyse. This provides a scale that is smaller, but still easy to use.
Knowing how to convey information graphically is important in presenting statistics. The following is a list of general rules to keep in mind when preparing graphs.
There are many different types of graphs that can be used to convey information, including:
Knowing what type of graph to use with what type of information is crucial. Depending on the nature of the data some graphs are more appropriate than others. For example, categorical data like favorite school subjects are best displayed in a bar graph or circle graph while continuous numeric data such as height are illustrated by a line graph or histogram. For more information on appropriate graph types, see "Types of data" in Teacher’s Guide to Data Discovery.
A graph is not always the most appropriate tool to present information. Sometimes text or a data table can provide a better explanation to the readers—and save you considerable time and effort.
You might want to reconsider the use of a graph when
If you have decided that using a graph is the best method to relay your message, then there are four guidelines to remember:
|If your graph...||Use the following terms...|
|describes components||share of, percent of the, smallest, the majority of|
|compares items||ranking, larger than, smaller than, equal to|
|establishes a time series||change, rise, growth, increase, decrease, decline, fluctuation|
|determines a frequency||range, concentration, most of, distribution of x and y by age|
|analyses relationships in data||increase with, decrease with, vary with, despite, correspond to, relate to|