Tutorials


Graphing


Graphs, Charts, and Tables

Graphs are an important means of displaying data.

Most science and math courses will require you to correctly construct a graph given a data set. Reading and interpreting graphs will be imperative in all areas of your life! Your banker might show you a graph of your loan versus the actual value of your new car. It is important that you understand what relationship the graph is demonstrating in order to make decisions about your loan. 

Different types of graphs are used to demonstrate different types of data or different relationships. Be sure to choose the best type of graph for your data.


Scatterplot of average income(in dollars) and average education (in years) from a 1971 study with 102 Canadian occupations.

Scatter plot 

A scatter plot is used to demonstrate that there is a correlation between two sets of data. For example, you may have sampled a population of people to show that there is a correlation between years of education and annual income. Though we would expect there to be a correlation between the two, we cannot draw a line of best fit as some individuals with high levels of education will still have relatively low income and visa versa. 
 Line graph  A line graph shows a direct relationship between two sets of data. One would use a line graph to show the change of a variable over time. For example, the population of a given area over a specified period of time.



 

 

Pie graph

A pie graph show the parts of a whole. For example, all of the electricity generated in a country in a given year was generated from a specific source. 
 

Histogram

Histograms are used to show the distribution of data. For example, every passenger on the Titanic fits into one age category. Everyone has a category but no one fits in more than one category. A histogram is an excellent way to display the age distribution of all passengers and also the distribution of survivors to non-survivors in each category. In a histogram, the order of the bars is significant and cannot be rearranged. So we would not move the age category 0-5 years to be situated beside the 70-75 years. Additionally, all of the categories together should equal 100% of the data. 

Shure, L. (2015). The Titanic Passenger Age Distribution. Used under the Fair Dealing Guidelines of the Canadian Copyright Law.


Parker, F. (2015). Bar Graphs and Double Bar Graphs. Used under the Fair Dealings Guidelines of the Canadian Copyright Law.

Bar graph


A bar graph is used to compare groups, rather than distributions. They differ from histograms in that the total of all bars may represent more or less than 100%. For example, the bar graph to the left may not represent all pet owners. Some people might own a snake and are not represented here. Likewise, some people may have been counted twice, for example, if they own a dog and a cat. The bars of a bar graph should not touch whereas the bars of a histogram do touch.



Identify your manipulated and responding variables


Your graph should not include controlled variables because controlled variables do not affect your results. You want your graph to show the effect of the manipulated variable on the responding variable. Your manipulated variable should always be on the x-axis and your responding variable on the y-axis.

In the graph to the left, distance is the manipulated variable and electrical current is the responding variable.

  1. Label your axes with appropriate titles and units of measurement. For example, the graph above states the title (distance) and the unit of measurement (km).
  2. Choose an appropriate scale for each axes. The scale is the space in between labels. Notice that the graph above used 0.5 km and 0.1 A to make the best use of space. Your scale must increase in equal intervals.
  3. Give your graph a title. Boring descriptive titles are best! The title should tell the reader exactly what the graph is representing.

Provided that you have correctly followed the instructions above, plotting your points should be easy. If your graph is looking crowded or you are having trouble being accurate, you may want to review your scale in step 2.

What relationship does your graph illustrate?


Graphs are used to visually portray a relationship between two variables. The NASA graph shows that the average current of the Spirit right front wheel remained consistent until about 2.0 km or 126 days at which time the current steadily increased. The graph does not provide information on why this relationship occurs.