How to use Charts, Tables, and Graphs

Statistics are facts that help us understand our world. Statistics in graph or table form can also provide very convincing evidence to support a point.

"Give me an undigested heap of figures and I cannot see the wood for the trees. Give me a diagram and I am positively encouraged to forget detail until I have a real grasp of the overall picture."

M J Moroney

Does this quotation apply to you? Most of us can make better sense of numbers when they appear in graphs. Graphs can make trends apparent and illustrate clearly some changes, differences, and inequalities.

Consider some information presented in three ways: paragraph form, chart form, and graph form.

A graph is a visual display of the relationship between variables: the values of one set of variables are plotted along the horizontal axis and a second variable is plotted along the vertical axis.
A bar graph is a graphic representation of the frequency distribution of a variable. Bars are drawn so their bases are on a linear scale representing different intervals and their heights show the frequencies of the values within each of the intervals.
Line graphs show effectively trends over periods of time. If you take a bar graph and connect by a line the mid-points at the top of the bars, then remove the bars from the display, the result is a line graph. Line graphs display trends of rates (such as death rate, infant mortality rate, growth rate) musch better than bar graphs.
A bar chart is a method of presenting data so that each item is in its own category. The frequencies (or percentages) are listed along the Y axis and the categories of the variable along the X axis. The heights of the bars correspond to the frequencies. The bars should be equal in width, and they should not be touching each other.
A pie chart is a circular diagram divided into segments, each representing a category or part of a category. The total area of the circle is 100%, and it represents the total population that is being shown.

Misuse of graphics

"It pays to be wide awake in studying any graph. The thing looks so simple, so frank, and so appealing that the careless are easily fooled. "

M J Moroney

You should understand how charts and graphs can be used to mislead people.

Exaggerating or compressing the scale: The oldest trick in the book is to mislead people by exaggerating or compressing the scale of the graph. The figures may show the same data, such as the death rate in women with breast cancer in England and Wales between 1951 and 1981. The first graph can show an alarming increase in the trend while another may look much less impressive. The difference may be as simple as the second having a true zero on the Y axis. Researchers must be cautious of drawing graphs with the base cut on the vertical axis; a true zero should be included.
No scale provided: This is very commonly used by drug companies to push their drugs in the market. Neat trends are shown to demonstrate the beneficial effects of a drug-without any scale! One must always be careful while interpreting graphs and charts that do not have scales. Also, watch when a scale is given but no units are mentioned!
Based on insufficent data: Graphs with great looking trends and comparisons are drawn without any mention about the sample size. What if only ten people were tested? The trial of the drug could have been made on only a few patients. This fact can be neatly concealed-60% that is claimed may represent only 6 people!
Too much data: When graphs and charts have too much information, they succeed confuse the reader. When an overwhelming amount of information is provided, very little is learned.

Guidelines for making good graphs

Before making a graph or chart, decide on the point that you wish to present, and then chose the appropriate method.
Emphasize one idea at a time in a graph or table.
Use conventional graphing methods.
Give careful attention to scale.
Graphs and tables must be self-contained-without reference to the text. Clear labels are essential.
Units used must be specified.
Few colours are better than many!
Use colours and fonts consistently in a series of graphs and tables.

Some terms to know

The range of the data set is the difference between the largest and smallest number in the set. To find the range, you simply subtract the smallest number from the largest number in the set.
The mean of the data set is its average. To find the mean, you add all the numbers and divide the answer by how many numbers you have.
The median is the number that is in the exact middle of the data set.
The mode is the number that appears the most often if you are working with only one variable.