6. How to Read Charts, Tables, and Graphs

The American humourist Mark Twain once said, "There are three kinds of lies: lies, damned lies, and statistics."

If you are not a numbers person, you might be tempted to ignore statistics because they can be used to mislead people. However, statistics are also crucial facts that help us understand our world. Statistics in graph or table form can also provide very convincing evidence for a point.

You should learn how to read graphs, tables, and charts, and also how to construct and use them to present numerical evidence.

"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 the quotation above apply to you? Most of us can make better sense of numbers when they appear in graph form. Graphs can make trends apparent and illustrate clearly changes, differences, and inequalities.

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

  • Graphs are visual displays of the relationships between variables. The values of one set of variables are plotted along the horizontal axis with a second variable along the vertical axis.

  • Bar graph is a graphic representation of the frequency distribution of a variable. Bars are drawn in such a way that their bases lie on a linear scale representing various intervals, and their heights are proportional to the frequencies of the values within each of the intervals.

  • Line graph is a graphic representation of changes over time. If the mid-points of the top of the bars of a histogram are connected by a line and if the bars were omitted from the display, the resulting graph is a line graph. Line graphs show trends over periods of time. Trends of rates (death rate. infant mortality rates, etc.) are displayed better with line graphs than with histograms.

  • Bar chart is a method of presenting data in such a way that each observation is one of several mutually exclusive categories. 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 of equal width, and they should not be touching each other.

  • 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%, which represents the total population 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 is to mislead people by exaggerating or compressing the scale of the graph. The figures can 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 suggest an alarming increase in the trend by not beginning at zero and showing the intervals as large as possible. If the second graph has a true zero on the y axis and the intervals are small, the results can look much less impressive. Researchers should use true zero if possible.

  • No scale provided: This is used very commonly 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, be wary when a scale is given but no units are mentioned!

  • The graph based on insufficient 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 be made on only a handful of patients, and this fact is neatly concealed.

  • Too much data: When graphs and charts have too much information, they confuse the reader. If an overwhelming amount of information is provided, nothing is learned.

Guidelines for making good graphs

  1. Before making a graph or chart, decide on the point that you wish to present, and then chose an appropriate method.

  2. Emphasize one idea at a time in a figure.

  3. Use conventional graphing methods.

  4. Pay careful attention to the scale.

  5. Construct graphs and tables that have meaningful information without reference to the text. Clear labels are essential.

  6. Specify the units used.

  7. Use few colours. Too many may look pretty, but they can confuse!

  8. Be consistent in the use of colours and fonts 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, subtract the smallest number from the largest number in the set.

  • The mean of the data set is its average. To find the mean, 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.