A pie graph is a good way to show the relative proportions of individual categories in relation to a whole. The size of each slice of the "pie" is proportional to its associated quantity divided by the whole. In the example below the "whole" is the production of electricity in the US. The pie graph makes it easy to see that chemical energy in the form of coal and gas are the source of almost two-thirds (64%) of the electric power generated in the US, with nuclear being the third largest contributor at 20%.
A bar graph represents each data point by the height of the bar. Bar graphs are effective at showing a pattern in relatively small sets of data, such as the seasonal variation with temperature. Bar graphs lose their visual effectiveness when they have more than a dozen or so bars. Notice the example has two bars for each month showing the high and low temperatures. It is common to use bar graphs to compare the patterns in two or more related data sets, such as the average high and low temperatures.
Many areas of research generate a lot of data that may be highly variable from point-to-point but has an overall pattern that is important to show. A good example is the number of days it rains or snows over a year. Plotting all 365 days separately does not describe the overall pattern that the average precipitation is approximately constant in the region described by the graph. A frequency table is a way to group data into bins than can be easier to represent on a graph. Combining many points into a bin helps smooth out fluctuations in the data to show the overall pattern.
Showing uncertainty on a graph
To correctly interpret the results of data it is necessary to know the size of the uncertainties (error) in measurement. Error bars on each data point are one method used to indicate the error on a graph. The size of the error bars are proportional to the error in each data point and may vary from one point to the next. A box and whiskers plot is another way to represent uncertainty when the data sets are too large to plot every point. The box represents the media (middle) fifty percent of the data in each group and the whiskers represent the upper and lower twenty five percent.