# Graph

In mathmatics, a graph is a type of chart that shows information, ideas, and relationships. There are numerous types of graphs used in many different contexts, and there are advantages and disadvantages to using any type of graph. A graph is most effective when it is used in the correct context, so it important to consider what type of graph best suits your purposes.

In statistics, examples of graphs used to represent data are bar graphs, histograms, picture graphs, pie charts, line graphs, line plots, and stem-and-leaf plots.

In algebra and geometry, number lines are used to graph ordered pairs, equations, and other mathematical relationships.

## Advantages and disadvantages of common graphs

These are just a few of the more commonly known and simpler graphs used. There are many more graphs that can be significantly more complex. Even with these relatively simple graphs, we can see that there are various advantages and disadvantages to using each. Learning more about each, as well as about the many other types of graphs we can use, can aid us in using the most effective graph for the data being studied.

### Bar graph

Advantages:

- Can be used to summarize large amounts of data in a relatively easy to interpret format
- Allows quick visualization of relative size/impact of each category being compared
- Can be helpful for highlighting trends
- Can be used as a quick visual check to see if the data seems reasonable or accurate

Disadvantages:

- Often requires more explanation of the categories chosen, measurements taken, etc.
- Because of the many ways you can choose to present a bar graph, it is possible to manipulate a bar graph to convey misleading information

### Line graph

Advantages:

- Useful for representing continuous data, such as change over time
- Allows possible extrapolation of data
- Having a line constructed from multiple data points can allow you to make estimates of missing data
- Allows comparison of two or more items to see if there is any kind of connection or relationship

Disadvantages:

- Can be difficult to determine exact values at a given point of the graph
- Too many lines, or even two lines that have values that are too similar, can make comparing data difficult

### Pie chart

Advantages:

- Data that can be presented on a pie chart can be interpreted simply and quickly
- Removes the necessity for an audience to process data that may otherwise be in the form of a table; even though the data is the same, a pie chart makes it much simpler
- Parts of the chart can be moved/removed, like pieces of a pie, to emphasize certain aspects of the data

Disadvantages:

- Doesn't show exact values, only values as they relate in proportion to other pieces of the pie
- Too many pieces of the pie makes the data difficult to interpret or compare
- Only represents one data set and multiple pie charts are necessary to compare other data sets

### Histogram

Advantages:

- Can be used to display large ranges of data and information
- Useful for highlighting trends within and across ranges of data
- Helps with visualization of the distribution of the data

Disadvantages:

- Histograms are subject to the choice of varying bin sizes; bin sizes that are too large or small can cause you to miss out on important information. If they are too small, it can also make it difficult to read the histogram
- Histograms can't compare multiple sets of data in one chart