Bar chart

A bar chart or bar graph is a chart with rectangular bars with lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. A vertical bar chart is sometimes called a column bar chart.

A bar graph is a chart that uses either horizontal or vertical bars to show comparisons among categories. One axis of the chart shows the specific categories being compared, and the other axis represents a discrete value. Some bar graphs present bars clustered in groups of more than one (grouped bar graphs), and others show the bars divided into subparts to show cumulate effect (stacked bar graphs).

HistoryThe first bar graph appeared in the 1786 book The Commercial and Political Atlas, by William Playfair (1759-1823). Playfair was a pioneer in the use of graphical displays and wrote extensively about them.[citation needed]

This bar chart by William Playfair from 1786 showed the "Exports and Imports of Scotland to and from different parts for one Year from Christmas 1780 to Christmas 1781."

UsageBar charts have a discrete range. Bar charts are usually scaled so that all the data can fit on the chart. Bars on the chart may be arranged in any order. Bar charts arranged from highest to lowest incidence are called Pareto charts. Normally, bars showing frequency will be arranged in chronological (time) sequence. Grouped bar graph usually present the information in the same order in each grouping. Stacked bar graphspresent the information in the same sequence on each bar.

Bar graphs charts provide a visual presentation of categorical data.[1] Categorical data is a grouping of data into discrete groups, such as months of the year, age group, shoe sizes, and animals. These categories are usually qualitative. In a column bar chart, the categories appear along the horizontal axis; the height of the bar corresponds to the value of each category.

Bar graphs can also be used for more complex comparisons of data with grouped bar charts and stacked bar charts.[1] In a grouped bar chart, for each categorical group there are two or more bars. These bars are color-coded to represent a particular grouping. For example, a business owner with two stores might make a grouped bar chart with different colored bars to represent each store: the horizontal axis would show the months of the year and the vertical axis would show the revenue. Alternatively, a stacked bar chart could be used. The stacked bar chart stacks bars that represent different groups on top of each other.The height of the resulting bar shows the combined result of the groups. However, stacked bar charts are not suited to datasets where some groups have negative values. In such cases, grouped bar charts are preferable.

A bar graph is very useful for recording discrete data. Bar graphs also look a lot like a histogram, which record continuous data. The difference is not that bar graphs (can) have spaces between columns and histograms don't (have to) have spaces, the difference is the type of data that each represent. For more onthe difference, please see this description from shodor.org

Line graphIn the mathematical discipline of graph theory, the line graph of an undirected graph G is another graph L(G) that represents the adjacencies between edges of G. The name line graph comes from a paper by Harary & Norman (1960) although both Whitney (1932) and Krausz (1943) used the construction before this.[1] Other terms used for the line graph include the covering graph, the derivative, the edge-to-vertex dual, the conjugate, the representative graph, and the ϑ-obrazom,[1] as well as the edge graph, the interchange graph, the adjoint graph, and the derived graph.[2]

Hassler Whitney (1932) proved that with one exceptional case the structure of a connected graph G can berecovered completely from its line graph.[3] Many other properties of line graphs follow by translating the properties of the underlying graph from vertices into edges, and by Whitney's theorem the same translation can also be done in the other direction. Line graphs are claw-free, and the line graphs of bipartite graphs are perfect. Line graphs can be characterized by nine forbidden subgraphs, and can be recognized in linear time.

Various generalizations of line graphs have also been studied, including the line graphs of line graphs, line graphs of multigraphs, line graphs of hypergraphs, and line graphs of weighted graphs.