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Visually Representing Numerical Data | Splitting up the Whole with Pie Graphs | Showing the overlap with Venn Diagrams | Comparing Categories with Bar Graphs | Seeking Trends with Line Graphs | Showing Orderly Data with Histograms | Functions as Graphs in the Coordinate System | Summary Seeking Trends with Line Graphs The advantage of a bar graph is that the categories aren’t organized in any special way you can write them alphabetically or in any order you want, resulting in different patterns of high and low bars in the bar graph. However, if the categories are related to each other by time, then they should appear in specific chronological order, and the bars in the bar graph can appear in only that specific way. The idea is to be able to predict the future by looking at the trend in the heights of the bars. To make it easier to visualize these trends, a Line Graph is used; instead of bars, points of data are constructed at the top center of the bars and those points are connected. The bars themselves are erased so as not to block the view of the time-related trend. An example of a time-related Line Graph could be quarterly financial reports of a company’s profits over two years:
What kind of future-related predictions come to mind when you look at the line graph? One predication is that there will be another bump in profits during the next 4th quarter. Perhaps it is a company that depends on the season of the year. Another prediction, which is a little less certain, is that profits in the other quarters will be somewhere in the 40 to 60 thousand range. There was an increase in profits in all quarters of the first year, but in the second year, the other three quarters were fairly level, so a conservative prediction is that they’ll stay the same, with perhaps a little bump up because the seasonally related sales this year were better than last. Trying to predict the future is very important to people who try to make a profit from it, so Line Graphs like this are very common in the business world. For example, many online sources of information on stocks give line graph representations of each stocks prices over the past hours, days and weeks so that people can try to make well-informed decisions. For example, BigCharts.com provided this Line Graph of the price of a particular stock named VCNT as it was tracked each month:
There are many other online sources of similar through free and pay services, if you are interested. There are also sources of data for weather. Can you name a few predictable cyclical fluctuations that would probably show up on a Line Graph of the temperature where you live? [Hyperlink to the following Hints: hourly temperature has cycles because of night cooling, seasonal average weekly temperature also cycles, possibly with illustrations or live links to graphs] Now let's do Practice Exercise 17-2
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