Graphs are used to give a pictorial representation of numerical data.  Such visuals are often less abstract than a table of raw numbers. Since children develop an understanding of abstractions if they can ground these in concrete physical experiences, it is helpful to begin by using concrete representations of data -- such as arranging the class into a human  histogram based on eye color, or making pie graphs out of paper, clay or wood -- and then moving on to graphing on paper.
 

Types of graphs:

Bins of data:  Histograms

If we were to determine the number of people in a group who had attached earlobes and compare it to the number with unattached earlobes, we would use a histogram.  This looks like a bar graph, but the groups represent classes of data, and the bars represent how many objects (people, trees, companies) are in each class.

Discrete data: Bar graphs

If we were to measure five people and graph their heights, we would use a bar graph.  We can't connect the points on this graph and make a line graph, because the data between the points doesn't make sense.  That is, if Mark and John were two of the people, there is nothing "between" them, no "Jark" or "Mohn."

Continuous data (often change over time):  Line graphs

If we were to measure the temperature of a cup of hot water every minute for ten minutes, we could use a line graph.  In this case, though we only take a reading every 60 seconds, the points in between the readings make sense.  That is, there could be a reading at 2 minutes and 42 seconds, and the line approximates where this reading would be.  Often, rather than simply connecting the points, we use a line or curve of best fit to represent the trend of the data.

Pie graphs

A pie graph is used to show the parts of a whole, such as percentages of one's monthly budget spent on each category of expense.  The sections of a pie graph are usually expressed as a percent, with the total adding up to 100%.

        Imagine you are going to graph the data you got as you measured the temperature of a cup of hot water as it cooled.  You have determined that a line graph would be appropriate here.  What graphing conventions would you use as you constructed your line graph?
 

Data Table:

It is often helpful to begin with a data table:
 

Time (min)	Temperature (degrees C)
0	49
1	44
2	40
3	36
4	33
5	30
6	28
7	26
8	25
9	24
10	23

 

Labeled Axes with units

X axis is independent variable
In this case, the X axis is the "time in minutes".  We chose "independently" when to measure the temperature.

Y axis is dependent variable
In this case, Y is "the temperature of the water in degrees Celsius".  The world controlled this, and we were "dependent" on what happened.

 

Title

Use the convention "dependent variable vs. independent variable." In this case, it would be "Temperature of Water vs. Time."

Line or curve of best fit for line graphs
Rather than simply connecting the dots in a line graph, we can get a sense of the basic pattern (often a straight line or a curve) that the points make.  Some points may be above the line or curve of best fit, some might be below it.  Since data collection is imperfect and data can be  impacted by variables beyond our control, we use the line or curve represents the general trend of the data.

Interpolation is when we use a line or curve of best fit to make a judgment about what a value would be between two known points or measurements.

Extrapolation is when we use a line or curve of best fit to make a judgment about what a value would be beyond the last known point or measurement.

Examples of Graphs from the Media
 

For examples of many different types of graphs and statistics for discussion and analysis (including graphs from the media that are used to misrepresent data), go to Jeff's Graphs in the Media page:

http://faculty.rcoe.appstate.edu/goodmanjm/human_wonder_research/math/graphs/graphs.html