Additional Math Pages & Resources

Thursday, December 16, 2010

Displaying Data Discretely

When I propose to display data discretely, I mean to show it with picture graphs (a discrete unit of measure on the graph) versus line, pie or other kinds of charts. I didn't mean "Leave out the embarrassing facts!"

Picture graphs are the simplest forms of charts, and are closest to representing the reality of what you are displaying. They are easiest for kids to understand. For example, here's a chart showing hot dogs eaten at a picnic:

Notice that the kids who ate the hot dogs are shown. Once we understand the idea of a picture graph, we can add some additional information, so the viewer doesn't have to squint at the tiny picture to identify the kids:

If the names are added we don't really need to have their pictures, so we can simplify a bit. Here is the chart using only the names. Now it's getting more abstract (farther from reality).

I am going to add another level of complexity. I am asking you to imagine that each 1 of the hot dogs shown represents 2 hot dogs in reality. Andrew ate 4, Hannah had 2, etc. The hot dog pictures are not really meaning a single dog in a bun, but two units of hot-dogginess. We have to do math in our heads to calculate Devin's picnic intake of 5 hot dogs.

In order to show this, math gurus invented the legend, or explanatory note. We put a legend at the bottom of the chart indicating that one dog picture = 2 hot dogs. We could have made it 3, 5, 10 or whatever we wanted.

In preparation for another level of abstraction, I have now added grid lines to the chart and value labels at the bottom of each grid line. We still have the hot dogs (we are about to remove them).

Here's the final version of our chart. It's turned from a picture graph to a bar graph. No more drawing little hot dogs, no more pictures of kids, just a boring old chart.

Isn't math fun? I think I will run down to Costco and pick up a hot dog for lunch.

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