 SCIENTIFIC GRAPHS: HOW TO MAKE THEM—AND MAKE SENSE OF THEM Program Objectives 1. Students will understand what a graph is: a device by which numbers are translated into visual units to make their meaning clearer. 2. Students will recognize three kinds of graphs commonly used in science: bar graphs, line graphs, and pie charts. They will understand how each is constructed and what their particular characteristics, advantages and limitations are. 3. Students will understand the five-step process of making and using graphs in connection with scientific experiments: 3. Collect the data produced by the experiment. 4. Lay out the scales for the graph. 5. Transfer the data to the graph. 6. Draw the bars, lines or segments of the graph. 7. Interpret the graph. • Part 1. Summary of Content A graph is a way of making figures visible. The principle is demonstrated first with a simple graph that shows, much more dramatically than figures, how human population has grown since 0 A.D. The program then illustrates the construction of a simple bar graph, comparing stacks of physical objects (coins) to the bars on the graph. A more meaningful bar graph follows, showing the relationship between smoking and deaths from lung cancer. A bar graph is then constructed from the data of a simple experiment in population genetics: Students measure the lengths of their feet, and the range of variations is plotted on a graph, producing a rough bell curve. Finally, the same graph is turned into a line graph to show that either kind of graph would be appropriate in this instance. The concept of the line graph will be analyzed in detail in the following parts. • Part 2. Summary of Content In science, the most commonly used type of graph is the line graph. It shows not only the differences among values, but also the direction and rate of change among them. This part centers around an experiment on the absorption by leaf pigments of light at varying wavelengths over the visible spectrum. The experiment is illustrated, showing the use of a spectrometer to obtain data on the percentages of transmission and absorption at wavelengths from 400 to 700 nanometers. The horizontal and vertical scales for the graph are then laid out, and the data translated to points on the graph. A line is drawn through the dots to create a line graph. The graph is then interpreted: the wavelengths of violet and blue, orange and red are largely absorbed. The wavelengths of green are largely reflected. That’s why leaves look green. The graph is then interpreted further: The wavelengths of yellow are reflected almost as much as the green wavelengths, and the wavelengths of orange and red are absorbed less than those of violet and blue. • Part 3. Summary of Content There is a special kind of line graph that is very useful in science: a graph that reveals a mathematical principle behind a body of data. Part 3 begins with a very simple example to demonstrate the principle—a graph that shows how long it takes to drive various distances at a steady average rate of speed. The graph is a straight line, based on the formula that distance divided by rate equals time. The graph can be extended down to zero, and upward indefinitely. You can even extrapolate values for distance and time from the graph. Such a graph is based upon a mathematical principle, and can be used to predict values beyond those actually measured. The same concept is applied to a graph based on an experiment that verifies Boyle’s law. While the experiment is being conducted data is collected on the volume of a contained gas (air) at increasing pressures. The data is then transferred to points on the graph, which are connected to form a distinctive curve. The curve suggests that the graph is that of a mathematical equation; specifically, an equation for inverse variation. Rechecking the data with this insight indeed reveals that each pair of values for pressure and volume, multiplied together, produces approximately the same constant number. If the equation is graphed, its curve is almost identical to the one based on our experiment. Furthermore, new values for pressure and volume, beyond those measured, can be predicted from the graph. Also, Boyle’s Law has been verified: the pressure and volume of a gas vary inversely, and their product is a constant. Without the graph, you might be able to figure out the mathematical relationship. But with the graph, and some knowledge of mathematics, the relationship becomes evident. That’s the usefulness of graphs of this kind. • Part 4. Summary of Content In addition to bar graphs and line graphs, there is another form of graph that is very useful in science. It shows values that add up to form a whole, as proportional slices of a round pie. It’s called a pie graph or pie chart. A simple example is used to introduce the concept: a pie graph that illustrates the hours spent on different activities in a 24-hour day. First the 360-degree scale used for pie charts is explained and illustrated. Next the process by which values are translated to degrees is explored: each value is divided by the total of all values, and the resulting fraction is multiplied by 360. The use of a protractor to plot the degrees on the graph is then graphically illustrated. The program also analyzes a more complex example: a pie graph that shows how the animal kingdom breaks down among its major phyla, and how the phyla compare in the number of species they contain. The graph is built up, slice by slice, by translating the figures into degrees and then plotting them on the circle. The resulting graph shows dramatically that arthropods is the largest phylum, made up primarily of insects. The program concludes with a summary comparison of the three kinds of graphs discussed: the bar graph, which simply compares values, side by side; the line graph, which slows the rate and direction of change; and the pie chart, which shows fractions of a whole. All these graphs have the same basic function: they allow you to make numbers visible, which help to make better sense out of those numbers. • Questions For Discussion And Review Part 1. Introduction 1. What are the advantages of displaying collected data in a graph? 2. List and describe three kinds of graphs. 3. Each of the three kinds of graphs performs a particular function well. Explain. • Part II. Simple Line Graphs 1. What two purposes do line graphs best display? 2. List the steps of graph construction staring with the collection of data. 3. In plotting wavelengths of visible light, what would be chosen as the baseline limits? 4. Line graphs involve comparisons of an independent variable with a dependent variable. In the graph involving the absorption of light by plant pigments, which variable is independent? 5. On which axis is the independent variable plotted? 6. Explain the meaning of percent absorption and nanometers, which are the units used to measure the variables. 7. Would this data be well displayed as a pie graph? Explain. 8. What was the DDT concentration in 1971? 9. What was the change in concentration tendency during the collection period? 10. What was the probable concentration of DDT in 1975? 11. What was the probable concentration of DDT in 1978? 12.Assuming that the collection period each year was during the month of June, what was the probable DDT concentration in January of 1972? • Part IV. Pie Graphs 1. What is the outstanding feature of pie graphs? 2. Pie graphs are based on a circle. On what basis is the circle divided into parts? |
|
|