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Home | Contents | 1-3 Science | 4.1 Experiments | 4.2 Units | 4.3 Measurement | 4.4 Safety | 5 Data | 6-7 Reports | 8 Appendix

VCS Science Handbook Sections 5.0-5.4

5.0.0 Data: Gathering, Displaying, and Analyzing

  • Collecting data (facts about an experiment or observations) is at the heart of what most scientists do. It is what separates the first scientists in the 16th century from the Ancient Greek philosophers that dominated the intellectual climate nearly two millennia earlier. You, too, will collect and analyze data in order to learn about the world, and you will often be asked to display it neatly in the form of a graph. The rules for sections 5.1.0, 5.2.0, and 5.3.0 are adapted from the Afterschool Training Toolkit, Tutoring to Enhance Science Skills, accessed 31 July 2007.

  • 5.1.0 Gathering data: data tables
  • Data tables provide a neat and organized way to record and present data. A clearly structured data table helps to prevent confusion about the goal of the experiment and prevents data from getting “lost” (like writing a bunch of numbers on the margin of your lab sheet). In a data table, columns are vertical groups of cells, and rows are horizontal groups of cells.

  • A few simple rules will help you to make excellent data tables. Refer to Figure 6 to see where the bold items in the rules go into the data table.
    • 5.1.1 Write a title that is clear and that reflects the purpose of the data table. It should be thorough and descriptive, so do not be shy about writing ~15 words if necessary. Mention the independent and dependent variables (see Figure 7).

    • 5.1.2 Write the name of the independent variable (like time) in the first column. If there is a unit for the independent variable (like seconds), then include it in parentheses.

    • 5.1.3 Write the name of the dependent variable (like mass consumed) in the column next to the independent variable. If there is a unit for the dependent variable (like grams), then include it in parentheses. If more than one trial is done, then write the trials in sub-columns below the dependent variable.

    • 5.1.4 Include a column for a derived quantity when making calculations based on the data. Write the name of the quantity (like mass consumed per second) in the far right column. If there is a unit for the derived quantity (like g/s), then include it in parentheses.

    • 5.1.5 Check that data is recorded accurately and that calculations are correct.
handbook-fig06.gif
Figure 6 Typical structure of a data table
      • Section 4.1 described an experiment in which a researcher set out to determine how the position of a truck’s tailgate affected its fuel consumption. Sample data collected from the experiment are shown in Figures 7 and 8. In Figure 7, notice that the scientist decided to test three angles of the tailgate instead of just two (up and down), and that he repeated each test three times to help ensure the validity of the results. Figure 8 shows an alternate way to arrange and display the data, but it does not show three separate trials for each tailgate position. To a large extent, taking measurements every five miles substitutes for taking one measurement every twenty-five miles and repeating the journey three times.

      • We will see in sections 5.2.0 and 5.3.0 that the data in Figure 7 are better suited to drawing a bar graph, and the data in Figure 8 are better suited to drawing a line graph.
handbook-fig07.gif
Figure 7 Sample data table containing data from the tailgate experiment
handbook-fig08.gif
Figure 8 Another sample data table containing data from the tailgate experiment

  • 5.2.0 Displaying data: bar graphs
  • Bar graphs are used to display information that compares quantities or how often something occurs, such as results from a survey or the amount of fuel consumed by a pickup truck under different conditions. To easily create great looking graphs online, go to Create a Graph.

  • A few simple rules will help you to make excellent bar graphs. Refer to Figure 9 to see where the bold items in the rules go into the bar graph.
    • 5.2.1 Draw the axes so that the graph uses most of the allotted space.

    • 5.2.2 Space the independent variables evenly on the horizontal (x) axis. Subdivide the vertical axis into equal intervals by subtracting the smallest data value from the largest value, dividing by the number of grid lines on the axis, and then rounding; the resulting number is the numerical value of each line on the vertical (y) axis. Write the numbers along the axis.

    • 5.2.3 Write the name of the independent variable under the x-axis. If there is a unit for the independent variable, then include it in parentheses.

    • 5.2.4 Write the name of the dependent variable next to the y-axis. Write the unit for the dependent variable in parentheses.

    • 5.2.5 Write a title that tells the viewer what the graph shows.

    • 5.2.6 Plot data accurately using a ruler or a spreadsheet program like Microsoft Excel.

    • 5.2.7 Use colors, textures, or other features to make the graph easier to read.

    • 5.2.8 Use a key if necessary.
    • handbook-fig09.gif
      • The data in Figure 7 can be graphed in different ways depending on what aspects of the experiment we want to emphasize. To show how the data vary with different trials, graph the data like shown in Figure 10. However, since we are mostly interested in how the position of the tailgate affects fuel usage, then the graph in Figure 11 will better serve our purposes. Notice that both graphs show the same information, but the columns are just arranged differently.

      • To determine the vertical scale, first subtract the smallest value from the largest (1.42 – 1.21 = 0.21). Second, divide 0.21 by the number of grid lines on the y-axis (0.21/30 = 0.007). Lastly, round (0.007 rounds to 0.01). Thus, each grid line represents 0.01 gallons of gas, as you can see in both graphs below.
handbook-fig10.png
Figure 10 Bar graph emphasizing differences between trials constructed from the data in Figure 7
handbook-fig11.png
Figure 11 Bar graph emphasizing differences in tailgate position constructed from the data in Figure 7

  • 5.3.0 Displaying data: line graphs
  • Line graphs are best when both the independent and dependent variables change regularly, such as the growth of a plant with time or the amount of sugar that can be dissolved in water at different temperatures.

  • A few simple rules will help you to make excellent line graphs. Refer to Figure 12 to see where the bold items in the rules go into the line graph.
    • 5.3.1 Draw the axes so that the graph uses most of the allotted space.

    • 5.3.2 Scale the x- and y-axis using the same technique described in 5.2.2. This ensures that your data points span the height and width of the graph. Write the numbers along each axis.

    • 5.3.3 Write the name of the independent variable under the x-axis. Write the unit for the independent variable in parentheses.

    • 5.3.4 Write the name of the dependent variable next to the y-axis. Write the unit for the dependent variable in parentheses.

    • 5.3.5 Write a title that tells the viewer what the graph shows.

    • 5.3.6 Plot data accurately using a ruler or a spreadsheet program like Microsoft Excel. Make sure your data points are clearly visible.

    • 5.3.7 Draw a curve or line of best fit through the data points. Make it dashed where it extends beyond the data to indicate uncertainty.

    • 5.3.8 Use colors, textures, or other features to make the graph easier to read.

    • 5.3.9 Use a key if necessary.
handbook-fig12.gif
      • The data in Figure 8 are well-suited to a line graph since both variables (distance and fuel consumption) vary regularly. A simple graph of the “tailgate up” data is shown in Figure 13.
handbook-fig13.png
Figure 13 Line graph of part of the Figure 8 data
The measurements made by the experimenter are shown by the white circles; the lines connecting the data points are called interpolations (“inter-” = between), and they represent how much fuel would be consumed at intermediate distances. These lines can be drawn because it appears that the fuel is being used at a steady rate. The dashed line represents an extrapolation (“extra-” = beyond) because it extends past the last data point; it represents a logical guess about how much fuel would be consumed if the experimenter drove thirty miles. In this case, the amount of fuel consumed after thirty miles would be about 1.5 gallons. This is sometimes called a progress curve because it shows how some event progresses, in this case how fuel consumption progresses with distance. (Progress curves usually have time as the independent variable.)
handbook-fig14.png Figure 14 Line graph showing all of the Figure 8 data
We can compare the “tailgate up” data with the other tailgate positions by plotting the data on the same graph (see Figure 14). However, some way of distinguishing the data is necessary to do this. In this example, different types of data points are used and a key is used to identify them. The lines could also be labeled directly. Notice that the “tailgate up” line is shallower than the others, meaning the truck uses less fuel when the tailgate is up than when it is in other positions.
handbook-fig15.png Figure 15 A rate graph of the Figure 8 data
The slope (or steepness) of a line is defined as the rise (the distance on the y-axis from one point to another) divided by the run (the distance on the x-axis between the same two points used to calculate the rise). Let’s calculate the slope of the line in Figure 13. The first point has coordinates (0x, 0.00y), and the last point has coordinates (25x, 1.25y). Therefore, the rise is 1.25 – 0.00 = 1.25 gallons, and the run is 25 – 0 = 25 miles, giving a slope of (1.25 gallons/25 miles) = 0.05 gallons/mile. This number is a rate since it measures the speed of a process. Because the slopes of the lines in Figures 13 and 14 are constant, the rates are also constant. They are plotted in Figure 15, which shows a rate graph. The most efficient tailgate position is the one that uses the least amount of gasoline per mile.
handbook-fig16.png Figure 16 An alternate rate graph of the Figure 8 data
By inverting the rates shown in Figure 15, we can find the more familiar measure of gas mileage, miles per gallon. Plotting those new rates gives the line graph shown in Figure 16. (The idea to illustrate different kinds of graphs was taken from The College Board’s Biology Lab Manual, 2001, Appendix II.)

  • 5.4.0 Displaying data: graph rubric
  • The following rubric is a generic rubric useful for assessing most kinds of graphs. Point values are in parentheses.
Parts
Weighting
Exceeds Standard (1.5)
Meets Standard (1)
Approaches Standard (0.5)
Below Standard (0)
Score
Title
(x 1)

Descriptive title that mentions independent and dependent variables (>10 words)
(See 5.1.1, 5.2.5, and 5.3.5)
Simple title (< 10 words) or a title that does not include ind./dep. variables
Minimal title (such as “Cooling Curve”) or title missing

Axes
Labeling (x 1)

Both axes labeled (with variables, units)
(See 5.2.3, 5.2.4, 5.3.3, and 5.3.4)
One or more axes missing variables or units
Axes not labeled

Orientation (x 1)

Independent and dependent variables on the correct axis
(See 5.2.3, 5.2.4, 5.3.3, and 5.3.4)
Independent and dependent variables on the incorrect axis
Independent and dependent variables on the incorrect axis or worse

Markers (x 1)
Tick marks customized for the data displayed
Both axes have tick marks at regular, appropriate intervals
One axis has tick marks at regular, appropriate intervals
Neither axis has tick marks at regular, appropriate intervals

Data
Plotting (x 1)
Properly plotted data + other relevant data (such as trend lines)
Properly plotted data
(See 5.2.6 and 5.3.6)
One data point improperly plotted
More than one data point improperly plotted or data points missing

Identification (x 1)
Data sets identified by color
Different data sets clearly identified (such as in a key)
(See 5.2.8 and 5.3.9)
Different data sets identified, but not clearly
Different data sets not identified

Format
Type (x 1)

Graph is appropriate for the type of data displayed
(See 5.2.0 and 5.3.0)
Graph is not appropriate for the type of data displayed
Graph is not appropriate for the type of data displayed

Scaling (x 1)

Graph has proper scaling
(See 5.2.2 and 5.3.2)
Excessive space on either x- or y-axis.
Excessive space on both x- and y-axis.

Size (x 1)

Large
(See 5.2.1 and 5.3.1)
Medium
Small

Method (x 1)
Any required annotations also done in Excel
Made in Excel (or other graphing software)
(See 5.2.6 and 5.3.6)
Made in Excel but with hand-labeled components (like data sets or variables)
Made by hand

Total
10






  • 5.5.0 Analyzing data: forming conclusions
  • Refer to section 3.4.0 for a brief discussion about analyzing data and forming conclusions from data. This section will be limited to analyzing results from the sample experiment.
      • It should be clear that the process of making the line graphs in the preceding section involved some analysis, or thinking, about the data. For instance, the slopes of the lines in Figure 14 indicate that having the tailgate up is the best position for conserving fuel in the pickup truck and that fuel consumption depends upon distance. However, the flat lines in Figures 15 and 16 reveal that distance does not affect the rate at which fuel is consumed.

      • It also appears that having the tailgate halfway down is not much better for gas mileage than having it all the way down, which might lead us to believe there is something significant or important about having a continuous wall around the bed of the pickup. However, the way in which we plot that information can alter our perceptions. For instance, examine Figures 17 and 18. Figure 17 has a line of best fit between the data points, and it suggests that the “tailgate halfway” position lies exactly between the other two positions but that we cannot see it in the other graphs due to some inaccuracy in the measurements. Figure 18 connects the data points, suggesting that the measurements are accurate and that having the tailgate up really is much better than the other positions. Because we are uncertain about the meaning and reliability of our data, both lines are drawn broken and subject to interpretation.
handbook-fig17.png
handbook-fig18.png
Figure 17 Rate graph with line of best fit
Figure 18 Rate graph with connected data points