Overview
This lecture covers the basics of graphing as a method of data analysis in scientific experiments, including how to properly construct, label, and interpret graphs.
Why Use Graphs
- Graphs provide a visual representation of data for easier analysis and conclusions.
- Pictorial data makes trends and relationships easier to identify compared to only numerical data.
Constructing a Proper Graph
- Use an x-axis (horizontal) and y-axis (vertical) on your graph.
- The independent variable (controlled by the experimenter) is placed on the x-axis.
- The dependent variable (changes in response to the independent variable) is placed on the y-axis.
- All other variables should be kept constant to ensure valid results.
- Axes must use regular, increasing interval divisions (e.g., 0, 10, 20, 30).
- Label axes with both variable names and appropriate units (e.g., Temperature (K), Time (s)).
- Add a clear title in the format "Y versus X" (e.g., Temperature versus Time).
Plotting Data Points and Point Protectors
- Plot each measurement as a point at the correct x, y location.
- Draw a circle (point protector) around each data point to indicate measurement uncertainty and to keep data visible after drawing lines or curves.
Best Fit Lines and Interpretation
- Draw a best fit line or curve that represents the overall trend of the data.
- The best fit line should have roughly equal numbers of points above and below it.
- Do not always start at (0,0); use y = mx + b where b is not necessarily zero.
- Most lab data is linear and can use a straight line for best fit.
Types of Relationships
- Direct (positive) relationship: as one variable increases, so does the other.
- Indirect (inverse) relationship: as one variable increases, the other decreases.
Using Graphs for Prediction
- Interpolation: estimating values within the range of collected data.
- Extrapolation: predicting values outside the collected data range.
- To interpolate or extrapolate, move from the known value on one axis to the best fit line, then across to the other axis.
Application Example with Reference Tables
- Reference tables (e.g., vapor pressure vs. temperature) use the same graphing principles.
- To find a value, locate the known variable, move to the curve, then across or down to the other axis.
Key Terms & Definitions
- Independent Variable — The variable manipulated by the experimenter, placed on the x-axis.
- Dependent Variable — The variable measured in response to changes in the independent variable, on the y-axis.
- Point Protector — A circle around a data point to indicate uncertainty and visibility.
- Best Fit Line — A straight or curved line representing the trend of the data points.
- Interpolation — Estimating values within the range of the collected data points.
- Extrapolation — Predicting values beyond the collected data range.
Action Items / Next Steps
- Practice plotting sample data with proper axes, labels, units, and titles.
- Use interpolation and extrapolation techniques on provided reference tables.
- Prepare for next class by reviewing graphing examples in the textbook.