Data and Graphs
Learn
Transforming raw data into meaningful visualizations is essential for scientific communication. This lesson covers data organization, graph selection, and basic statistical analysis for research projects.
Organizing Raw Data
- Data Tables: Organize with clear column headers, units, and consistent formatting
- Significant Figures: Match precision to your measurement tools
- Outliers: Identify and document unusual data points; do not delete without justification
- Missing Data: Note any gaps and explain why data is missing
Choosing the Right Graph
| Graph Type | Best For | Example |
|---|---|---|
| Line Graph | Continuous data showing change over time | Temperature changes during a reaction |
| Bar Graph | Comparing categories or discrete groups | Plant growth with different fertilizers |
| Scatter Plot | Showing correlation between two variables | Height vs. arm span measurements |
| Histogram | Distribution of continuous data | Distribution of test scores |
| Pie Chart | Parts of a whole (percentages) | Composition of elements in a sample |
Graph Components
Every scientific graph must include:
- Title: Descriptive title stating what the graph shows
- Axis Labels: Clear labels with units (e.g., "Time (seconds)")
- Scale: Appropriate intervals that make data easy to read
- Legend: Key for multiple data sets
- Data Points: Clearly visible markers
- Error Bars: When applicable, show uncertainty or standard deviation
Basic Statistical Measures
- Mean (Average): Sum of values divided by number of values
- Median: Middle value when data is ordered
- Range: Difference between highest and lowest values
- Standard Deviation: Measure of how spread out values are from the mean
- Percent Error: |Experimental - Accepted| / Accepted x 100%
Examples
Example 1: Calculating Mean and Range
Data: Plant heights (cm): 12.3, 14.7, 11.8, 15.2, 13.5
Mean: (12.3 + 14.7 + 11.8 + 15.2 + 13.5) / 5 = 67.5 / 5 = 13.5 cm
Range: 15.2 - 11.8 = 3.4 cm
Example 2: Calculating Percent Error
Experimental value: 9.65 m/s2 (measured acceleration due to gravity)
Accepted value: 9.81 m/s2
Percent Error: |9.65 - 9.81| / 9.81 x 100% = 0.16 / 9.81 x 100% = 1.6%
Example 3: Selecting Graph Type
Scenario: You measured enzyme activity at 5 different temperatures (20, 30, 40, 50, 60 degrees C).
Best Choice: Line graph - Temperature is a continuous variable, and you want to show the trend of enzyme activity as temperature changes.
Why not bar graph? Bar graphs are better for discrete categories. Here, temperatures represent a continuous range.
Practice
Apply your data analysis skills to these problems.
1. Calculate the mean, median, and range for the following data set: 45, 52, 48, 67, 51, 49, 53
2. A student measured the density of aluminum as 2.58 g/cm3. The accepted value is 2.70 g/cm3. Calculate the percent error.
3. What type of graph would you use to display the following data? Justify your choice: Number of birds observed at a feeder each month for one year.
4. What type of graph would best show the relationship between study time and test scores for 30 students? Explain.
5. Examine this data: Trial 1: 5.2g, Trial 2: 5.4g, Trial 3: 5.1g, Trial 4: 8.9g, Trial 5: 5.3g. Identify the outlier and explain how you would handle it in your analysis.
6. A graph shows "Distance" on the y-axis but no units. Why is this problematic, and what specific information should be added?
7. Convert the following data into a properly formatted data table: "On Monday we recorded 15 butterflies, Tuesday had 22, Wednesday dropped to 18, Thursday was 25, and Friday ended with 20 butterflies."
8. Two students graphed the same data. Student A used a y-axis scale from 0-100, while Student B used 40-60. Both data points fall between 45-55. Which scale is more appropriate and why?
9. Your data shows: Group A mean = 25.3, standard deviation = 2.1; Group B mean = 26.8, standard deviation = 8.4. Which group has more consistent results? Explain.
10. Create a sketch showing what a line graph would look like if enzyme activity increased from 20-40 degrees C, peaked at 40 degrees, then decreased from 40-60 degrees C. Label all required components.
Check Your Understanding
Q1: When is it appropriate to use a bar graph versus a line graph?
Q2: What does a large standard deviation tell you about a data set?
Q3: Why are error bars important in scientific graphs?
Q4: How does the choice of axis scale affect how data is interpreted?
Next Steps
- Practice creating graphs by hand and using software tools
- Review how to calculate and interpret standard deviation
- Continue to the next lesson on CER Writing to learn how to communicate your findings