Grade: Grade 12 Subject: Science Unit: Science Electives Lesson: 4 of 6 SAT: ProblemSolving+DataAnalysis ACT: Science

Data and Graphs

Learn

Data analysis and visualization are essential skills for interpreting experimental results and communicating scientific findings. This lesson covers how to organize data, choose appropriate graph types, and draw valid conclusions.

Types of Data

  • Quantitative data: Numerical measurements (height, mass, temperature, time)
  • Qualitative data: Descriptive observations (color, texture, behavior)
  • Continuous data: Can take any value within a range (temperature: 23.5C)
  • Discrete data: Only whole number values (number of organisms: 15)

Choosing the Right Graph

  • Line graph: Shows trends over continuous data (time series, temperature changes)
  • Bar graph: Compares discrete categories (species counts, treatment groups)
  • Scatter plot: Shows relationship between two variables (correlation studies)
  • Histogram: Shows frequency distribution of continuous data
  • Pie chart: Shows proportions of a whole (composition percentages)

Essential Graph Components

  • Title: Describes what the graph shows (dependent vs. independent)
  • Axes labels: Include variable name and units
  • Scale: Appropriate intervals that fit the data range
  • Legend: Identifies different data series
  • Data points: Accurately plotted from raw data
  • Error bars: Show variability or uncertainty in measurements

Statistical Measures

  • Mean: Average of all values (sum divided by count)
  • Median: Middle value when data is ordered
  • Mode: Most frequently occurring value
  • Range: Difference between highest and lowest values
  • Standard deviation: Measure of data spread around the mean

Interpreting Trends

  • Positive correlation: As one variable increases, the other increases
  • Negative correlation: As one variable increases, the other decreases
  • No correlation: No consistent relationship between variables
  • Causation vs. correlation: Correlation does not imply causation

Examples

Example 1: Calculating Mean and Standard Deviation

Data set: Plant heights (cm): 12, 15, 14, 13, 16, 15, 14, 13, 15, 13

Mean: (12+15+14+13+16+15+14+13+15+13) / 10 = 140/10 = 14.0 cm

To find standard deviation:

  1. Find the difference from mean for each value
  2. Square each difference
  3. Find the mean of squared differences (variance)
  4. Take the square root (standard deviation)

Standard deviation = 1.15 cm

Example 2: Choosing Graph Types

Scenario A: Comparing average test scores between 4 different schools

Best choice: Bar graph (comparing discrete categories)

Scenario B: Tracking bacterial population growth over 24 hours

Best choice: Line graph (continuous time series data)

Scenario C: Examining relationship between study hours and exam scores

Best choice: Scatter plot (looking for correlation between two variables)

Practice

Complete these practice problems to strengthen your data analysis skills.

1. Calculate the mean of this data set: 25, 30, 28, 32, 25, 29, 31, 27

2. What type of graph would best display the percentage of different gases in the atmosphere?

3. A scatter plot shows points that form an upward-sloping pattern from left to right. What type of correlation does this indicate?

4. Find the median of: 45, 52, 38, 61, 47, 55, 42

5. Why are error bars important on scientific graphs?

6. A study finds that ice cream sales and drowning deaths both increase in summer. Does ice cream cause drowning? Explain.

7. What information should always be included on the axes of a scientific graph?

8. Calculate the range of this data: 15.2, 18.7, 12.4, 20.1, 16.8, 14.3

9. When would a histogram be more appropriate than a bar graph?

10. A researcher claims a strong correlation (r = 0.95) proves that Variable A causes Variable B. Evaluate this claim.

11. What is the mode of this data set: 4, 7, 4, 9, 4, 8, 6, 4, 7

12. Describe what a line of best fit represents on a scatter plot.

Check Your Understanding

Question 1: Which measure of central tendency is least affected by extreme outliers?

  • A) Mean
  • B) Median
  • C) Mode
  • D) Range

Question 2: A line graph is most appropriate for displaying:

  • A) Proportions of a whole
  • B) Changes over continuous time
  • C) Comparison of categories
  • D) Frequency of data values

Next Steps

  • Practice calculating statistical measures with real data sets
  • Create graphs using data from your own experiments
  • Continue to the next lesson on CER Writing