1. Quantitative Skills 1: Graphing

2. Categories of data:
Qualitative data is not numerical and is usually subjective.
Quantitative data is numerical and lends itself to statistical analysis.
1.75 mL

3. Quantitative data can be either discrete or continuous.
Discrete data has finite values, such as integers, or bucket categories such as “red” or “tall”.
Continuous data has an infinite number of values and forms a continuum.

4. Which graph shows continuous data and which graph shows discrete data?
Graph A
Graph B

5. One of the first steps in data analysis is to create graphical displays of the data. Visual displays can make it easy to see patterns and can clarify how two variables affect each other.
AP Biology Quantitative Skills Manual

6. Line Graphs
Used when data on both scales of the graph (the x and y axes) are continuous.
The dots indicate measurements that were actually made.

7. Basic Traits of A Good Graph
1. A Good Title
A good title is one that tells exactly what information the author is trying to present with the graph.
Relation Between Study Time and Score on a Biology Exam in 2011
-or-
Study Time vs. Score on a Biology Exam in 2011
AP® Biology Investigative Labs: An Inquiry-Based Approach

8. Basic Traits of A Good Graph
Axes should be consistently numbered.
Axes should contain labels, including units.
AP® Biology Investigative Labs: An Inquiry-Based Approach

9. Basic Traits of A Good Graph
A frame should be put around the outside of the graph.
AP® Biology Investigative Labs: An Inquiry-Based Approach

10. Basic Traits of A Good Graph
Small marks, called index marks, can be drawn in.
AP® Biology Investigative Labs: An Inquiry-Based Approach

11. Basic Traits of A Good Graph
The independent variable is always shown on the x axis.
The dependent variable is always shown on the y axis.
Dependent
Variable
AP® Biology Investigative Labs: An Inquiry-Based Approach
Independent
Variable

12. Basic Traits of A Good Graph
The line should not be extended to the origin if the data do not start there.
AP® Biology Investigative Labs: An Inquiry-Based Approach

13. Extrapolation is a prediction of what the chart might look like beyond the measured set of data. A broken line is used, indicating this a prediction and not data actually collected.

14. The slope of a line indicates the rate at which the variables being graphed are changing.
y y2 – y1
m = =
x x2 – x1
Rise
Slope =
Run

15. Positive Slope Negative Slope Zero Slope Rate Increasing
Rate Decreasing
Constant Rate
Indicates some values
were skipped

16. Line charts can be plotted with multiple data sets, allowing for better comparison.
Makes use of a legend

17. Effective graphs use statistics as an essential part of the display
Effective graphs use statistics as an essential part of the display. Statistics is the study of the collection, organization, analysis, interpretation and presentation of data. 

18. Population vs. Sample
Often, researchers want to know things about a population (N), but it may not be feasible to obtain data for every member of an entire population.
A sample (n) is a smaller group of members of a population selected to represent the population. The sample must be random.

19. Descriptive statistics and graphical displays allow us to estimate how well sample data represent the true population.

20. If a sample is not collected randomly, it may not closely reflect the original population. This is called sampling bias.

21. A normal distribution, also known as a “bell curve” or “normal curve”, can be formed with continuous data.

22. The type of data being collected during an investigation should be determined before performing the actual experiment. The type of data will determine the statistical analyses that can be used.

23. Three Types of Data: Parametric data: data that fit a normal curve
Nonparametric data: data that do not fit a normal curve
Frequency or count data: generated by counting

24. Normal or parametric data
Measurement data that fit a normal curve or distribution.
Data is continuous, generally in decimal form.

25. Nonparametric data
Do not fit a normal distribution, may include large outliers, or may be count data that can be ordered.
Can be qualitative data.

26. Frequency or count data
Generated by counting how many of an item fit into a category.
Can be data that are collected as percentages.
AP Biology Quantitative Skills Manual

27. Two Types of Descriptive Statistics:
Comparative statistics: compare variables
Association statistics: look for correlations between variables

28. Comparative statistics compare phenomena, events, or populations (Is A different from B?).
Bar Graph or
Pie Chart
Bar Graph
Box-and-Whisker Plot
Parametric Data
(normal data)
Nonparametric Data
Frequency
Data
(counts)

29. Association statistics look for associations between variables (How are A and B correlated?).
Scatterplot
AP Biology Quantitative Skills Manual
Parametric Data
and
Nonparametric Data

30. Types of graphs commonly used with the three data types and suggested statistical tests:
Source: Redrawn from “Statistics for AS Biology,” available as part of a download at:

31. Bar Graphs
Used to visually compare two samples of categorical or count data.
Are also used to visually compare the calculated means with error bars of normal data .
AP Biology Quantitative Skills Manual

32. Sample standard error bars (also known as the sample error of the sample mean) are the notations at the top of each shaded bar that shows the sample standard error (SE).
AP Biology Quantitative Skills Manual

33. Scatterplots
Used when comparing one measured variable against another.
Used when looking for trends.
AP Biology Quantitative Skills Manual

34. If the relationship is thought to be linear, a linear regression line or best fit line can be plotted to help define the pattern.
AP Biology Quantitative Skills Manual

35. Box-and-Whisker Plots
Allow graphical comparison of two samples of nonparametric data (data that do not fit a normal distribution).

36. In a box-and-whisker graph, the ticks at the tops and bottoms of the vertical lines show the highest and lowest values in the dataset, respectively. The top of each box shows the upper quartile, the bottom of each box shows the lower quartile, and the horizontal line represents the median.
AP Biology Quantitative Skills Manual

37. Histograms (Frequency Diagrams)
Used to display the distribution of data, providing a representation of the central tendencies and the spread of data.
AP Biology Quantitative Skills Manual

38. Creating a histogram requires setting up bins — uniform range intervals that cover the entire range of the data. Then the number of measurements that fit in each bin are counted and graphed.
AP Biology Quantitative Skills Manual

39. If the data on a histogram show an approximate normal distribution, then these are parametric data. If the data do not approximate a normal distribution then they are nonparametric data.
AP Biology Quantitative Skills Manual

40. References: AP® Biology Investigative Labs: An Inquiry-Based Approach and AP® Biology Quantitative Skills: A Guide for Teachers