1. ENVIRONMENTAL SCIENCE
Chapter 2 Tools of Environmental Science
2.2 Statistics and Models

2. 2.2 Statistics and Models Objectives
Explain how scientists use statistics.
Explain why the size of a statistical sample is important.
Describe three types of models commonly used by scientists.
Explain the relationship between probability and risk.
Explain the importance of conceptual and mathematical models.

3. Introduction
Most studies in environmental science involve tremendous volumes of data that need to be organized and interpreted before they are useful.
Statistics is the collection and classification of numerical data.
Statistics are widely used in many other fields of study, such as sports.

4. How Scientists Use Statistics
Scientists use statistics for a variety of purposes such as making comparisons, summarizations, characterizations, and analyses.
A statistical population is a group of similar things that a scientist is interested in learning about.
Though a population may be made of similar individuals, there are differences that can be measured.
A mean is the number obtained taking the sum of the data for a given characteristic and dividing it by the number of individuals being measured.

5. How Scientists Use Statistics
The mean provides a single numerical measurement for a given aspect of a population.
Means of different populations can be compared.
A distribution is the relative arrangement of the members of a statistical population.
In a normal distribution, the data are grouped symmetrically around the mean – forming a bell-shaped curve.

7. How Scientists Use Statistics
Probability is the chance that something will happen.
For example, if you were to flip a coin, the probability that it would land “heads-up” is 50%
A sample is the group of individuals or events selected to represent the population.
Sample size is the number of objects or events sampled.
If you were to flip a coin 10 times, you sample size is 10 or if you were to flip the coin 1000 times, the sample size is 1000
A sample size should be large enough to give an accurate estimate for the whole population.

8. Statistics in Everyday Life
One common use of statistics in life is weather forecasts that give “50% chance of thundershowers this evening” on the news.
Statistics are also used when studying climate change and atmospheric carbon dioxide.
Being able to recognize and understand statistics allows one to be a better consumer of information – especially information about the environment on which we depend.

9. Statistics in Everyday Life
Risk is the probability of an undesirable outcome.
Public perception of risk can be much different than risk perception of experts.

10. Models Models are representations of objects or systems.
Scientists use many different kinds of models to learn about the natural world.
Physical models are three dimensional models that one can touch
Physical models closely resemble the object or system that they represent
A well known example of a physical model would be a DNA molecule section showing the double helix structure

11. Models Graphical models include maps and charts.
Graphical models are good for showing relationship between locations or routes
Conceptual models are verbal or graphical explanations for how a system works or is organized.
A conceptual model may be illustrated by a flow chart
Scientists can create flow charts to understand how a system fits together, components contained in the system, relationship between components, and cause and effect

12. Models
A mathematical model is one or more equations that represents the way a system or process works.
Like any model, mathematical models are only as good as the data from which they were built “garbage in, garbage out!”
Computer models are mathematical models processed with computer technology and may include massive amounts of data.

13. E = mc2

14. Which is a Scientific Model?

15. References
Normal Distribution Test Results -
Oil Risk (Figure 11) – Arms, Karen, Environmental Science, Holt
DNA Model -
Alabama Geological Map -

16. Reference
Runway Model -
Anatomical Model -