1. Math and Science

2. How Math is Used Mathematics is used to describe natural objects and populations Mathematics is used to describe natural objects and populations Mathematics is used to model natural systems Mathematics is used to model natural systems

3. Measuring Systems Measuring systems are constructed from a few minimum necessary elements Measuring systems are constructed from a few minimum necessary elements –Length –Mass –Time –Temperature

4. Describing Objects Measurements can be combined to describe an object Measurements can be combined to describe an object –Volume = length 3 (ex. cm 3, m 3 ) –Density = mass/volume (ex. g/cm 3, mg/m 3 ) –Concentration = mass/volume (ex. g/ml, mg/L)

5. Describing Processes Measurements can be combined to describe a process Measurements can be combined to describe a process –Velocity = length/time (ex. m/sec, km/hr)

6. Types of Data Discrete Data Discrete Data –Each item measured is a discrete or whole unit Continuous Data Continuous Data –Points along a continuum –Points along a subdivided scale

7. Types of Measurement Scales Nominal and Ordinal Scales Nominal and Ordinal Scales –Used to measure discrete data Interval and Ratio Scales Interval and Ratio Scales –Used to measure continuous data

8. Scales of Measurement Nominal and Ordinal Scales Nominal and Ordinal Scales –Used for discrete data –Sorting of whole units into groupings

9. Nominal Scale For discrete data Whole units sorted into groupings of equal value. Whole units sorted into groupings of equal value. –No measure of difference between items Ex. Numbers of males and females Ex. Numbers of males and females

10. Ordinal Scale For discrete data Whole units sorted into groupings of relative value Whole units sorted into groupings of relative value –Measure of difference between items in groups Ex. Fish ranked by size small fish, medium fish, and big fish Ex. Fish ranked by size small fish, medium fish, and big fish

11. Colorimetric Comparisons Nominal or Ordinal?

12. Scales of Measurement Interval and Ratio Scales Interval and Ratio Scales Used for continuous data Used for continuous data Indicates the distance between items Indicates the distance between items

13. Interval and Ratio Scales The ratio between any two intervals is independent of the unit of measurement and of the zero point. No matter which scale you use the ratio of intervals remains the same.

14. Ratio Scale Has a true zero point Ex. Length, volume, weight

15. Interval Scale Zero point is arbitrarily set Ex. Temperature (arbitrary zero based on temperature at which water freezes)

16. Concentration of Added Nitrogen 123456 Nitrogenmg/L0.11101001,000 Ratio or Interval?