Math and Science

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Math and Science
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How Math is Used

• Mathematics is used to describe natural objects
  and populations
• Mathematics is used to model natural systems

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Measuring Systems

• Measuring systems are constructed from a few
  minimum necessary elements
• Length
• Mass
• Time
• Temperature

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Describing Objects

• Measurements can be combined to describe an
  object
• Volume length 3 (ex. cm 3 , m 3)
• Density mass/volume (ex. g/cm3, mg/m3)
• Concentration mass/volume (ex. g/ml, mg/L)

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Describing Processes

• Measurements can be combined to describe a
  process
• Velocity length/time (ex. m/sec, km/hr)

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Types of Data

• Discrete Data
• Each item measured is a discrete or whole unit
• Continuous Data
• Points along a continuum
• Points along a subdivided scale

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Types of Measurement Scales

• Nominal and Ordinal Scales
• Used to measure discrete data
• Interval and Ratio Scales
• Used to measure continuous data

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Scales of Measurement

• Nominal and Ordinal Scales
• Used for discrete data
• Sorting of whole units into groupings

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Nominal Scale

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

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Ordinal Scale

• For discrete data
• 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

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Colorimetric Comparisons
Nominal or Ordinal?
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Scales of Measurement

• Interval and Ratio Scales
• Used for continuous data
• Indicates the distance between items

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

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

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Concentration of Added Nitrogen
1 2 3 4 5 6
Nitrogen mg/L 0 .1 1 10 100 1,000
Ratio or Interval?