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While Physical and Conceptual models are interesting to look at,

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While Physical and Conceptual models are interesting to look at, They won t represent any numerical data that can be used to make predictions about the future ... – PowerPoint PPT presentation

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Title: While Physical and Conceptual models are interesting to look at,


1
While Physical and Conceptual models are
interesting to look at,
  • They wont represent any numerical data that can
    be used to make predictions about the future
    behavior of the object.

2
Physical and Conceptual models are useful, but
they are only the first step towards making a
model that can make predictions.
  • The next step is most often a graph.
  • A Graphical Model shows how two variables are
    related with a picture that is easy to
    understand.
  • Because this type of graph uses numbers it is
    also called a Mathematical Model.
  • There are many different types of graphs.
  • They fall into four general forms.

3
Line Graphs
4
Bar Graphs
5
Pie Graphs
Student and faculty response to the poll 'Should
Avenue High School adopt student uniforms?'
6
Pictographs
7
In this class we will be using line graphs more
than any other type so we are going to look at
them more closely then the other types.
  • In the line graphs we use a series of lines to
    represent the two variables that are related in
    any given experiment.
  • These lines show where the information from the
    experiment intersects.
  • This information is plotted according to whether
    the variable is dependant or independent.
  • Because the line graphs uses a coordinate system
    of lines we are mapping the numbers out
    according to where they are found on each
    opposing AXIS.
  • There are two axis on any line graph, and they
    are known as the X and the Y axis.
  • The X axis is found along the bottommost line
    of the graph or horizontal line, and is known as
    the Independent Variable.
  • The Y axis is found along the far left side of
    the graph and it is the vertical line also known
    as the Dependent Variable.

8
What does that mean Dependent and Independent?
  • When something is Independent it means that it
    doesnt rely on anything else in order to achieve
    its results.
  • Time is probably the best example of an
    Independent Variable.
  • No matter what you do, Time Marches On!
  • And you cant change units of measurement.
  • For example you cant change the order of a
    distance measurement, that is to say 3 feet
    follows 2 feet not 4!
  • And when something is Dependent it means that it
    does rely on something else in order to achieve
    its results.
  • Actions are usually found on this axis.
  • Such as Speed and Temperature.

9
So why use a graph such as the types that we have
been discussing?
  • One purpose of making a graph is to organize the
    data into a model that you can use and make sense
    of in order to make predictions.
  • Pictures are easier to understand than data
    tables with just numbers in them.
  • This is where a graphical model comes into play.
  • It shows the exact relationship between the
    variables.

10
Graph vs. Data Table
Temperature (deg C) Temperature (deg C) Mean Impact Energy (joules) Mean Impact Energy (joules)

20   70.4  
100   77.3  
11
In many experiments we are looking for a cause
and effect relationship.
  • That is to say, How does changing one variable
    change the other?
  • Graphs are good ways to see whether there is a
    connection between two variables or not.
  • You cant always see the connection with a data
    table, but with a graph the connection is always
    clear!
  • When there is a relationship between the
    variables the graph will show a clear pattern.

12
Does there have to be a relationship between the
variables?
  • The answer to this is NO!
  • This will show up as a random, scattered bunch of
    data points.
  • This information should never be thrown out!
  • It is meaningful!
  • It could mean that you messed up something and
    have to try again, or it could mean that the two
    variables really dont have any relationship to
    one another at all!
  • For example if you plotted the number of homes in
    Sylvania with 3 bedrooms vs. the number of
    students in this class that have blue eyes.
  • At any rate it will tell you something!

13
Now, when there is a pattern between the two
variables the pattern will be very self-evident.
  • These relationships can be strong or weak
    depending upon how one variable effects the
    other.
  • In a Strong relationship, a small change in one
    variable will cause a big change in the other.
  • In a Weak relationship, even a big change in one
    or the other variable wont have much of an
    effect on the other!
  • What do these look like?

14
Strong Relationship
  • The following two charts show the strong
    relationship between the available energy and the
    time prior Tornadic development.
  • The graph below shows the strong relationship
    between the value of the U.S. dollar and the
    price of gold.

15
Weak Relationship
  • In the following graph we see very little change
    in amplitude when frequency is changed.
  • And then we can see how little the temperature
    will change in a given time frame.

16
Some Relationships are Direct.
  • This means that as one variable increases the
    other increases as well.
  • For example if we plotted the amount of time
    spent on studying vs. the grades earned you would
    see a direct effect on the relationship between
    the two.
  • You would start out with little time and low
    grades, and as the time spent studying increased,
    so would the grade!

17
The graph below shows the direct relationship
between age, weight, and the amount of exercise.
18
Some relationships are Inverse.
  • This means that as one variable increases, the
    other variable decreases.
  • For example if you graphed the amount of money
    that you started out with vs. the amount of money
    that you end up with, you will see an inverse
    relationship.
  • You would start out with a lot and end up with a
    little! And the graph would be slanted downwards.

19
A cars value goes down as the mileage goes up!
20
And then you can have random scatterings of points
  • In these situations you want to choose the best
    fitting line that represents as many of the
    points as possible.
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