Analysing Data

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					    Analyzing Experimental Data
           Lazy Parabola
        B as a function of A

          Created for CVCA Physics
                      by
              Dick Heckathorn
               30 August 2K+4


        page 26 Practice 3   Lazy Parabola
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         A. Getting Ready

    1. “On”, “Mode”
       Normal, Float, Degree,
       Func, Connected,
       Sequential, Full Screen
    2. To Exit:
       “2nd” “Quit”

2
              B. Storing Data
    1. “Stat”, “Edit”
    2. Clear all columns
       Cursor over each header, “Clear”,
       “Down arrow”
    3. With cursor over blank headers:
       a. “2nd”, “Ins”, „A‟ (one header)
       b. “2nd”, “Ins”, „B‟ (2nd header)
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             B. Storing Data

    4. Input data into appropriate
       column.
    5. „A‟ 100 64 49 36 25 16
       „B‟ 1.99 1.59 1.39 1.19 1.00 0.80

       [note...„B‟ is a function of „A‟]

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    C. Clear Previous Graphs

    1.   “y=”
    2.   clear any equations
    3.   “2nd”, “stat plot”
    4.   Enter “4” - PlotsOff
    5.   “Enter”


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         D. Preparing to Plot

1. “2nd”, “Stat Plot”
2. With cursor at 1, “Enter”
3. a. on
   b. Type: select 1st graph
   c. Xlist to „A‟: (“2nd”, “List”, “A”)
   d. Ylist to „B‟: (“2nd”, “List”, “B”)
   e. Mark: select square
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          E. Graphing The Data
    1. “Zoom”, “9: ZoomStat”
       (This allows all points to be plotted
       using all of the screen.)
    2. “Windows”
       a. Set Xmin= & Ymin= to zero
       b. “Graph”
          (All of 1st quadrant shown)
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              F. Analysis
             Shape of line is?
    a lazy parabola
    which indicates
    „n‟ has a power greater than „0‟
     but less than „1‟.
                       0  n 1
                B A
    So plot „B‟ vs „ An ‟ where n = 0.5 .
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          G. Analysis of B vs   A.5


    1. “Stat”, “Edit”
    2. Cursor at top of blank column
       “2nd”, “INS”, „AHALF‟
    3. Move cursor on top of „AHALF‟
    4. Type: “2nd”, “”, “2nd”, “list”, „A‟
    5. “Enter”
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        G. Analysis of B vs      A.5

1. “2nd”, “Stat Plot”
2. With cursor at 1, “Enter”
3. a. on
   b. Type: select 1st graph
   c. Xlist to „A‟: (“2nd”, “List”, “AHALF”)
   d. Ylist to „B‟: (“2nd”, “List”, “B”)
   e. Mark: select square
10
       G. Analysis of B vs    A.5


 1. “Zoom”, “9: ZoomStat”
    (This allows all points to be plotted
    using all of the screen.)
 2. “Windows”
    a. Set Xmin= and Ymin= to zero
    b. “Graph”
    (This shows all of 1st quadrant)
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          G. Analysis of B vs A.5

                Shape of line is
                a straight line.
                We can now….
     Find the equation of the straight line.

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         H. Finding the Equation

 1.   “Stat”, “Calc” “4:LinReg(ax+b)
 2.   “2nd”, “list”, „AHALF‟, „,‟
 3.   “2nd”, “list”, „B‟, “Enter”
 4.   On screen we see:
      a. LinReg
         y = ax+b a = .20 b = .01
         [a = slope, b = y-intercept]
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             H. The Equation is:
        Using y = mx+b concept where the
     calculator uses y = ax+b, substitute in the
         value for „a‟ and „b‟ and one gets:

               y  0.20 x   0.5
                                   0.01
     Since b is very close to 0, we can ignore it.
        Replace „y‟ with „B‟ and „x‟ with „A‟

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                  B  0.20 A       0.5
               I. Thought

              B  0.20 A    0.5


     What do we say is the relationship
          between „B‟ and „A‟ ?

        We say the relationship is:

     „B‟ is directly proportional to the
              square root of „A‟.
15
      J.   Plotting Line of Best Fit
 1. “y=”, “VARS”, “5:Statistics...”,
    “EQ”, “1:RegEq”, “Graph”
 2. And there you have it, the line of
    the best fit line for the data points
    plotted.
 3. In real life data gathering, all the
    points will not fall on the line due to
    normal measurement error.
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               K. Summary
     That‟s all there is to it. If the data
       yields a straight line, find the
       equation of the straight line.


     If it is a hyperbola or a parabola,
      then you must make additional
     plots until you get a straight line.
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      K. A Final, Final Thought

      At this time, write out a brief
     summary using bullet points for
               what you did.

      Do not go on unless you have
         completed the above.

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                L. A Shortcut

     1. Using original data plot „B‟ as a
        function of „A‟.
     2.   “Stat”, “Calc”, “A:PwrReg”,
     3.   “2nd”, “List”, „A, „,‟
     4.   “2nd”, “List”, „B‟
     5.   “Enter”

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             L. A Shortcut -2-
     6. On the screen we see:
        a. PwrReg
           y = a*x^b
           a = .20
           b = .50


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            L. A Shortcut -3-
                         y = a*x^b
 7. Substituting:
    0.20 for „a‟ and   y  0.20x   0.50
    0.50 for „b‟
 8. Substituting:
    „B‟ for „y‟ and    B  0.20A   0.50

    „A‟ for „x‟

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              M. A Summary

              B  0.20A    0.50



     9. How does this equation
        compare to that found earlier?

           They should be the same.

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     That‟s all folks!




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