# Analysing Data

Document Sample

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
1

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
“Down arrow”
3. With cursor over blank headers:
a. “2nd”, “Ins”, „A‟ (one header)
b. “2nd”, “Ins”, „B‟ (2nd header)
3
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‟]

4
C. Clear Previous Graphs

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

5
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”
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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 .
8
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)
11
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‟

14
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,
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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