In an experiment to measure the value of pi, the following results are obtained for pi:
3.14 3.11 3.20 3.06 3.08
a) Calculate the Mean Value.
b) Calculate the Average Deviation from the Mean
c) Calculate the: True Standard Deviation
d) Calculate the: Standard Deviation of the Mean.
e) If the correct value is 3.14159, calculate the: Percent Error

Question

14-06-2021
Physics

contestada

In an experiment to measure the value of pi, the following results are obtained for pi:
3.14 3.11 3.20 3.06 3.08
a) Calculate the Mean Value.
b) Calculate the Average Deviation from the Mean
c) Calculate the: True Standard Deviation
d) Calculate the: Standard Deviation of the Mean.
e) If the correct value is 3.14159, calculate the: Percent Error

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whitneytr12 whitneytr12 · Answer 1 · 2021-06-15T03:08:51+02:00

Answer:

a)[tex]MV=3.118[/tex]

b)[tex]AD=0.0416[/tex]

c)[tex]TSD=0.00302[/tex]

d)[tex]SD=0.00242[/tex]

e)[tex]%E=0.75%[/tex][tex]PE=0.75\%[/tex]

Explanation:

a)

The mean value equation is:

[tex]MV=\frac{\Sum x}{n}[/tex]

Where:

x represents the values of pi
n is the number of pi values

[tex]MV=\frac{3.14+3.11+3.20+3.06+3.08}{5}[/tex]

[tex]MV=3.118[/tex]

b)

The average deviation equations is:

[tex]AD=\frac{\Sum |x-MV|}{n}[/tex]

[tex]AD=\frac{0.208}{5}[/tex]

[tex]AD=0.0416[/tex]

c)

The true Standard Deviation equation is:

[tex]TSD=\sqrt{\frac{\Sum (x-MV)^{2}}{n-1}}[/tex]

[tex]TSD=\sqrt{\frac{0.01208}{5-1}}[/tex]

[tex]TSD=0.00302[/tex]

d)

The Standard Deviation equation is:

[tex]TSD=\sqrt{\frac{\Sum (x-MV)^{2}}{n}}[/tex]

[tex]TSD=\sqrt{\frac{0.01208}{5}}[/tex]

[tex]SD=0.00242[/tex]

e)

The percent error equation is:

[tex]%E=\frac{|Measured value - True value|}{|True value|}[/tex][tex]PE=\frac{|Measured value - True value|}{True value}[/tex]

[tex]%E=\frac{|Measured value - True value|}{|True value|}[/tex][tex]PE=\frac{|3.118-3.14159|}{3.14159}*100[/tex]

[tex]%E=\frac{|Measured value - True value|}{|True value|}[/tex][tex]PE=0.75\%[/tex]

[tex]%E=0.75%[/tex]

I hope it helps you!