Question

	Calculations
Trial	L=X2-X1 (m)	W=Y2-Y1 (m)
1	0.2789	0.189
2	0.2807	0.1878
3	0.2796	0.1904
4	0.2800	0.2957
5	0.2804	0.2457
6	0.2795	0.1048
7	0.2808	0.1607
8	0.2787	0.1881
9	0.2789	0.1879
10	0.2814	0.1868
Average	0.2799	0.1937
Stad. Dev. σ	0.000921894	0.049755635
Stad. Error. α	0.000291529	0.015734113
Area: Average	0.054211894
Area: Stad. Dev.σA	4.58694E-05
Area:Stad. Error αA	4.58694E-06

I might get my calculations wrong.

Lav (m)	2.799E-01	σL (m)	9.2E-04	αL (m)	2.9E-04
Wav (m)	1.937E-01	σw (m)	5.0E-02	αw (m)	1.6E-02
Aav	5.421E-02	σA	4.6E-05	αA	4.6E-06

Questions 1. What percentage of your length measurements falls in the range Lav±σL? What percentage of your length measurements falls in the range of Lav±2σL?

2. What percentage of your width measurements falls in the range Wav±σw? What percentage of your width measurements falls in the range Wav±2σL?

3. According to the statistical theory of random errors, what percentage would be expected for the answers to questions 1 and 2? Lav±σL? % Lav±2σL %

4. Do any of your length measurements have deviations greater than 3σL from Lav? Do any of your width measurement have deviations greater than 3σw from Wav? If so, indicate which ones and calculate how many times larger than σL or σw is the deviation.

5. Based upon your answers to the question (1) through (4), is your data reasonably consistent with the assumption that only random errors are present in the experiment? State clearly the basis for your answer.

6. State the most probable value of the length, width, and the area of the journal and their respective uncertainties( use the standard error) as determined by statistical theory. Length= m ± m Width= m ± m Area= ±

Answer 1

1.

Lav-σL	0.278978		Lav-2σL	0.278056
Lav + σL	0.280822		Lav + 2σL	0.281744

		Percentage of data between these ranges
No. of Trials between (Lav-σL) and (Lav + σL)	6	60%
No. of Trials between (Lav-2σL) and (Lav + 2σL)	10	100%

2.

Wav-σw	0.143944365		Wav-2σw	0.094189
Wav+σw	0.243455635		Wav+2σw	0.293211

		Percentage of data between these ranges
No. of Trials between (Wav-σw) and (Wav + σw)	7	70%
No. of Trials between (Wav-2σw) and (Wav + 2σw)	9	90%

3. As per statistics theory,

In a normal (Gaussian, random) distribution of data, about two-thirds (~68%) of the data values will fall within one standard deviation of the mean value.

In a normal (Gaussian, random) distribution, about 95% of the data values will fall within two standard deviations of the mean value.

4.

No length measurement can have deviations greater than 3σL from Lav as all values lie within (Lav-2σL) and (Lav + 2σL)

Wav-3σw	0.044433095
Wav+3σw	0.342966905

No. of Trials between (Wav-3σw) and (Wav + 3σw)

10

No width measurement can have deviations greater than 3σW from Wav as all values lie within (Wav-3σW) and (Wav + 3σW)

As per HOMEWORKLIB POLICY, only first 4 questions are needed to be answered. Please upload other questions as a different question.