ESM 350, Structure and Electronic Properties of Solids

Homework 2:  Gaussian Distribution  

The inlet pressure in a reactor was measured 100 times. 
The following is a summary of the results:

Pressure	 # of results	 (X-x)^2
3.970		1

3.980		3

3.990		12

4.000		25

4.010		33

4.020		17

4.030		6

4.040		2

4.050 		1

1. Calculate the mean (X) standard deviation (S), and standard deviation 
   of the mean (Sm) for this set of data. 

2. Plot a Histogram of the points. 

3. When given a set of data, Sturgis Rule is frequently used to 
   determine if the number of "bins" is sufficient for statistical analysis.

   Sturgis Rule: N=1+3.3 log n,
   where N is the number of bins and n is the total number of measurements. 
   Using Sturgis Rule please determine if we have sufficient Bins in this case.

4. Calculate the percent of results which deviate by 
   (a) one standard deviation, Sm from the mean 
   (b) two standard deviations, +/- 2Sm, from the mean 
   (c) three +/- 3Sm. 
   Compare with the results expected from a Gaussian disctribution.

5. In the third column plot the quantity (X-x)^2,
   where X is the mean of the pressure values,x.

6. Plot N(x) vs (X-x)^2 on a semi log scale and find the slope and intercept.

7. Compare to your expectation for a Gaussian distribution for N(x) 

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03/21/03 JQ.