Uncertainty

background [prelab assignment (30 points) due at the begining of lab]

1. describe below Excel commands / concepts and its syntax; include a copy in your lab NB. (10 points)

NORM. DIST

NORM.INV

absolute versus relative cell reference

AVERAGE()

STDEV()

2. what is the equation that describes the Normal probability density function (pdf) ? what are the parameters in this pdf ? (3 points)

3. what is a histogram ? sketch a histogram of the Normal pdf. (3 points)

4. what is "propagation of errrors" ? what is "percent error" ? (3 points)

5. what is a Monte Carlo simulation (you will be developing some Monte Carlo simulations) ? (3 points)

6. describe "claims evidence reasoning" pedagogy. (3 points)

7. what is regression analysis ? rationale / basis of least-squares analysis ? (5 points)

purpose

fulfill CB "lab data anlaysis" expectations

refer to various tabs in the Excel student template

pdf tab: calculate the probabiltiy in a Normal pdf, then explore the role of the mean and standard deviation in determining the shape of the graph of the Normal pdf

mean_SD tab: simulate a Normal pdf, then compare the theoretical value of the parameters in a Normal pdf versus its empirical values; calculate % error for each parameter in the Normal pdf

histogram tab: describe the histogram of simulated data from a Normal pdf

prop errors tab: compare the relative SD in z, where

z = x - y

z = x + y

z = x + a y

z = x y

z = x / y

prop errors - theory tab: explore / analyze data; e.g. impact / influence of SD(x) (and "a" ) on SD(z). calculate the % error in SD(z) between theoretical versus Monte Carlo value, where z = x + y; SD(x) = SD(y) = 100

regression tabs: relate "sum of square difference" versus "quality" of how well the "best-fit" line describes the (simulated) experimental data as a function of the relative values of the slope and / or y-intercept between theory versus empirical value.

materials

computer with access to the internet & Excel spreadsheet software

Excel student template

methods / data analysis

information in Excel-based student template - fill-in various cells with appropriate formulas

content of lab report [35 points]

Using a CER format (refer to the preceding purpose section), in regards to the Excel student template, address each tab:

pdf tab

mean_SD tab

histogram tab

prop errors tab

prop errors - theory tab (hint: a graph would be helpful)

regression tab: y = mx

regression tab: y = mx + b

in regards to evidence, use screen shots / image of the appropriate content in the preceding Excel template or generate your own table / graphs.

identify / label each of the CER components for each of the student Excel template tabs.

resources

Excel template - teacher version

propogation of errors - pdf

statistics of experimental data - pdf

Claims Evidence Reasoning (CER) - website