![Differential Error Analysis…
δV is = ? Here is what you should have…
dV/dH = (π/2)HL-(3/4) πH2+(1/2) πH2
dV/dL = (π/4) H2
δV is =
[((dV/dH)δH)^2+((dV/dL)δL)^2]^0.5
What is the final function?](https://image.slidesharecdn.com/945ddd99-1038-4949-8168-2dd2681a0036-160215214814/85/1-Excel-Basics-Diff-Error-Prop-23-320.jpg)
1 Excel Basics & Diff Error Prop
- 2. Today We Will… Using Basic Functions Evaluating Functions Designing a Work Sheet Start Graphing Linest
- 3. Got Questions? We’ll Try and Have Answers Be patient there are only two of us
- 4. Intro to Excel & Math You can only have one = sign and it must be first! Only () work in excel does not like other brackets! (Excel colors them to help you tell them apart and bolds them when you move the cursor over them, yea this barely helps complain to them)
- 5. Standard Math Cont... * Is multiplication =5*8 gives 40 + Is Plus =5+8 gives 13 - Is Minus =5–8 gives - 3 / Is divide =5/8 gives 0.625 ^ is power =5^8 gives 390,625 By the way Excel doesn’t like spaces
- 6. Basic Commands =sum(A1:An) =average(A1:An) =median(A1,An) =mode(A1,An) =counta(A1,An) Note! Two Data Sets are used in the next 2 ! =slope(Y1:Yn,X1:Xn) =intercept(Y1:Yn,X1:Xn) Now I want YOU! To Find the command for R2 value for a line using the help menu Using the Help menu is supper critical!
- 7. Ok I want You to open Excel and… Start with the equation for your grade in the class Grade in Class: say in Cell C3 A1..A3 grades on midterms B1 WT midterm A5 grade on final B3 WT final C3= A1*B1+A2*B1+A3*B1+A5*B3 Example: So if you have the first line and would like Excel to calculate it you need to write it like the 2nd. = 𝐴 𝐵 ∗ 𝐸 − 𝐷 =(A/B)*E-D
- 8. Can You Set Up A Set A Set of Macro’s That Will … It Tells You What Grade You Would Need on the Final With x1,x2,x3 as mid term grades. Can you change it to add an arbitrary number of tests? Start by writing the equation forward and yes you are assigning the weight of the midterms. Your professor wouldn’t come to your house to write this into Excel for you. Assume no Home Work. Then see if you can add HW!
- 9. Combining Functions =average(data) Would Result in the same value as: =sum(data)/count(data)
- 10. What Does Excel Do When it Ignores a Value? What would the result of this calculation be? =average(A1:A9) Cells A1:A9 = 1,1,2,2,0,0, , ,ten It would be = 1 why?
- 11. What Does Excel Do When it Ignores a Value? How Many Data Points Were There? 1,1,2,2,0,0, , ,ten There is 6 Data Points Blank Cells & Text Mean NOTHING to Excel (1+1+2+2+0+0) / 6 = 1 Text and blank cells are ignored completely! (when you use the right function) PAY ATTENTION
- 12. Choosing From Multiple Functions Standard Deviation, σ, Has multiple commands (degrees o’ freedom= n) =stdev() n-1 =stdeva() n-1 =stdevpa() n =stdevp() n Which to use for small data sets? Which to use for large data sets?
- 13. Some Functions Ignore Text These two ignore text =stdev =stdevp These two will utilize text (for use in logic calculations) =stdevpa =stdeva Note the “a”
- 14. Getting Data Into Excel Excel Reads Text Try importing data as csv (Coma Separated Variable) txt (Text (Tab Delimited/Separated) Please Get the data set on Housing Prices and get it into Excel
- 15. Linest! Very Central To This Course! Using the housing data on the thumb drive being passed around. I am going to finish the lecture then return to this. (one slide I promise) Then Break / Work on the Housing Data Then like ten more slides, and work on more data! (Then the torture is over!)
- 16. After Linest… What is Left To Do Today? Can you find the Average Value of a two story house? (find and use “sort”) The Modal Value of a House? (not using sort) Can you change the format of the cells to report more less digits? Show Sigfigs? Set it so it shows house price in Scientific notation Can you set up borders around cells? Can you highlight cells? Graph House Price vs. (try everything it takes seconds)
- 17. Ok New Stuff: Differential Error Propagation Bruce Phebus
- 18. Why on Earth Do We Need This? ►This course is about both knowing how to get the answer and knowing what it means ►Differential Error Propagation- is about understanding the uncertainty in measurement and how that effects the value calculated
- 19. Definitions: They often are used to mean the same thing but… Uncertainty – How unsure you are in the value. You should always know this! Error – How wrong you are with your value. You don’t often “really” know this
- 20. Review: Volume Equations: ►Volume of a Cylinder Vcylinder = πr2l ►Volume of a Sphere Vsphere = 4/3πr3 What if you only had the Height & Length?
- 21. OK’ So we all have: Volume of Pill is = πr2l + 4/3πr3 in Height & Length? π(H/2)2(L-H) + 4/3π(H/2)3 H = Height of Pill L = Length of Pill
- 22. The partials differential with respect to the Input values is? ►You now need to find dV/dH = ? dV/dL = ? Because they go into: δV is = ((dV/dH)δH)^2+(dV/dL)δL)^0.5 𝛿V = 𝑑V 𝑑H 𝛿H 2 + 𝑑V 𝑑L 𝛿L 2 1 2
- 23. Differential Error Analysis… δV is = ? Here is what you should have… dV/dH = (π/2)HL-(3/4) πH2+(1/2) πH2 dV/dL = (π/4) H2 δV is = [((dV/dH)δH)^2+((dV/dL)δL)^2]^0.5 What is the final function?
- 24. The Questions for Today What is the volume of each Pill? in mm3 What is the uncertainty in that Volume? Which value is dominant in calculating the uncertainty? δH 0.003 mm δL 0.005 mm How would you get the above values?
- 25. How do you get δH & δL In Real Life? There Are Two Primary Ways o Know the Uncertainty in Measurement o Take the standard deviation of a population Known! to be perfect by some other means Using the Standard Deviation is the poorer option but is often used incorrectly! Why?
- 26. Answer These Questions • What was the volume difference between the largest and smallest pill? • Compare uncertainty in volume to its volume? Get an error in percent? • Which Uncertainty is dominant?<=Uber Necessary NEXT WEEK BRING A RULLER I Don’t advise Printing one!