1. PH24010 Data Handling and Statistics Use of MathCAD to handle statistical data Data storage in vectors and matrices MathCAD’s built-in functions: –Mean, standard deviation etc –Probability distributions Extending MathCAD through defining functions and programming Revision of PH1570

2. Arrays, Matrices & Vectors Way of storing related data –Experimental Results (datasets) –Coefficients One variable name, many data points Indexing –var 0, var 1, var 2, var 3 …

3. Arrays, Vectors & Matrices - Terminology Vector – 1-dimensional Matrix – 2-dimensional Array – general term, covers both

4. MathCAD and arrays Matrix toolbar has tools to: –Create and –Operate on matrices Many functions f(x) operate on matrices

5. Creating an array Same for defining ordinary variable Follow : with –[:::] from toolbar or – or –Insert|Matrix Dialog box for rows & columns

6. Creating arrays 3 –element vector – empty Placeholders to fill in Can use units

7. Data Tables Define array and input data in one operation Re-sizes to fit data From Insert|Data|Table

8. Addressing Arrays with Indices Index addressing allows access to individual elements of array Examine & Set elements Indices start at 0 Indices use [ key 2D matrices use two indices for row, column selection

9. Indices #1 Vector Example Simple 2 element vector Examine elements Set element 0 Result of setting

10. Indices #2 Matrix Example Sample matrix Examine elements Subscript too big Set element Result

11. Statistical Functions on Vectors #1 From f(x) dialog box under “Statistics” Averaging –mean() ‘Average value’ –median() ‘Half way item’ –mode() ‘Most common value’

12. Statistical Functions on Vectors #2 Variance & Standard Deviation 2 forms of each Analysis of sample –Stdev(), Var() Analysis of whole population –stdev(), var() Note capitalisation

13. Summation #1 Summation operator on matrix palette Sum of all elements in a vector

14. Summation #2 Operators on Calculus palette Do summation on any expression 2 forms –Plain => defines local RV –Range Variable => uses existing RV

15. Summation #3 Sum of first 5 integers Sum of elements 20- 30 of vector Counts

16. Writing Programs in MathCAD Can do much without programming Some algorithms need programs –Iterative, repeat until solution Can make other tasks simpler Hide detail inside a program

17. The Golden Rule of Programming Applies to all programming K.I.S.S. principle –Keep –It–It –Simple –Stupid

18. A MathCAD program All MathCAD programs are functions Expression over multiple lines Lines executed in order Local Variables Value of last line is result

19. A simple MathCAD program #1 Common subexpression calculated 3 times in function  Can re-write using a program

20. fExample(a,b) as a 2 line program 1 st line calculates sqrt & assigns to local variable ‘r’ 2 nd line calculates expression & returns answer

21. MathCAD Programs #1 Programming Palette from toolbar Select keywords from palette, DO NOT TYPE Add Line to add lines to program Watch selection box, carefully

22. MathCAD Programs #2 Assignments are local to program Assignments in program use  Can use full range of MathCAD functions in program Last line is result of program Use Vectors & Arrays to return multiple results

23. MathCAD Programs Online Help Tutorials –Getting started  Defining functions –Features In-Depth  Programming Quicksheets –Programming

24. Review of Lecture