1. Data Analysis in Excel Analysis of Uncertainty

2. Learning Objectives Learn to use statistical Excel functions: average, median, min, max, stdev, var, varp, standardize, normdist, norminv, normsinv

3. RAT 9b

4. General Excel Behavior - Analyzes the range of cells you specify - Skips blank cells

5. Mean Excel =AVERAGE(cellrange) =AVERAGE(B72:B81) Example: SamplePopulation

6. Mode Value that occurs most often in discretized data ExcelExample: =MODE(cellrange) =MODE(B2:B81) If tie, reports first value in list

7. Median The middle value in sorted data Excel =MEDIAN(cellrange) =MEDIAN(D2:D81) Example: Note: When using this command, there is no need to sort the data first.

8. Maximum, Minimum, and Range Excel Example: =MIN(cellrange) =MIN(D2:D81) =MAX(cellrange) =MAX(D2:D81) There is no explicit command to find the range. However, it can be easily calculated. = MAX(D2:D81) - MIN(D2:D81)

9. Standard Deviation and Variance Population Sample Excel =STDEVP(cellrange) =STDEV(cellrange) =VARP(cellrange) =VAR(cellrange) Variance = 2 Variance = s 2

10. Example - Exam Grades Data set: grades.xlsgrades.xls 78 students, 1 did not take exam Verify the following: Mean is 79.41 Mode is 79 - occurs 6 times Median is 79.5 median close to mean suggests no major outliers Remember, student who did not take exam is not included in data More

11. Example Cont. Verify max is 99 min is 60 Range is 99-60 = 39 Population variance is 60.7 Population std. dev. is 7.79

12. Team Exercise - 15 min Collect ages (in months) of team members and members of teams around you (at least 15 values) Enter as a column in Excel Compute mean, mode, median, max, min, range, sample variance and std. dev. using Excel commands

13. Review: The Normal Distribution The normal distribution is sometimes called the Gauss curve. mean x RF Relative Frequency

14. Review: Standard Normal Distribution Define: Then Area = 1.00 z

15. Z-transform Excel =STANDARDIZE(x,mean,stddev) Example: =STANDARDIZE(85,75,10) gives 1.0

16. Standard Normal Cumulative Distribution Excel Example: =NORMSDIST(z) =NORMSDIST(1.0) =0.8413 area from minus infinity to z NOT 0 to z, like Z-table

17. Normal Data in Excel To avoid Z transform, use: =NORMDIST(x,mean,stddev,true) Example =NORMDIST(85,75,10,true) = 0.8413

18. Exam Grade Histogram

19. Excel Example Normal distribution with =5, =0.2 Find area from 4.8 to 5.4 Solution 1: =STANDARDIZE(4.8,5,0.2)Gives -1 =STANDARDIZE(5.4,5,0.2)Gives 2 =NORMSDIST(2)-NORMSDIST(-1) = 0.8186 Solution 2: =NORMDIST(5.4,5,0.2,TRUE)- NORMDIST(4.8,5,0.2,TRUE) = 0.8186

20. Inverse Problem Given, and probability, find x =NORMINV(prob,mean,stddev) Given probability, find z =NORMSINV(prob) Note: The probability is the area under the curve from minus infinity to x (or z)

21. Inverse Problem: Example 1 A batch of bolts have length =5.00 mm, =0.20 mm. 99% of the bolts are shorter than what length? Solution 1: =NORMINV(0.99,5,0.2) gives 5.47 mm Solution 2: =NORMSINV(0.99) = 2.33 5.00+0.20*2.33 = 5.47 mm

22. Inverse Problem: Example 2 A batch of bolts have length =5.00 mm, =0.20 mm. The bolt length is specified as 5.00 mm tolerance. What is the value of the tolerance such that 99% of the bolts are encompassed? Solution: =NORMINV(0.995,5,0.2) = 5.52 mm =NORMINV(0.005,5,0.2) = 4.48 mm Tolerance = 5.52 - 5.00 = 0.52 mm Note: It is symmetrical; therefore 0.5% on either side

23. Bolt Specification

24. Team Exercise The clock frequency of a batch of Intel microprocessors was measured to be a normal distribution with =475 MHz, =50 MHz. What fraction of processors can be sold in each category? >600 MHz 400 - 450 MHz 550 - 600 MHz350 - 400 MHz 500 - 550 MHz< 350 MHz 450 - 500 MHz

25. Think-Pair-Share In the next 1 minute, as an individual list three specific things that you dont understand about todays topic Now take 2 minutes to merge your list with the person sitting next to you AND add 1 new item to the list In the next 5 minutes share the results with the other half of your team, delete questions that you can answer for each other, AND prioritize the remaining questions your list