Data Analysis in Excel Analysis of Uncertainty

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

RAT 9b

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

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

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

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.

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)

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

Example - Exam Grades Data set: grades.xlsgrades.xls 78 students, 1 did not take exam Verify the following: Mean is 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

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

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

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

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

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

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

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

Exam Grade Histogram

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) = Solution 2: =NORMDIST(5.4,5,0.2,TRUE)- NORMDIST(4.8,5,0.2,TRUE) =

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)

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 = 5.47 mm

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 = = 0.52 mm Note: It is symmetrical; therefore 0.5% on either side

Bolt Specification

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 MHz MHz MHz MHz< 350 MHz MHz

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