Data Analysis in Excel Analysis of Uncertainty

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 Sample 1 x n Population n xi i 1 Excel AVERAGE(cellrange) 1 N N x i i 1 Example: AVERAGE(B72:B81)

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

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

Maximum, Minimum, and Range Excel Example: MIN(cellrange) MAX(cellrange) MIN(D2:D81) 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 1 N Sample N (x i ) 2 i 1 Variance 2 n 1 2 s ( xi x ) (n 1) i 1 Variance s2 Excel STDEVP(cellrange) VARP(cellrange) STDEV(cellrange) VAR(cellrange)

Example - Exam Grades Data set: grades.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 More is not included in data

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

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. 1 RF 2 1 2 x / 2 e 2 mean RF Relative Frequency x

Review: Standard Normal Distribution z x / Define: Then Area 1.00 0.5 1 2 z e 2 RF 0.4 0.3 0.2 2 0.1 0.0 -4.0 -3.0 -2.0 -1.0 0.0 z 1.0 2.0 3.0 4.0

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

Standard Normal Cumulative Distribution area from minus infinity to z 0.5 0.4 0.3 NOT 0.2 0.1 0.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 Excel NORMSDIST(z) 2.0 3.0 4.0 0 to z, like Z-table Example: NORMSDIST(1.0) 0.8413

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

Exam Grade Histogram 25 Frequency 20 Actual Scores Normal Approx 15 10 5 0 50 55 60 65 70 75 80 Score Bins 85 90 95 100

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

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 5.00 0.20*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 5.52 - 5.00 0.52 mm Note: It is symmetrical; therefore 0.5% on either side

Bolt Specification 2.5 PDF 2 1.5 1 0.5 99% Area Tail Tail 0 4 4.5 5 Length 5.5 6

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 550 - 600 MHz 500 - 550 MHz 450 - 500 MHz 400 - 450 MHz 350 - 400 MHz 350 MHz

Think-Pair-Share In the next 1 minute, as an individual list three specific things that you don’t understand about today’s 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