Data Analysis in Excel ACADs (08-006) Covered Keywords average, median, min, max, standard deviation, variable, varp, standardize, normal distribution, norminv, normsinv Description Supporting Material

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

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

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

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

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