1. Data Analysis in Excel ACADs (08-006) Covered Keywords Description
Average, median, min, max, standard deviation, variable, varp, standardize, normal distribution, norminv, normsinv
Description
Supporting Material
If you edit other slides, use Arial (Headings) 36 flush left for titles and Arial (Body) 24 for body text.

2. Analysis of Uncertainty
Data Analysis in Excel
Analysis of Uncertainty

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

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

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

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

7. 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.

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 = s2
Variance = s2

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

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

12. Exam Grade Histogram
This is the Normal overlaid with the actual grade data using the population mean and standard deviation, with data binned as 0-5, 5-10, etc. A bin listed as 70 contains the data for the bin. This is the Histogram Chart sheet generated from the data in the Grade Histogram sheet. Note the talk does not discuss how to use the Excel histogram too.
Note that the actual scores are only approximately Normally distributed. In particular, the high score is 99, but the Normal distribution predicts 1% of scores are above it. Similarly, 60 is the low score, but the distribution predicts that 1% of scores will be below it.

13. 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) =

14. 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)

15. 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
*2.33 = 5.47 mm
The distribution is available on the N(5,0.2) Data sheet in the spreadsheet.

16. 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

17. Bolt Specification
This is the N(5,0.2) Curve sheet.