ACADs (08-006) Covered

Keywordsaverage, median, min, max, standard deviation, variable, varp, standardize, normal distribution, norminv, normsinv

Description

Supporting Material

1.1.1.2 1.1.1.4

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:

n

iixn

x1

1

N

iixN 1

1

Sample Population

Mode

Value that occurs most often in discretized data

Excel Example:=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)

2

1

)(1

N

iix

N2

1

)()1(

1xx

ns

n

ii

Variance = 2 Variance = s2

Review:The Normal Distribution

The normal distribution is sometimes called the “Gauss” curve.

22 /2

1

2

1RF

xe

mean

x

RF

RelativeFrequency

Standard Normal Cumulative Distribution

Excel Example:=NORMSDIST(z) =NORMSDIST(1.0)

=0.8413

0.0

0.1

0.2

0.3

0.4

0.5

-4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0

area from minus infinity to z

NOT

0 to z, like Z-table

Exam Grade Histogram

0

5

10

15

20

25

50 55 60 65 70 75 80 85 90 95 100

Score Bins

Fre

qu

en

cy

Actual ScoresNormal Approx

Excel Example

Normal distribution with =5, =0.2Find 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

0

0.5

1

1.5

2

2.5

4 4.5 5 5.5 6

Length

PD

F

99% AreaTail Tail