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:

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

Example - Exam Grades

Data set: grades.xls78 students, 1 did not take exam

Verify the following:Mean is 79.41Mode is 79 - occurs 6 times

Median is 79.5 median close to mean suggests no major

outliersRemember, student who did not take exam

is not included in data More

Example Cont.

Verifymax is 99min is 60Range is 99-60 = 39Population variance is 60.7Population 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 ExcelCompute 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.

22 /2

1

2

1RF

xe

mean

x

RF

RelativeFrequency

Review: Standard Normal Distribution

Define:

Then / xz

2RF

2

2

1z

e

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 = 1.00

z

Z-transform

Excel

=STANDARDIZE(x,mean,stddev)

Example:

=STANDARDIZE(85,75,10) gives 1.0

/ xz

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

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

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

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 400 - 450 MHz550 - 600 MHz 350 - 400 MHz

500 - 550 MHz < 350 MHz 450 - 500 MHz

Think-Pair-Share

In the next 1 minute, as an individual list three specific things that you don’t

understand about today’s topicNow 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