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 RangeExcel 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

iixN

2

1

)()1(

1 xxn

sn

ii

Variance = 2 Variance = s2

Example - Exam GradesData set: grades.xls

78 students, 1 did not take examVerify the following:

Mean is 79.41Mode is 79 - occurs 6 timesMedian is 79.5

median close to mean suggests no major outliers

Remember, student who did not take exam is not included in data More

Example Cont.Verify

max is 99min is 60Range is 99-60 = 39Population variance is 60.7Population std. dev. is 7.79

Team Exercise - 15 minCollect 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 /21

21RF

xe

mean

x

RFRelativeFrequency

Review: Standard Normal DistributionDefine:

Then / xz

2RF

2

21 z

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 ExcelTo 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

Freq

uenc

y

Actual ScoresNormal Approx

Excel ExampleNormal 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 2A 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 mmNote: 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 6Length

PDF

99% AreaTail Tail

Team ExerciseThe 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-ShareIn 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 listIn 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