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Data Analysis in Excel
Analysis of Uncertainty
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Learning Objectives
Learn to use statistical Excel functions:average, median, min, max, stdev, var,
varp,standardize, normdist, norminv, normsinv
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RAT 9b
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General Excel Behavior
- Analyzes the range of cells you specify
- Skips blank cells
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Mean
Excel
=AVERAGE(cellrange) =AVERAGE(B72:B81)
Example:
n
iixn
x1
1
N
iixN 1
1
Sample Population
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Mode
Value that occurs most often in discretized data
Excel Example:=MODE(cellrange) =MODE(B2:B81)
If tie, reports first value in list
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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.
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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)
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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
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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
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Example Cont.
Verifymax is 99min is 60Range is 99-60 = 39Population variance is 60.7Population std. dev. is 7.79
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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
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Review:The Normal Distribution
The normal distribution is sometimes called the “Gauss” curve.
22 /2
1
2
1RF
xe
mean
x
RF
RelativeFrequency
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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
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Z-transform
Excel
=STANDARDIZE(x,mean,stddev)
Example:
=STANDARDIZE(85,75,10) gives 1.0
/ xz
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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
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Normal Data in Excel
To avoid Z transform, use:
=NORMDIST(x,mean,stddev,true)
Example
=NORMDIST(85,75,10,true)
= 0.8413
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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
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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
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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)
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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
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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
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Bolt Specification
0
0.5
1
1.5
2
2.5
4 4.5 5 5.5 6
Length
PD
F
99% AreaTail Tail
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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
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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