Data Analysis in Excel
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Transcript of Data Analysis in Excel
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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
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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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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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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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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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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