data analysis in excel
Post on 03-Jan-2016
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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
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
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