Download chapt_9b - Gordon State College

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
Sample
1
x 
n
Population
n

i 1
xi
  1
Excel
=AVERAGE(cellrange)
N
N
x
i 1
i
Example:
=AVERAGE(B72:B81)
Mode
Value that occurs most often in discretized
data
Excel
=MODE(cellrange)
Example:
=MODE(B2:B81)
If tie, reports first value in list
Median
The middle value in sorted data
Excel
=MEDIAN(cellrange)
Example:
=MEDIAN(D2:D81)
Note: When using this command,
there is no need to sort the data first.
Maximum, Minimum, and
Range
Excel
=MIN(cellrange)
=MAX(cellrange)
Example:
=MIN(D2:D81)
=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
 
1
N
Sample
N
 (x
i
 )
2
i 1
Variance = 2
n
1
2
s
(
x

x
)

i
(n  1) i 1
Variance = s2
Excel
=STDEVP(cellrange)
=VARP(cellrange)
=STDEV(cellrange)
=VAR(cellrange)
Example - Exam Grades
Data set: grades.xls
78 students, 1 did not take exam
Verify the following:
Mean is 79.41
Mode is 79 - occurs 6 times
Median 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 99
min is 60
Range is 99-60 = 39
Population variance is 60.7
Population 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 Excel
Compute 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.
1
RF 
 2
1
2
 x   /  2
e 2
mean
RF
Relative
Frequency
x
Review:
Standard Normal Distribution
Define:
z  x    / 
Area = 1.00
Then
RF 
0.5
1 2
 z
e 2
0.4
0.3
0.2
2
0.1
0.0
-4.0
-3.0
-2.0
-1.0
0.0
z
1.0
2.0
3.0
4.0
Z-transform
z  x    / 
Excel
=STANDARDIZE(x,mean,stddev)
Example:
=STANDARDIZE(85,75,10) gives 1.0
Standard Normal
Cumulative Distribution
area from minus
infinity to z
0.5
0.4
0.3
NOT
0.2
0.1
0.0
-4.0
-3.0
-2.0
-1.0
0.0
1.0
Excel
=NORMSDIST(z)
2.0
3.0
4.0
0 to z, like Z-table
Example:
=NORMSDIST(1.0)
=0.8413
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
25
Frequency
20
Actual Scores
Normal Approx
15
10
5
0
50
55
60
65
70
75
80
Score Bins
85
90
95
100
Excel Example
Normal distribution with =5, =0.2
Find 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
2.5
PDF
2
1.5
1
0.5
99% Area
Tail
Tail
0
4
4.5
5
Length
5.5
6
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
550 - 600 MHz
500 - 550 MHz
450 - 500 MHz
400 - 450 MHz
350 - 400 MHz
< 350 MHz
Think-Pair-Share
In 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 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