Solution to
Homework #1
MGS 8110, Regression & Forecasting
Summer 2012
Solution HW #1
MGS 8110
1
READING:
Review the material in Lectures L00A, L00D, L00E & L00I.
Read Chapters 2 of the textbook.
Read Chapters 3 through 5. This is a lot of reading and you have 7 weeks
to complete this reading assignment. Please step up and take a big bite
out of it this week because you have minimal calculations to do this
week (see below).
Submittals for this HW.
The last worksheet in DATA HW01.xls is the Answer Sheet. Fill in the
blank cells and submit this sheet. Present 3 significant digits when
appropriate. Hints are shown in Blue on the Answer Sheet. Eliminate
the color coding before printing the Answer Sheet. Look over the
Answer sheet before doing any calculation so that you know what is
required.
Solution HW #1
MGS 8110
2
Part A Access Class Notes
Download the class notes, homework, etc. from our Web page.
http://www.gsu.edu/~mgtrks/
Click on the MGS 8110, then Lecture 00. The downloads are PowerPoint
presentations and can be printed 2 or 6 per page (in Power Point 2003
go to FILE/PRINT, then “Print what = handouts” and “Slides per page =
6”) (in Power Point 2007 go to View on toolbar, then / Handout Master /
Slides Per Page /).
Solution HW #1
MGS 8110
3
Part B MS Equation Practice using MS Equation by duplicating the
equations shown at the right. Change the x's to y's to verify that you
used MS Equations and did not just cut-&-paste the box shown at the
right. Submittal: Paste you three equations in one box on the right
side of your Answer Sheet.
 b  b 2  4ac
X 
2a
N  X :  ,  
1
2 
e
1   X   
 

2  
2
 .975 Acme


Life  7.08   .377  HiPower
 1.012  Stancell


Solution HW #1
MGS 8110
4
Part C
Basic Excel Calculations
C0. Access the Osyter Data in the first worksheet of DATA HW01.xls. The definition of the variables is given in the
second worksheet.
C1. Create an exact copy of the date in the first worksheet. That is, make a duplicate copy of the 1st worksheet. Label
the tab for the first worksheet "DATA - original". Label the tab for the third worksheet "DATA - Analysis #1".
C2. Create an "Index Column" at the far left of the data array. Each row of data should be given a sequential number
from 1 to 30.
C3. Make a duplicate copy of the data in the third worksheet and label the tab of the fourth worksheet "DATA - Analysis
#2".
Until told different, you should be doing the subsequent calculations in the worksheet, DATA - Analysis #1. This is
the first of the two new worksheets.
C4. Create four cells at the bottom of the column of data and calculate the Mean, Standard Deviation, Skewness and
Kurtosis for Weight, Volume, 3D & 2D. Which of variables appears to be Normally Distributed.
C5. Create a column to the right of the 2D column and classify the oysters by volume. Label the column "Class". Less than
10 cc is "S" (Small), 10 to 13 cc is "M" (Medium) and greater than 13 is "L" (Large). Use a nested IF command.
C6. Add three cells at the bottom of the Class column and state the number of Small, Medium and Large oysters in the
sample. Use the COUNTIF command in Excel.
C7. Add two columns to the right of the “Class” and convert the Weight in grams to Weight in ounces and convert the
volume in cc to volume in fluid ounces. Label the columnsWt_oz and Vol_oz.
C8. Add another column to the right of Vol_oz column and calculate the Ratio of Weight to Volume. State these values as
percentages. Title the column "Ratio WtVol". Does it matter if you use the two columns with metric units or the two
columns with US units?
C9. Create three cells at the bottom of the Ratio WtVol column and calculate the 1st Quartile, 2nd Quartile and 3rd
Quartile. Use the Excel command QUARTILE.
C10. Create a fourth cell at the bottom of the Ratio WtVol column and calculate the 90th Percentile. Use the Excel
command PERCENTILE.
C11 Add another column to the right of the Ratio WtVol column. Print the rank of each oyster in terms of volume. The
oyster with a rank of 1 has the highest volume of the 30 oysters. Use the RANK function. Title the column
"Rank.Vol".
C12. For the variable "Pixels_3D", create three cells at the bottom of the column: 1) Median, 2) Percentage for the Mean,
3) Percentage for the Median and 4) the Difference between the Percentage Mean and Percentage Median. HINT:
use the PercentRank function in Excel to calculate the two percentage rows, that is for 2) and 3).
C13. Based on the difference between the % Mean and the % Median, is Pixels_3D normally distributed? Base on the
calculated values of Skewness and Kurtosis is Pixels_3D normally distributed?
Solution HW #1
MGS 8110
5
Part C Basic Excel
Calculations
C0. Access the Osyter Data in the
first worksheet of DATA
HW01.xls. The definition of the
variables is given in the second
worksheet.
C1. Create an exact copy of the
date in the first worksheet.
That is, make a duplicate copy of
the 1st worksheet. Label the
tab for the first worksheet
"DATA - original". Label the tab
for the third worksheet "DATA
- Analysis #1".
C2. Create an "Index Column" at the
far left of the data array. Each
row of data should be given a
sequential number from 1 to 30.
Solution HW #1
Oyster_ID
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Oyster_Weight_g Oyster_Volume_cc Pixels_3D
12.92
13.04
5136699
11.4
11.71
4795151
17.42
17.42
6453115
6.79
7.23
2895239
9.62
10.03
3672746
15.5
15.59
5728880
9.66
9.94
3987582
7.02
7.53
2678423
12.56
12.73
5481545
12.49
12.66
5016762
10.12
10.53
3942783
10.64
10.84
4052638
12.99
13.12
5334558
8.09
8.48
3527926
14.09
14.24
5679636
10.73
11.11
4013992
15.17
15.35
5565995
15.5
15.44
6303198
5.22
5.67
1928109
7.75
8.26
3450164
10.71
10.95
4707532
7.91
7.97
3019077
6.93
7.34
2768160
13.63
13.21
4945743
7.67
7.83
3138463
11.27
11.38
4410797
10.98
11.22
4558251
8.87
9.25
3449867
13.68
13.75
5609681
14.27
14.37
5292105
MGS 8110
Pixels_2D
47907
41458
60891
29949
41616
48070
34717
27230
52712
41500
31216
41852
44608
35343
47481
40976
65361
50910
22895
34804
37156
29070
24590
48082
32118
45112
37020
39333
51351
53281
6
Part C
Basic Excel Calculations
C4. Create four cells at the bottom of the
column of data and calculate the Mean,
Standard Deviation, Skewness and Kurtosis
for Weight, Volume, 3D & 2D. Which of
variables appears to be Normally
Distributed.
Oyster_ID Oyster_Weight_g Oyster_Volume_cc Pixels_3D Pixels_2D
1
12.92
13.04
5136699
47907
2
11.4
11.71
4795151
41458
3
17.42
17.42
6453115
60891
4
6.79
7.23
2895239
29949
5
9.62
10.03
3672746
41616
6
15.5
15.59
5728880
48070
7
9.66
9.94
3987582
34717
8
7.02
7.53
2678423
27230
9
12.56
12.73
5481545
52712
10
12.49
12.66
5016762
41500
11
10.12
10.53
3942783
31216
12
10.64
10.84
4052638
41852
13
12.99
13.12
5334558
44608
14
8.09
8.48
3527926
35343
15
14.09
14.24
5679636
47481
16
10.73
11.11
4013992
40976
17
15.17
15.35
5565995
65361
18
15.5
15.44
6303198
50910
=IF(AND(B35>=-1,B35<=1,B36>=-1,B36<=1),"Yes","NO")
19
5.22
5.67
1928109
22895
20
7.75
8.26
3450164
34804
21
10.71
10.95
4707532
37156
22
7.91
7.97
3019077
29070
=STDEV(C2:C31)
23
6.93
7.34
2768160
24590
24
13.63
13.21
4945743
48082
25
7.67
7.83
3138463
32118
=KURT(E2:E31)
26
11.27
11.38
4410797
45112
=AVERAGE(B2:B31)
27
10.98
11.22
4558251
37020
28
8.87
9.25
3449867
39333
=SKEW(D2:D31)
29
13.68
13.75
5609681
51351
30
14.27
14.37
5292105
53281
Mean =
St Dev =
Skewness =
Kurtosis =
Normal ?
Solution HW #1
MGS 8110
11.05
3.10
0.07
-0.79
Yes
11.27
2.96
0.08
-0.74
Yes
4,384,827
1,169,077
-0.16
-0.82
Yes
44364.20
10289.51
0.28
-0.15
Yes
7
Part C Basic
ExcelOyster_Weight_g
Oyster_ID
12.92
Calculations 1
C5.
C6.
Oyster_Volume_cc Pixels_3D Pixels_2D
13.04
5136699
47907
2
11.4
11.71
4795151
41458
Create a column3 to the right
17.42
17.42
6453115
60891
=IF(C2<=10,"S",IF(C2>13,"L","M"))
of the 2D column
4 and classify
6.79
7.23
2895239
29949
5
9.62
10.03
3672746
41616
the oysters by volume.
Label
6
15.5
15.59
5728880
48070
OR
the column "Class".
Less than
7
9.66
9.94
3987582
34717
10 cc is "S" (Small), 10 to 13
8
7.02
7.53
2678423
27230
=IF(C2<=10,"S",IF(C2<13,"M",IF(C2>13,"L","***")))
cc is "M" (Medium)
9 and
12.56
12.73
5481545
52712
greater than 1310
is "L" (Large).
12.49
12.66
5016762
41500
Use a nested IF11command. 10.12
10.53
3942783
=B2*gmToz 31216
10.64
10.84
4052638
41852
Add three cells12at the
13
12.99
13.12
5334558
44608
OR
bottom of the Class
column
14
8.09
8.48
3527926
35343
and state the number
of
15
14.09
14.24
5679636
47481
=B2*$G$40
Small, Medium and
16 Large 10.73
11.11
4013992
40976
17
15.35
5565995
65361
oysters in the sample.
Use15.17
the COUNTIF command in
Excel.
C7. Add two columns to the right
of the “Class” and convert the
Weight in grams to Weight in
ounces and convert the
volume in cc to volume in fluid
ounces. Label the
columnsWt_oz and Vol_oz.
Solution HW #1
Class
Wt_oz
L
0.456
M
0.402
L
0.614
S
0.240
M
0.339
L
0.547
S
0.341
S
0.248
M
0.443
M
0.441
M
=C2*ccToz0.357
M
0.375
L
0.458
OR
S
0.285
L
0.497
=C2*$G$41
M
0.378
L
0.535
S
0.244
Vol_oz
0.441
0.396
0.589
0.244
0.339
0.527
0.336
0.255
0.430
0.428
0.356
0.367
0.444
0.287
0.482
0.376
0.519
0.248
L
0.481
0.447
=COUNTIF($F$2:$F$31,"S")
gm to oz
cc to oz
MGS 8110
0.035274 "gmToz"
0.033814 "ccToz"
S
0.271
0.265
M
0.398
0.385
=COUNTIF($F$2:$F$31,"L")
M
0.387
0.379
S
0.313
0.313
L
0.483
0.465
L
0.503
0.486
10
10
10
8
Part C
Basic Excel Calculations
C8. Add another column to the right of Vol_oz column and
calculate the Ratio of Weight to Volume. State these
values as percentages. Title the column "Ratio WtVol".
Does it matter if you use the two columns with metric units
or the two columns with US units?
C9. Create three cells at the bottom of the Ratio WtVol
column and calculate the 1st Quartile, 2nd Quartile and 3rd
Quartile. Use the Excel command QUARTILE.
C10. Create a fourth cell at the bottom of the Ratio WtVol
column and calculate the 90th Percentile. Use the Excel
command PERCENTILE.
C11 Add another column to the right of the Ratio WtVol
column. Print the rank of each oyster in terms of volume.
The oyster with a rank of 1 has the highest volume of the
30 oysters. Use the RANK function. Title the column
"Rank.Vol".
Solution HW #1
MGS 8110
Ratio WtVol
Rank Vol
0.991
1.033576
10
0.974
1.015559
13
1.000
1.043176
1
0.939
0.97969
29
0.959
1.000533
20
0.994
1.037153
2
0.972
1.01379
21
0.932
0.972522
=Weight/Volume) 27
0.987
1.029245
11
0.987
1.029168
12
=G2/H2
0.961
1.002558
19
0.982
1.023929
18
0.990
1.032839
9
0.954
0.995199
23
0.989
1.032187
6
0.966
1.007495
16
=RANK(C2,Volume)
0.988
1.030943
4
1.004
1.047229
3
or
0.921
0.960384
30
0.938
0.978766
24
=RANK(Volume,Volume)
0.978
1.020311
17
0.992
1.035322
25
0.944
0.984906
28
1.032
1.076342
8
=QUARTILE(I$2:I$31,$K33)
0.980
1.021859
26
0.990
1.033092
why the $ signs 14
0.979
1.020862
15
0.959
1.000321
22
0.995
1.037865
7
=PERCENTILE(J2:J31,0.9)
0.993
1.035916
5
0.960
0.981
0.991
0.9954
1.001
1.023
1.033
1.0384
1
2
3
Percentile 90%
9
Part C
Basic Excel Calculations
C0. Access the Osyter Data in the first worksheet of DATA HW01.xls. The definition of the variables is given in the
second worksheet.
C1. Create an exact copy of the date in the first worksheet. That is, make a duplicate copy of the 1st worksheet. Label
the tab for the first worksheet "DATA - original". Label the tab for the third worksheet "DATA - Analysis #1".
C2. Create an "Index Column" at the far left of the data array. Each row of data should be given a sequential number
from 1 to 30.
C3. Make a duplicate copy of the data in the third worksheet and label the tab of the fourth worksheet "DATA - Analysis
#2".
Until told different, you should be doing the subsequent calculations in the worksheet, DATA - Analysis #1. This is
the first of the two new worksheets.
C4. Create four cells at the bottom of the column of data and calculate the Mean, Standard Deviation, Skewness and
Kurtosis for Weight, Volume, 3D & 2D. Which of variables appears to be Normally Distributed.
C5. Create a column to the right of the 2D column and classify the oysters by volume. Label the column "Class". Less than
10 cc is "S" (Small), 10 to 13 cc is "M" (Medium) and greater than 13 is "L" (Large). Use a nested IF command.
C6. Add three cells at the bottom of the Class column and state the number of Small, Medium and Large oysters in the
sample. Use the COUNTIF command in Excel.
C7. Add two columns to the right of the “Class” and convert the Weight in grams to Weight in ounces and convert the
volume in cc to volume in fluid ounces. Label the columnsWt_oz and Vol_oz.
C8. Add another column to the right of Vol_oz column and calculate the Ratio of Weight to Volume. State these values as
percentages. Title the column "Ratio WtVol". Does it matter if you use the two columns with metric units or the two
columns with US units?
C9. Create three cells at the bottom of the Ratio WtVol column and calculate the 1st Quartile, 2nd Quartile and 3rd
Quartile. Use the Excel command QUARTILE.
C10. Create a fourth cell at the bottom of the Ratio WtVol column and calculate the 90th Percentile. Use the Excel
command PERCENTILE.
C11 Add another column to the right of the Ratio WtVol column. Print the rank of each oyster in terms of volume. The
oyster with a rank of 1 has the highest volume of the 30 oysters. Use the RANK function. Title the column
"Rank.Vol".
C12. For the variable "Pixels_3D", create three cells at the bottom of the column: 1) Median, 2) Percentage for the Mean,
3) Percentage for the Median and 4) the Difference between the Percentage Mean and Percentage Median. HINT:
use the PercentRank function in Excel to calculate the two percentage rows, that is for 2) and 3).
C13. Based on the difference between the % Mean and the % Median, is Pixels_3D normally distributed? Base on the
calculated values of Skewness and Kurtosis is Pixels_3D normally distributed?
Solution HW #1
MGS 8110
10
Part C
Basic Excel Calculations
C12. For the variable "Pixels_3D", create three cells at the bottom of the column: 1) Median, 2)
Percentage for the Mean, 3) Percentage for the Median and 4) the Difference between the
Percentage Mean and Percentage Median. HINT: use the PercentRank function in Excel to
calculate the two percentage rows, that is for 2) and 3).
C13. Based on the difference between the % Mean and the % Median, is Pixels_3D normally
distributed? Base on the calculated values of Skewness and Kurtosis is Pixels_3D normally
distributed?
Mean =
St Dev =
Skewness =
Kurtosis =
Normal ?
11.05
3.10
0.07
-0.79
Yes
=MEDIAN(Vol3D)
11.27
2.96
0.08
-0.74
Yes
4,384,827
1,169,077
-0.16
-0.82
Yes
44364.20
10289.51
0.28
-0.15
Yes
Median = 4,484,524
% Mean
48.0%
% Median
50.0%
Difference
-2.0%
=PERCENTRANK(Vol3D,D33)
=PERCENTRANK(Vol3D,D39)
Solution HW #1
MGS 8110
=D40-D41
11
Part D
Population Differences
Now go to the worksheet, DATA - Analysis #2.
D1. Sort the data in terms of the Class.. You are creating three sub populations: Small,
Medium and Large. In Excel click on the Data icon on the uppermost toolbar, then click on
Sort.
D2. Calculate the Average, Standard Deviation and the Coefficient of Variation for "Volume in
cc" for each of the three sub-populations.
Oyster_ID Oyster_Weight_g Oyster_Volume_cc Pixels_3D Pixels_2D Class
Mean
StDev Coef Var
D3. How good are these
estimate
of the 7.23
Means? 2895239
Calculate
a 95 %S confidence
interval
for each
4
6.79
29949
7.950
1.169
0.147
7
9.66
9.94
3987582
34717
S
of the three means..
Solution HW #1
8
14
19
20
22
23
25
28
2
5
9
10
11
12
16
21
26
27
1
3
6
13
15
17
18
24
29
30
7.02
7.53
2678423
27230
=G2-2*H2/SQRT(10)
8.09
8.48
3527926
35343
5.22
5.67
1928109
=G2+2*H2/SQRT(10) 22895
7.75
8.26
3450164
34804
7.91
7.97
3019077
29070
6.93
7.34
2768160
24590
7.67
7.83
3138463
32118
8.87
9.25
3449867
39333
11.4
11.71
4795151
41458
9.62
10.03
3672746
41616
12.56
12.73
5481545
52712
12.49
12.66
5016762
41500
10.12
10.53
3942783
31216
10.64
10.84
4052638
41852
10.73
11.11
4013992
40976
10.71
10.95
4707532
37156
11.27
11.38
4410797
45112
10.98
11.22
4558251
37020
12.92
13.04
5136699
47907
=G22-2*H22/SQRT(10)
= 13.668
17.42
17.42
6453115
60891
15.5
15.59
5728880
48070
or 12.99
13.12
5334558
44608
14.09
14.24
5679636
47481
=$G$22-NORMSINV(0.975)*$H$22/SQRT(10) = 13.685
15.17
15.35
5565995
65361
15.5
15.44
6303198
50910
or
13.63
13.21
4945743
48082
13.68
13.75
5609681
=$G$22-TINV(0.05,9)*$H$22/SQRT(10) = 13.552 51351
14.27
14.37
5292105
53281
MGS 8110
S
S
S
S
S
S
S
S
M
M
M
M
M
M
M
M
M
M
L
L
L
L
L
L
L
L
L
L
7.210
8.690
L CI for Mean
U CI for Mean
=AVERAGE($C2:$C11)
11.316
10.772
11.860
0.860
0.076
L CI for Mean
U CI for Mean
=STDEV($C12:$C21)
14.553
13.668
15.438
1.400
0.096
L CI for Mean
U CI for Mean
=H22/G22
12
Part E
Data Analysis Add-in
E0.
Load the Add-in "Data analysis" to your Excel (see slides 44 thru 50 of L00D). Access
the Oyster Data.
E1. Use / Data Analysis / Descriptive Statistics to calculate basic statistics for th four
variables: Weight, Volume, 3D and 2D.
Oyster_Weight_g
Oyster_Volume_cc Pixels_3D
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Solution HW #1
11.1
0.566
10.9
15.5
3.10
9.60
-0.792
0.074
12.2
5.2
17.4
331.6
30
MGS 8110
11.3
0.541
11.2
#N/A
2.96
8.78
-0.741
0.077
11.8
5.7
17.4
338.2
30
4,384,827
213,443
4,484,524
#N/A
1,169,077
1,366,740,731,439
-0.825
-0.157
4,525,006
1,928,109
6,453,115
131,544,817
30
Pixels_2D
41,287
1,879
41,479
#N/A
10,290
105,874,081
-0.155
0.278
42,466
22,895
65,361
1,238,609
30
13
Part E
Data Analysis Add-in
E2. Calculate the correlation between 4 variables using / Data Analysis / Correlation / in Excel.
Weight_g Volume_cc
Oyster_Weight_g
1.000
Oyster_Volume_cc
0.999
1.000
Pixels_3D
0.976
0.977
Pixels_2D
0.918
0.920
Solution HW #1
MGS 8110
Pixels_3D
Pixels_2D
1.000
0.893
1.000
14
Part F Normal Distribution
The transaction time at an ATM is approximately normally distributed with a mean of 20
seconds and a standard deviation of 8 seconds.
F1. What is the probability that a transaction takes more than 30 seconds?
F2. What is the probability that a transaction takes more than 35 seconds?
F3. What is the probability that a transaction takes less than 15 seconds?
F4. What is the probability that a transaction takes between 15 and 25 seconds?
F5. Ten percent of the customers will have a transaction time greater than what value (in
seconds)?
Solution HW #1
MGS 8110
15
Part F Normal Distribution
The transaction time at an ATM is approximately normally
distributed with a mean of 20 seconds and a standard deviation of 8 seconds.
F1. What is the probability that a transaction takes more than 30 seconds?
F2. What is the probability that a transaction takes more than 35 seconds?
F3. What is the probability that a transaction takes less than 15 seconds?
F4. What is the probability that a transaction takes between 15 and 25 seconds?
F5. Ten percent of the customers will have a transaction time greater than what value (in
seconds)?
F6. Calculate a so-called 95% Confidence interval for transaction times, that is calculate the
2.5 percentile point and the 97.5 percentile point.
F7. In class you were told that you could frequently approximate a 95% Confidence Interval by
multiplying the standard deviation by 2 and then adding and subtracting that from the
average. The actual formula is shown below. Calculate this approximate 95% CI.
CI .95  X  2 X
Solution HW #1
0.106
0.030
0.266
0.468
=1-NORMDIST(30,20,8,1)
=1-NORMDIST(35,20,8,1)
=NORMDIST(15,20,8,1)
=NORMDIST(25,20,8,1)-NORMDIST(15,20,8,1)
30.3
4.32
35.68
=NORMINV(0.9,20,8)
=NORMINV(0.025,20,8)
=NORMINV(0.975,20,8)
4.00
36.00
=20-2*8
=20+2*8
MGS 8110
16
B
Paste your MS Equations somewhere on this Answer Sheet.
Hints are shown in blue.
Answer Sheet
0.106
0.030
0.266
0.468
=1-NORMDIST(30,20,8,1)
=1-NORMDIST(35,20,8,1)
=NORMDIST(15,20,8,1)
=NORMDIST(25,20,8,1)-NORMDIST(15,20,8,1)
30.3
4.32
35.68
=NORMINV(0.9,20,8)
=NORMINV(0.025,20,8)
=NORMINV(0.975,20,8)
4.00
36.00
=20-2*8
=20+2*8
St Dev
Skewness
Kurtosis
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
S
M
L
S
S
M
M
M
M
L
S
L
M
L
L
S
S
M
S
S
L
S
M
M
S
L
L
Normally distributed?
0.240
0.339
0.547
0.341
0.248
0.443
0.441
0.357
0.375
0.458
0.285
0.497
0.378
0.535
0.547
0.184
0.273
0.378
0.279
0.244
0.481
0.271
0.398
0.387
0.313
0.483
0.503
0.244
0.339
0.527
0.336
0.255
0.430
0.428
0.356
0.367
0.444
0.287
0.482
0.376
0.519
0.522
0.192
0.279
0.370
0.269
0.248
0.447
0.265
0.385
0.379
0.313
0.465
0.486
C5
Excel IF statement used for the first cell in the Class column.
C6
Excel COUNTIF statement used for the Small count.
C9 & C10
0.960
0.981
0.991
0.9954
C13
Yes of No
Yes of No
D2 & D3
E
Solution HW #1
Average
1.001
1.023
1.033
1.0384
1st Quartile
2nd Quartile
3rd Quartile
90th Percentile
Ratio WtVol
Rank Vol
0.991
10
1.033576
0.974
13
1.015559
1.000
1
1.043176
0.939
0.97969
29
0.959
1.000533
20
0.994
1.037153
2
0.972
1.01379
21
0.932
0.972522
27
0.987
1.029245
11
0.987
1.029168
12
0.961
1.002558
19
0.982
1.023929
18
0.990
1.032839
9
0.954
0.995199
23
0.989
1.032187
6
0.966
1.007495
16
0.988
1.030943
4
1.004
1.047229
3
0.921
0.960384
30
0.938
0.978766
24
0.978
1.020311
17
0.992
1.035322
25
0.944
0.984906
28
1.032
1.076342
8
0.980
1.021859
26
0.990
1.033092
14
0.979
1.020862
15
0.959
1.000321
22
0.995
1.037865
7
0.993
1.035916
5
C12
4,484,524
48.0%
50.0%
-2.0%
Median
% Mean
% Median
Difference
Normally Distributed based on difference between Mean and Median?
Normally Distributed based on Skewness & Kurtosis?
Small
Medium
Large
7.950
7.210
8.690
11.316
10.772
11.860
14.553
13.668
15.438
0.147
0.076
Weight_g
Mean
11.1
Standard Error 0.566
Median
10.9
Mode
15.5
Standard Deviation3.10
Sample Variance 9.60
Kurtosis
-0.792
Skewness
0.074
Range
12.2
Minimum
5.2
Maximum
17.4
Sum
331.6
Count
30
0.096
Mean
Lower limit
Upper Limit
Coeficient of Variation
Volume_cc Pixels_3D Pixels_2D
11.3
4,384,827
41,287
0.541
213,443
1,879
11.2
4,484,524
41,479
#N/A
#N/A
#N/A
2.96
1,169,077
10,290
1,366,740,731,439
105,874,081
8.78
-0.741
-0.825
-0.155
0.077
-0.157
0.278
11.8
4,525,006
42,466
5.7
1,928,109
22,895
17.4
6,453,115
65,361
338.2
131,544,817 1,238,609
30
30
30
MGS 8110
F1
0.106
Prob (t > 30)
F2
F3
F4
F5
F6
0.030
0.266
0.468
Prob (t > 35)
Prob (t < 15)
Prob (15 < t < 25)
t upper 10%
lower CI
upper CI
lower CI
upper CI
F7
30.3
4.3
35.7
4.0
36.0
17