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Author's title

Author*Unverified author*
R Software Modulerwasp_variability.wasp
Title produced by softwareVariability
Date of computationSun, 22 Dec 2013 14:58:00 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/22/t1387742312zgo3xp1xbn63gjx.htm/, Retrieved Sun, 05 Dec 2021 16:54:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232572, Retrieved Sun, 05 Dec 2021 16:54:12 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact56
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Variability] [] [2013-12-22 19:58:00] [20efb5145ec2a2ddd8dcd418764211fa] [Current]
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Dataseries X:
20
25
15
15
25
25
25
21
30
25
20
40
13
30
25
20
25
20
25
20
20
15
15
12
20
5
20
15
25
22
20
22
25
20
20
35
30
25
20
20
20
25
25
15
20
35
25
25
30
23
10
22
25
25
22
30
20
25
25
22
25
25
25
22
25
12
18
20
20
22
30
25
22
20
50
30
25
20
30
22
25
30
22
25
22
22
25
25
25
20
22
15
20
30
20
25
30
35
22
12
30
15
10
30
9
25
20
20
35
25
35
30
12
25
15
25
25
20
20
6
15
40
20
40
25
25
20
15
15
22
24
22
20
25
25
25
35
40
20
22
22
20
25
25
18
25
20
25
30
20
22
35
22
25
25
25
25
22
23
35
15
25
18
22
25
25
28
30
20
25
25
30
22
30
10
10
25
20
22
25
25
15
22
25
25
28
22
30
25
20
25
25
20
30
20
30
50
19
20
28
20
25
35
25
25
15
16
20
20
25
30
20
25
25
25
20
20
25
25
30
22
20
25
25
18
18
20
25
25
30
25
20
25
20
20
20
22
18
22
20
15
25
25
20
25
15
22
25
25
15
12
25
30
22
15
22
25
12
18
30
25
25
40
24
25
15
25
20
25
25
25
20
30
20
25
30
22
25
25
25
50
19
50
25
35
20
20
20
20
20
25
25
25
20
20
20
20
25
18
25
22
22
30
30
8
20
25
30
50
22
20
10
25
25
25
25
18
25
20
25
30
18
20
25
22
22
20
20
25
20
20
20
20
25
20
10
20
25
30
25
50
30
30
50
15
25
25
22
20
22
30
25
18
22
22
30
40
25
20
10
20
9
15
20
15
20
30
12
15
12
20
15
12
25
20
25
25
25
30
20
25
15
15
22
10
15
10
20
25
20
20
38
20
20
20
40
25
25
30
25
10
20
25
12
15
25
20
22
22
20
25
25
25
15
40
20
20
16
25
15
20
25
20
30
50
20
25
20
30
30
25
25
12
25
25
25
20
20
20
15
20
25
15
25
50
30
20
20
25
12
15
20
20
35
22
15
18
30
22
12
12
20
20
15
25
15
20
20
25
18
30
20
25
25
25
20
20
25
20
22
15
15
22
20
10
25
20
20
15
12
20
5
20
15
15
25
25
25
15
25
22
25
20
18
22
25
35
25
25
25
35
30
22
30
50
15
25
24
20
25
25
25
12
15
22
25
25
25
25
15
20
20
15
35
30
20
22
65
20
25
22
20
25
25
20
25
15
20
12
15
10
25
15
30
35
25
25
25
25
25
40
40
25
25
20
25
25
22
25
30
25
25
30
25
25
30
25
25
20
22
22
20
25
22
25
22
40
25
25
25
22
20
35
20
35
25
22
25
25
25
25
25
40
25
30
25
20
25
25
30
22
22
20
15
15
25
25
20
20
15
25
15
20
22
25
15
15
18
5
15
25
18
40
25
25
20
30
20
25
25
25
22
22
25
25
30
25
25
25
25
20
20
25
25
25
25
20
30
25
22
30
20
20
30
25
25
30
20
25
25
24
25
30
18
15
22
22
25
22
22
25
15
20
22
18
35
20
20
20
25
25
30
15
25
22
26
25
20
25
25
25
22
25
25
20
22
30
15
30
25
20
25
25
35
22
20
25
20
20
18
20
22
25
10
20
25
20
20
30
25
20
15
20
25
10
20
25
22
22
25
25
15
25
20
10
25
16
25
35
25
15
25
25
30
25
10
22
20
25
20
20
25
22
18
30
19
25
20
25
20
25
20
22
12
30
12
22
25
25
25
25
30
30
10
22
22
25
20
22
20
25
20
15
25
20
25
20
30
15
40
25
20
22
22
30
20
40
20
25
20
25
20
50
50
25
25
40
30
22
30
20
25
25
30
25
25
20
18
18
28
25
22
15
40
40
12
12
18
12
25
26
18
25
22
15
25
15
15
15
25
15
12
22
20
20
25
20
12
9
15
12
15
25
20
20
15
15
30
21
25
22
22
50
15
25
15
25
22
18
50
20
50
20
20
30
25
20
22
25
50
40
25
25
25
25
30
40
25
30
20




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time12 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 12 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232572&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]12 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232572&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232572&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time12 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Variability - Ungrouped Data
Absolute range60
Relative range (unbiased)8.64960371229667
Relative range (biased)8.65441305584999
Variance (unbiased)48.1182783339513
Variance (biased)48.0648135802469
Standard Deviation (unbiased)6.93673398177783
Standard Deviation (biased)6.93287916959808
Coefficient of Variation (unbiased)0.299441727833471
Coefficient of Variation (biased)0.299275325082175
Mean Squared Error (MSE versus 0)584.707777777778
Mean Squared Error (MSE versus Mean)48.0648135802469
Mean Absolute Deviation from Mean (MAD Mean)4.83887407407407
Mean Absolute Deviation from Median (MAD Median)4.82777777777778
Median Absolute Deviation from Mean3.16555555555556
Median Absolute Deviation from Median3
Mean Squared Deviation from Mean48.0648135802469
Mean Squared Deviation from Median49.4233333333333
Interquartile Difference (Weighted Average at Xnp)5
Interquartile Difference (Weighted Average at X(n+1)p)5
Interquartile Difference (Empirical Distribution Function)5
Interquartile Difference (Empirical Distribution Function - Averaging)5
Interquartile Difference (Empirical Distribution Function - Interpolation)5
Interquartile Difference (Closest Observation)5
Interquartile Difference (True Basic - Statistics Graphics Toolkit)5
Interquartile Difference (MS Excel (old versions))5
Semi Interquartile Difference (Weighted Average at Xnp)2.5
Semi Interquartile Difference (Weighted Average at X(n+1)p)2.5
Semi Interquartile Difference (Empirical Distribution Function)2.5
Semi Interquartile Difference (Empirical Distribution Function - Averaging)2.5
Semi Interquartile Difference (Empirical Distribution Function - Interpolation)2.5
Semi Interquartile Difference (Closest Observation)2.5
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)2.5
Semi Interquartile Difference (MS Excel (old versions))2.5
Coefficient of Quartile Variation (Weighted Average at Xnp)0.111111111111111
Coefficient of Quartile Variation (Weighted Average at X(n+1)p)0.111111111111111
Coefficient of Quartile Variation (Empirical Distribution Function)0.111111111111111
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)0.111111111111111
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)0.111111111111111
Coefficient of Quartile Variation (Closest Observation)0.111111111111111
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)0.111111111111111
Coefficient of Quartile Variation (MS Excel (old versions))0.111111111111111
Number of all Pairs of Observations404550
Squared Differences between all Pairs of Observations96.2365566679026
Mean Absolute Differences between all Pairs of Observations6.99692745025337
Gini Mean Difference6.99692745025337
Leik Measure of Dispersion0.503760313512314
Index of Diversity0.998789371421997
Index of Qualitative Variation0.999900371835147
Coefficient of Dispersion0.219948821548822
Observations900

\begin{tabular}{lllllllll}
\hline
Variability - Ungrouped Data \tabularnewline
Absolute range & 60 \tabularnewline
Relative range (unbiased) & 8.64960371229667 \tabularnewline
Relative range (biased) & 8.65441305584999 \tabularnewline
Variance (unbiased) & 48.1182783339513 \tabularnewline
Variance (biased) & 48.0648135802469 \tabularnewline
Standard Deviation (unbiased) & 6.93673398177783 \tabularnewline
Standard Deviation (biased) & 6.93287916959808 \tabularnewline
Coefficient of Variation (unbiased) & 0.299441727833471 \tabularnewline
Coefficient of Variation (biased) & 0.299275325082175 \tabularnewline
Mean Squared Error (MSE versus 0) & 584.707777777778 \tabularnewline
Mean Squared Error (MSE versus Mean) & 48.0648135802469 \tabularnewline
Mean Absolute Deviation from Mean (MAD Mean) & 4.83887407407407 \tabularnewline
Mean Absolute Deviation from Median (MAD Median) & 4.82777777777778 \tabularnewline
Median Absolute Deviation from Mean & 3.16555555555556 \tabularnewline
Median Absolute Deviation from Median & 3 \tabularnewline
Mean Squared Deviation from Mean & 48.0648135802469 \tabularnewline
Mean Squared Deviation from Median & 49.4233333333333 \tabularnewline
Interquartile Difference (Weighted Average at Xnp) & 5 \tabularnewline
Interquartile Difference (Weighted Average at X(n+1)p) & 5 \tabularnewline
Interquartile Difference (Empirical Distribution Function) & 5 \tabularnewline
Interquartile Difference (Empirical Distribution Function - Averaging) & 5 \tabularnewline
Interquartile Difference (Empirical Distribution Function - Interpolation) & 5 \tabularnewline
Interquartile Difference (Closest Observation) & 5 \tabularnewline
Interquartile Difference (True Basic - Statistics Graphics Toolkit) & 5 \tabularnewline
Interquartile Difference (MS Excel (old versions)) & 5 \tabularnewline
Semi Interquartile Difference (Weighted Average at Xnp) & 2.5 \tabularnewline
Semi Interquartile Difference (Weighted Average at X(n+1)p) & 2.5 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function) & 2.5 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function - Averaging) & 2.5 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function - Interpolation) & 2.5 \tabularnewline
Semi Interquartile Difference (Closest Observation) & 2.5 \tabularnewline
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit) & 2.5 \tabularnewline
Semi Interquartile Difference (MS Excel (old versions)) & 2.5 \tabularnewline
Coefficient of Quartile Variation (Weighted Average at Xnp) & 0.111111111111111 \tabularnewline
Coefficient of Quartile Variation (Weighted Average at X(n+1)p) & 0.111111111111111 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function) & 0.111111111111111 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging) & 0.111111111111111 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation) & 0.111111111111111 \tabularnewline
Coefficient of Quartile Variation (Closest Observation) & 0.111111111111111 \tabularnewline
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit) & 0.111111111111111 \tabularnewline
Coefficient of Quartile Variation (MS Excel (old versions)) & 0.111111111111111 \tabularnewline
Number of all Pairs of Observations & 404550 \tabularnewline
Squared Differences between all Pairs of Observations & 96.2365566679026 \tabularnewline
Mean Absolute Differences between all Pairs of Observations & 6.99692745025337 \tabularnewline
Gini Mean Difference & 6.99692745025337 \tabularnewline
Leik Measure of Dispersion & 0.503760313512314 \tabularnewline
Index of Diversity & 0.998789371421997 \tabularnewline
Index of Qualitative Variation & 0.999900371835147 \tabularnewline
Coefficient of Dispersion & 0.219948821548822 \tabularnewline
Observations & 900 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232572&T=1

[TABLE]
[ROW][C]Variability - Ungrouped Data[/C][/ROW]
[ROW][C]Absolute range[/C][C]60[/C][/ROW]
[ROW][C]Relative range (unbiased)[/C][C]8.64960371229667[/C][/ROW]
[ROW][C]Relative range (biased)[/C][C]8.65441305584999[/C][/ROW]
[ROW][C]Variance (unbiased)[/C][C]48.1182783339513[/C][/ROW]
[ROW][C]Variance (biased)[/C][C]48.0648135802469[/C][/ROW]
[ROW][C]Standard Deviation (unbiased)[/C][C]6.93673398177783[/C][/ROW]
[ROW][C]Standard Deviation (biased)[/C][C]6.93287916959808[/C][/ROW]
[ROW][C]Coefficient of Variation (unbiased)[/C][C]0.299441727833471[/C][/ROW]
[ROW][C]Coefficient of Variation (biased)[/C][C]0.299275325082175[/C][/ROW]
[ROW][C]Mean Squared Error (MSE versus 0)[/C][C]584.707777777778[/C][/ROW]
[ROW][C]Mean Squared Error (MSE versus Mean)[/C][C]48.0648135802469[/C][/ROW]
[ROW][C]Mean Absolute Deviation from Mean (MAD Mean)[/C][C]4.83887407407407[/C][/ROW]
[ROW][C]Mean Absolute Deviation from Median (MAD Median)[/C][C]4.82777777777778[/C][/ROW]
[ROW][C]Median Absolute Deviation from Mean[/C][C]3.16555555555556[/C][/ROW]
[ROW][C]Median Absolute Deviation from Median[/C][C]3[/C][/ROW]
[ROW][C]Mean Squared Deviation from Mean[/C][C]48.0648135802469[/C][/ROW]
[ROW][C]Mean Squared Deviation from Median[/C][C]49.4233333333333[/C][/ROW]
[ROW][C]Interquartile Difference (Weighted Average at Xnp)[/C][C]5[/C][/ROW]
[ROW][C]Interquartile Difference (Weighted Average at X(n+1)p)[/C][C]5[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function)[/C][C]5[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function - Averaging)[/C][C]5[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function - Interpolation)[/C][C]5[/C][/ROW]
[ROW][C]Interquartile Difference (Closest Observation)[/C][C]5[/C][/ROW]
[ROW][C]Interquartile Difference (True Basic - Statistics Graphics Toolkit)[/C][C]5[/C][/ROW]
[ROW][C]Interquartile Difference (MS Excel (old versions))[/C][C]5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Weighted Average at Xnp)[/C][C]2.5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Weighted Average at X(n+1)p)[/C][C]2.5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function)[/C][C]2.5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function - Averaging)[/C][C]2.5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function - Interpolation)[/C][C]2.5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Closest Observation)[/C][C]2.5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)[/C][C]2.5[/C][/ROW]
[ROW][C]Semi Interquartile Difference (MS Excel (old versions))[/C][C]2.5[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Weighted Average at Xnp)[/C][C]0.111111111111111[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Weighted Average at X(n+1)p)[/C][C]0.111111111111111[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function)[/C][C]0.111111111111111[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)[/C][C]0.111111111111111[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)[/C][C]0.111111111111111[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Closest Observation)[/C][C]0.111111111111111[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)[/C][C]0.111111111111111[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (MS Excel (old versions))[/C][C]0.111111111111111[/C][/ROW]
[ROW][C]Number of all Pairs of Observations[/C][C]404550[/C][/ROW]
[ROW][C]Squared Differences between all Pairs of Observations[/C][C]96.2365566679026[/C][/ROW]
[ROW][C]Mean Absolute Differences between all Pairs of Observations[/C][C]6.99692745025337[/C][/ROW]
[ROW][C]Gini Mean Difference[/C][C]6.99692745025337[/C][/ROW]
[ROW][C]Leik Measure of Dispersion[/C][C]0.503760313512314[/C][/ROW]
[ROW][C]Index of Diversity[/C][C]0.998789371421997[/C][/ROW]
[ROW][C]Index of Qualitative Variation[/C][C]0.999900371835147[/C][/ROW]
[ROW][C]Coefficient of Dispersion[/C][C]0.219948821548822[/C][/ROW]
[ROW][C]Observations[/C][C]900[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232572&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232572&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Variability - Ungrouped Data
Absolute range60
Relative range (unbiased)8.64960371229667
Relative range (biased)8.65441305584999
Variance (unbiased)48.1182783339513
Variance (biased)48.0648135802469
Standard Deviation (unbiased)6.93673398177783
Standard Deviation (biased)6.93287916959808
Coefficient of Variation (unbiased)0.299441727833471
Coefficient of Variation (biased)0.299275325082175
Mean Squared Error (MSE versus 0)584.707777777778
Mean Squared Error (MSE versus Mean)48.0648135802469
Mean Absolute Deviation from Mean (MAD Mean)4.83887407407407
Mean Absolute Deviation from Median (MAD Median)4.82777777777778
Median Absolute Deviation from Mean3.16555555555556
Median Absolute Deviation from Median3
Mean Squared Deviation from Mean48.0648135802469
Mean Squared Deviation from Median49.4233333333333
Interquartile Difference (Weighted Average at Xnp)5
Interquartile Difference (Weighted Average at X(n+1)p)5
Interquartile Difference (Empirical Distribution Function)5
Interquartile Difference (Empirical Distribution Function - Averaging)5
Interquartile Difference (Empirical Distribution Function - Interpolation)5
Interquartile Difference (Closest Observation)5
Interquartile Difference (True Basic - Statistics Graphics Toolkit)5
Interquartile Difference (MS Excel (old versions))5
Semi Interquartile Difference (Weighted Average at Xnp)2.5
Semi Interquartile Difference (Weighted Average at X(n+1)p)2.5
Semi Interquartile Difference (Empirical Distribution Function)2.5
Semi Interquartile Difference (Empirical Distribution Function - Averaging)2.5
Semi Interquartile Difference (Empirical Distribution Function - Interpolation)2.5
Semi Interquartile Difference (Closest Observation)2.5
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)2.5
Semi Interquartile Difference (MS Excel (old versions))2.5
Coefficient of Quartile Variation (Weighted Average at Xnp)0.111111111111111
Coefficient of Quartile Variation (Weighted Average at X(n+1)p)0.111111111111111
Coefficient of Quartile Variation (Empirical Distribution Function)0.111111111111111
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)0.111111111111111
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)0.111111111111111
Coefficient of Quartile Variation (Closest Observation)0.111111111111111
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)0.111111111111111
Coefficient of Quartile Variation (MS Excel (old versions))0.111111111111111
Number of all Pairs of Observations404550
Squared Differences between all Pairs of Observations96.2365566679026
Mean Absolute Differences between all Pairs of Observations6.99692745025337
Gini Mean Difference6.99692745025337
Leik Measure of Dispersion0.503760313512314
Index of Diversity0.998789371421997
Index of Qualitative Variation0.999900371835147
Coefficient of Dispersion0.219948821548822
Observations900



Parameters (Session):
par1 = 0.01 ; par2 = 0.99 ; par3 = 0.01 ;
Parameters (R input):
R code (references can be found in the software module):
num <- 50
res <- array(NA,dim=c(num,3))
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
iqd <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
iqdiff <- qvalue3 - qvalue1
return(c(iqdiff,iqdiff/2,iqdiff/(qvalue3 + qvalue1)))
}
range <- max(x) - min(x)
lx <- length(x)
biasf <- (lx-1)/lx
varx <- var(x)
bvarx <- varx*biasf
sdx <- sqrt(varx)
mx <- mean(x)
bsdx <- sqrt(bvarx)
x2 <- x*x
mse0 <- sum(x2)/lx
xmm <- x-mx
xmm2 <- xmm*xmm
msem <- sum(xmm2)/lx
axmm <- abs(x - mx)
medx <- median(x)
axmmed <- abs(x - medx)
xmmed <- x - medx
xmmed2 <- xmmed*xmmed
msemed <- sum(xmmed2)/lx
qarr <- array(NA,dim=c(8,3))
for (j in 1:8) {
qarr[j,] <- iqd(x,j)
}
sdpo <- 0
adpo <- 0
for (i in 1:(lx-1)) {
for (j in (i+1):lx) {
ldi <- x[i]-x[j]
aldi <- abs(ldi)
sdpo = sdpo + ldi * ldi
adpo = adpo + aldi
}
}
denom <- (lx*(lx-1)/2)
sdpo = sdpo / denom
adpo = adpo / denom
gmd <- 0
for (i in 1:lx) {
for (j in 1:lx) {
ldi <- abs(x[i]-x[j])
gmd = gmd + ldi
}
}
gmd <- gmd / (lx*(lx-1))
sumx <- sum(x)
pk <- x / sumx
ck <- cumsum(pk)
dk <- array(NA,dim=lx)
for (i in 1:lx) {
if (ck[i] <= 0.5) dk[i] <- ck[i] else dk[i] <- 1 - ck[i]
}
bigd <- sum(dk) * 2 / (lx-1)
iod <- 1 - sum(pk*pk)
res[1,] <- c('Absolute range','absolute.htm', range)
res[2,] <- c('Relative range (unbiased)','relative.htm', range/sd(x))
res[3,] <- c('Relative range (biased)','relative.htm', range/sqrt(varx*biasf))
res[4,] <- c('Variance (unbiased)','unbiased.htm', varx)
res[5,] <- c('Variance (biased)','biased.htm', bvarx)
res[6,] <- c('Standard Deviation (unbiased)','unbiased1.htm', sdx)
res[7,] <- c('Standard Deviation (biased)','biased1.htm', bsdx)
res[8,] <- c('Coefficient of Variation (unbiased)','variation.htm', sdx/mx)
res[9,] <- c('Coefficient of Variation (biased)','variation.htm', bsdx/mx)
res[10,] <- c('Mean Squared Error (MSE versus 0)','mse.htm', mse0)
res[11,] <- c('Mean Squared Error (MSE versus Mean)','mse.htm', msem)
res[12,] <- c('Mean Absolute Deviation from Mean (MAD Mean)', 'mean2.htm', sum(axmm)/lx)
res[13,] <- c('Mean Absolute Deviation from Median (MAD Median)', 'median1.htm', sum(axmmed)/lx)
res[14,] <- c('Median Absolute Deviation from Mean', 'mean3.htm', median(axmm))
res[15,] <- c('Median Absolute Deviation from Median', 'median2.htm', median(axmmed))
res[16,] <- c('Mean Squared Deviation from Mean', 'mean1.htm', msem)
res[17,] <- c('Mean Squared Deviation from Median', 'median.htm', msemed)
load(file='createtable')
mylink1 <- hyperlink('difference.htm','Interquartile Difference','')
mylink2 <- paste(mylink1,hyperlink('method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[18,] <- c('', mylink2, qarr[1,1])
mylink2 <- paste(mylink1,hyperlink('method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[19,] <- c('', mylink2, qarr[2,1])
mylink2 <- paste(mylink1,hyperlink('method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[20,] <- c('', mylink2, qarr[3,1])
mylink2 <- paste(mylink1,hyperlink('method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[21,] <- c('', mylink2, qarr[4,1])
mylink2 <- paste(mylink1,hyperlink('method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[22,] <- c('', mylink2, qarr[5,1])
mylink2 <- paste(mylink1,hyperlink('method_6.htm','(Closest Observation)',''),sep=' ')
res[23,] <- c('', mylink2, qarr[6,1])
mylink2 <- paste(mylink1,hyperlink('method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[24,] <- c('', mylink2, qarr[7,1])
mylink2 <- paste(mylink1,hyperlink('method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[25,] <- c('', mylink2, qarr[8,1])
mylink1 <- hyperlink('deviation.htm','Semi Interquartile Difference','')
mylink2 <- paste(mylink1,hyperlink('method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[26,] <- c('', mylink2, qarr[1,2])
mylink2 <- paste(mylink1,hyperlink('method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[27,] <- c('', mylink2, qarr[2,2])
mylink2 <- paste(mylink1,hyperlink('method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[28,] <- c('', mylink2, qarr[3,2])
mylink2 <- paste(mylink1,hyperlink('method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[29,] <- c('', mylink2, qarr[4,2])
mylink2 <- paste(mylink1,hyperlink('method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[30,] <- c('', mylink2, qarr[5,2])
mylink2 <- paste(mylink1,hyperlink('method_6.htm','(Closest Observation)',''),sep=' ')
res[31,] <- c('', mylink2, qarr[6,2])
mylink2 <- paste(mylink1,hyperlink('method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[32,] <- c('', mylink2, qarr[7,2])
mylink2 <- paste(mylink1,hyperlink('method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[33,] <- c('', mylink2, qarr[8,2])
mylink1 <- hyperlink('variation1.htm','Coefficient of Quartile Variation','')
mylink2 <- paste(mylink1,hyperlink('method_1.htm','(Weighted Average at Xnp)',''),sep=' ')
res[34,] <- c('', mylink2, qarr[1,3])
mylink2 <- paste(mylink1,hyperlink('method_2.htm','(Weighted Average at X(n+1)p)',''),sep=' ')
res[35,] <- c('', mylink2, qarr[2,3])
mylink2 <- paste(mylink1,hyperlink('method_3.htm','(Empirical Distribution Function)',''),sep=' ')
res[36,] <- c('', mylink2, qarr[3,3])
mylink2 <- paste(mylink1,hyperlink('method_4.htm','(Empirical Distribution Function - Averaging)',''),sep=' ')
res[37,] <- c('', mylink2, qarr[4,3])
mylink2 <- paste(mylink1,hyperlink('method_5.htm','(Empirical Distribution Function - Interpolation)',''),sep=' ')
res[38,] <- c('', mylink2, qarr[5,3])
mylink2 <- paste(mylink1,hyperlink('method_6.htm','(Closest Observation)',''),sep=' ')
res[39,] <- c('', mylink2, qarr[6,3])
mylink2 <- paste(mylink1,hyperlink('method_7.htm','(True Basic - Statistics Graphics Toolkit)',''),sep=' ')
res[40,] <- c('', mylink2, qarr[7,3])
mylink2 <- paste(mylink1,hyperlink('method_8.htm','(MS Excel (old versions))',''),sep=' ')
res[41,] <- c('', mylink2, qarr[8,3])
res[42,] <- c('Number of all Pairs of Observations', 'pair_numbers.htm', lx*(lx-1)/2)
res[43,] <- c('Squared Differences between all Pairs of Observations', 'squared_differences.htm', sdpo)
res[44,] <- c('Mean Absolute Differences between all Pairs of Observations', 'mean_abs_differences.htm', adpo)
res[45,] <- c('Gini Mean Difference', 'gini_mean_difference.htm', gmd)
res[46,] <- c('Leik Measure of Dispersion', 'leiks_d.htm', bigd)
res[47,] <- c('Index of Diversity', 'diversity.htm', iod)
res[48,] <- c('Index of Qualitative Variation', 'qualitative_variation.htm', iod*lx/(lx-1))
res[49,] <- c('Coefficient of Dispersion', 'dispersion.htm', sum(axmm)/lx/medx)
res[50,] <- c('Observations', '', lx)
res
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Variability - Ungrouped Data',2,TRUE)
a<-table.row.end(a)
for (i in 1:num) {
a<-table.row.start(a)
if (res[i,1] != '') {
a<-table.element(a,hyperlink(res[i,2],res[i,1],''),header=TRUE)
} else {
a<-table.element(a,res[i,2],header=TRUE)
}
a<-table.element(a,res[i,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')