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Author's title

Author*Unverified author*
R Software Modulerwasp_variability.wasp
Title produced by softwareVariability
Date of computationThu, 05 Dec 2013 16:17:22 -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/05/t1386278347lsyeak9chtbva22.htm/, Retrieved Thu, 28 Mar 2024 10:08:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=231250, Retrieved Thu, 28 Mar 2024 10:08:50 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact60
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Variability] [] [2013-12-05 21:17:22] [8f30ad625584f71e9e842ae520fabe96] [Current]
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Dataseries X:
8
10
10
13
14
12
11
8
8
10
10
12
12
12
11
12
12
12
12
12
12
10
12
10
11
10
10
12
10
12
7
12
18
12
11
13
10
10
10
8
12
10
10
8
14
9
8
12
15
14
1
9
7
8
12
57
12
10
10
8
8
16
14
13
10
12
9
12
11
10
8
8
9
12
8
12
10
12
9
8
12
8
12
10
12
9
28
10
12
9
14
12
12
99
13
13
14
12
12
10
11
12
14
10
12
12
6
12
10
12
12
12
9
12
12
13
8
12
10
10
10
9
12
9
10
8
12
10
8
8
9
12
12
10
10
9
11
10
9
15
10
8
10
8
9
9
6
16
12
12
12
12
10
12
8
9
12
12
8
14
10
12
8
11
10
12
12
12
12
8
10
7
10
10
12
11
9
10
12
14
13
10
11
10
10
8
10
10
10
8
8
4
14
8
12
12
10
8
12
12
10
10
12
12
9
11
14
10
8
12
8
10
11
12
10
10
12
8
9
12
8
8
10
10
10
14
10
12
12
13
9
12
12
10
12
6
8
12
10
9
11
11
9
10
15
12
7
7
10
9
10
10
9
12
10
9
12
10
7
12
10
10
12
8
12
10
10
9
8
8
12
12
10
12
10
9
10
10
8
10
12
12
16
10
9
12
12
10
7
12
10
10
6
9
6
18
13
10
12
15
12
12
9
7
12
13
14
13
12
8
8
10
10
8
12
10
12
12
12
9
12
7
12
8
8
12
14
10
5
9
8
13
10
10
14
10
99
10
12
17
14
8
14
12
12
10
10
8
12
12
12
10
12
10
10
12
12
12
12
13
12
8
10
12
8
10
10
12
12
12
12
12
12
14
10
12
14
12
14
12
13
8
12
14
10
10
11
16
12
10
10
99
8
11
12
12
11
10
20
9
14
12
10
12
10
12
12
8
12
12
10
99
12
2
10
10
10
12
12
12
12
88
9
12
14
8
12
10
10
10
7
8
10
1
10
10
9
15
10
12
12
12
11
12
12
14
8
12
12
10
14
8
10
12
10
10
10
12
9
12
11
8
14
12
10
12
10
8
14
12
12
12
8
12
12
10
12
12
12
9
11
10
15
10
9
9
10
7
10
9
10
10
10
15
12
12
10
12
8
12
11
8
14
8
12
10
15
9
13
12
14
12
12
17
10
13
12
12
10
12
10
12
10
10
10
1
8
12
10
10
10
12
12
11
12
8
8
12
12
10
12
9
10
12
12
12
12
10
10
9
12
10
9
12
7
14
10
10
9
10
8
10
12
12
10
9
10
9
12
10
12
10
9
7
12
11
12
9
13
12
12
7
8
12
12
12
11
12
13
10
12
10
12
12
15
12
12
13
10
10
8
11
12
12
12
12
10
10
12
15
12
10
10
7
12
10
11
10
10
10
10
11
7
15
8
10
6
8
9
8
7
10
12
14
11
8
10
8
8
14
12
15
12
12
9
12
12
9
11
15
11
12
7
15
9
10
15
15
8
11
12
10
10
12
7
12
10
11
12
10
10
8
9
8
10
10
14
10
10
12
12
7
12
10
12
9
9
13
14
10
12
12
12
12
12
10
10
8
12
8
14
10
70
12
10
8
8
11
10
8
7
8
50
9
12
12
7
10
8
10
10
10
8
12
7
13
13
8
8
11
6
12
9
12
13
13
12
12
10
8
12
10
10
15
12
10
12
8
8
12
12
10
12
9
12
12
10
9
10
10
10
12
12
12
12
8
10
12
15
10
8
15
10
9
12
99
10
10
11
11
12
12
14
12
14
9
10
12
13
10
11
10
12
12
12
13
14
9
10
10
12
12
10
99
8
99
12
99
12
10
12
10
12
12
12
10
12
12
10
10
12
99
12
12
9
99
12
12
9
12
12
12
15
12
12
12
8
8
12
8
12
12
10
10
12
99
8
8
99
10
10
5
9
9
99
9
10
12




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time13 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 13 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231250&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]13 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231250&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231250&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 time13 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Variability - Ungrouped Data
Absolute range98
Relative range (unbiased)8.41126959013911
Relative range (biased)8.41617555123872
Variance (unbiased)135.746626574515
Variance (biased)135.588413723029
Standard Deviation (unbiased)11.6510354292876
Standard Deviation (biased)11.6442438021122
Coefficient of Variation (unbiased)0.945661564499929
Coefficient of Variation (biased)0.945110319005987
Mean Squared Error (MSE versus 0)287.38344988345
Mean Squared Error (MSE versus Mean)135.588413723029
Mean Absolute Deviation from Mean (MAD Mean)3.58140577371347
Mean Absolute Deviation from Median (MAD Median)3.26923076923077
Median Absolute Deviation from Mean2.32051282051282
Median Absolute Deviation from Median1
Mean Squared Deviation from Mean135.588413723029
Mean Squared Deviation from Median137.332167832168
Interquartile Difference (Weighted Average at Xnp)2
Interquartile Difference (Weighted Average at X(n+1)p)2
Interquartile Difference (Empirical Distribution Function)2
Interquartile Difference (Empirical Distribution Function - Averaging)2
Interquartile Difference (Empirical Distribution Function - Interpolation)2
Interquartile Difference (Closest Observation)2
Interquartile Difference (True Basic - Statistics Graphics Toolkit)2
Interquartile Difference (MS Excel (old versions))2
Semi Interquartile Difference (Weighted Average at Xnp)1
Semi Interquartile Difference (Weighted Average at X(n+1)p)1
Semi Interquartile Difference (Empirical Distribution Function)1
Semi Interquartile Difference (Empirical Distribution Function - Averaging)1
Semi Interquartile Difference (Empirical Distribution Function - Interpolation)1
Semi Interquartile Difference (Closest Observation)1
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)1
Semi Interquartile Difference (MS Excel (old versions))1
Coefficient of Quartile Variation (Weighted Average at Xnp)0.0909090909090909
Coefficient of Quartile Variation (Weighted Average at X(n+1)p)0.0909090909090909
Coefficient of Quartile Variation (Empirical Distribution Function)0.0909090909090909
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)0.0909090909090909
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)0.0909090909090909
Coefficient of Quartile Variation (Closest Observation)0.0909090909090909
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)0.0909090909090909
Coefficient of Quartile Variation (MS Excel (old versions))0.0909090909090909
Number of all Pairs of Observations367653
Squared Differences between all Pairs of Observations271.493253149029
Mean Absolute Differences between all Pairs of Observations5.34460755114197
Gini Mean Difference5.34460755114197
Leik Measure of Dispersion0.522154190583493
Index of Diversity0.997793434131595
Index of Qualitative Variation0.998957720519146
Coefficient of Dispersion0.325582343064861
Observations858

\begin{tabular}{lllllllll}
\hline
Variability - Ungrouped Data \tabularnewline
Absolute range & 98 \tabularnewline
Relative range (unbiased) & 8.41126959013911 \tabularnewline
Relative range (biased) & 8.41617555123872 \tabularnewline
Variance (unbiased) & 135.746626574515 \tabularnewline
Variance (biased) & 135.588413723029 \tabularnewline
Standard Deviation (unbiased) & 11.6510354292876 \tabularnewline
Standard Deviation (biased) & 11.6442438021122 \tabularnewline
Coefficient of Variation (unbiased) & 0.945661564499929 \tabularnewline
Coefficient of Variation (biased) & 0.945110319005987 \tabularnewline
Mean Squared Error (MSE versus 0) & 287.38344988345 \tabularnewline
Mean Squared Error (MSE versus Mean) & 135.588413723029 \tabularnewline
Mean Absolute Deviation from Mean (MAD Mean) & 3.58140577371347 \tabularnewline
Mean Absolute Deviation from Median (MAD Median) & 3.26923076923077 \tabularnewline
Median Absolute Deviation from Mean & 2.32051282051282 \tabularnewline
Median Absolute Deviation from Median & 1 \tabularnewline
Mean Squared Deviation from Mean & 135.588413723029 \tabularnewline
Mean Squared Deviation from Median & 137.332167832168 \tabularnewline
Interquartile Difference (Weighted Average at Xnp) & 2 \tabularnewline
Interquartile Difference (Weighted Average at X(n+1)p) & 2 \tabularnewline
Interquartile Difference (Empirical Distribution Function) & 2 \tabularnewline
Interquartile Difference (Empirical Distribution Function - Averaging) & 2 \tabularnewline
Interquartile Difference (Empirical Distribution Function - Interpolation) & 2 \tabularnewline
Interquartile Difference (Closest Observation) & 2 \tabularnewline
Interquartile Difference (True Basic - Statistics Graphics Toolkit) & 2 \tabularnewline
Interquartile Difference (MS Excel (old versions)) & 2 \tabularnewline
Semi Interquartile Difference (Weighted Average at Xnp) & 1 \tabularnewline
Semi Interquartile Difference (Weighted Average at X(n+1)p) & 1 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function) & 1 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function - Averaging) & 1 \tabularnewline
Semi Interquartile Difference (Empirical Distribution Function - Interpolation) & 1 \tabularnewline
Semi Interquartile Difference (Closest Observation) & 1 \tabularnewline
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit) & 1 \tabularnewline
Semi Interquartile Difference (MS Excel (old versions)) & 1 \tabularnewline
Coefficient of Quartile Variation (Weighted Average at Xnp) & 0.0909090909090909 \tabularnewline
Coefficient of Quartile Variation (Weighted Average at X(n+1)p) & 0.0909090909090909 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function) & 0.0909090909090909 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging) & 0.0909090909090909 \tabularnewline
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation) & 0.0909090909090909 \tabularnewline
Coefficient of Quartile Variation (Closest Observation) & 0.0909090909090909 \tabularnewline
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit) & 0.0909090909090909 \tabularnewline
Coefficient of Quartile Variation (MS Excel (old versions)) & 0.0909090909090909 \tabularnewline
Number of all Pairs of Observations & 367653 \tabularnewline
Squared Differences between all Pairs of Observations & 271.493253149029 \tabularnewline
Mean Absolute Differences between all Pairs of Observations & 5.34460755114197 \tabularnewline
Gini Mean Difference & 5.34460755114197 \tabularnewline
Leik Measure of Dispersion & 0.522154190583493 \tabularnewline
Index of Diversity & 0.997793434131595 \tabularnewline
Index of Qualitative Variation & 0.998957720519146 \tabularnewline
Coefficient of Dispersion & 0.325582343064861 \tabularnewline
Observations & 858 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=231250&T=1

[TABLE]
[ROW][C]Variability - Ungrouped Data[/C][/ROW]
[ROW][C]Absolute range[/C][C]98[/C][/ROW]
[ROW][C]Relative range (unbiased)[/C][C]8.41126959013911[/C][/ROW]
[ROW][C]Relative range (biased)[/C][C]8.41617555123872[/C][/ROW]
[ROW][C]Variance (unbiased)[/C][C]135.746626574515[/C][/ROW]
[ROW][C]Variance (biased)[/C][C]135.588413723029[/C][/ROW]
[ROW][C]Standard Deviation (unbiased)[/C][C]11.6510354292876[/C][/ROW]
[ROW][C]Standard Deviation (biased)[/C][C]11.6442438021122[/C][/ROW]
[ROW][C]Coefficient of Variation (unbiased)[/C][C]0.945661564499929[/C][/ROW]
[ROW][C]Coefficient of Variation (biased)[/C][C]0.945110319005987[/C][/ROW]
[ROW][C]Mean Squared Error (MSE versus 0)[/C][C]287.38344988345[/C][/ROW]
[ROW][C]Mean Squared Error (MSE versus Mean)[/C][C]135.588413723029[/C][/ROW]
[ROW][C]Mean Absolute Deviation from Mean (MAD Mean)[/C][C]3.58140577371347[/C][/ROW]
[ROW][C]Mean Absolute Deviation from Median (MAD Median)[/C][C]3.26923076923077[/C][/ROW]
[ROW][C]Median Absolute Deviation from Mean[/C][C]2.32051282051282[/C][/ROW]
[ROW][C]Median Absolute Deviation from Median[/C][C]1[/C][/ROW]
[ROW][C]Mean Squared Deviation from Mean[/C][C]135.588413723029[/C][/ROW]
[ROW][C]Mean Squared Deviation from Median[/C][C]137.332167832168[/C][/ROW]
[ROW][C]Interquartile Difference (Weighted Average at Xnp)[/C][C]2[/C][/ROW]
[ROW][C]Interquartile Difference (Weighted Average at X(n+1)p)[/C][C]2[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function)[/C][C]2[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function - Averaging)[/C][C]2[/C][/ROW]
[ROW][C]Interquartile Difference (Empirical Distribution Function - Interpolation)[/C][C]2[/C][/ROW]
[ROW][C]Interquartile Difference (Closest Observation)[/C][C]2[/C][/ROW]
[ROW][C]Interquartile Difference (True Basic - Statistics Graphics Toolkit)[/C][C]2[/C][/ROW]
[ROW][C]Interquartile Difference (MS Excel (old versions))[/C][C]2[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Weighted Average at Xnp)[/C][C]1[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Weighted Average at X(n+1)p)[/C][C]1[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function)[/C][C]1[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function - Averaging)[/C][C]1[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Empirical Distribution Function - Interpolation)[/C][C]1[/C][/ROW]
[ROW][C]Semi Interquartile Difference (Closest Observation)[/C][C]1[/C][/ROW]
[ROW][C]Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)[/C][C]1[/C][/ROW]
[ROW][C]Semi Interquartile Difference (MS Excel (old versions))[/C][C]1[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Weighted Average at Xnp)[/C][C]0.0909090909090909[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Weighted Average at X(n+1)p)[/C][C]0.0909090909090909[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function)[/C][C]0.0909090909090909[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)[/C][C]0.0909090909090909[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)[/C][C]0.0909090909090909[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (Closest Observation)[/C][C]0.0909090909090909[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)[/C][C]0.0909090909090909[/C][/ROW]
[ROW][C]Coefficient of Quartile Variation (MS Excel (old versions))[/C][C]0.0909090909090909[/C][/ROW]
[ROW][C]Number of all Pairs of Observations[/C][C]367653[/C][/ROW]
[ROW][C]Squared Differences between all Pairs of Observations[/C][C]271.493253149029[/C][/ROW]
[ROW][C]Mean Absolute Differences between all Pairs of Observations[/C][C]5.34460755114197[/C][/ROW]
[ROW][C]Gini Mean Difference[/C][C]5.34460755114197[/C][/ROW]
[ROW][C]Leik Measure of Dispersion[/C][C]0.522154190583493[/C][/ROW]
[ROW][C]Index of Diversity[/C][C]0.997793434131595[/C][/ROW]
[ROW][C]Index of Qualitative Variation[/C][C]0.998957720519146[/C][/ROW]
[ROW][C]Coefficient of Dispersion[/C][C]0.325582343064861[/C][/ROW]
[ROW][C]Observations[/C][C]858[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=231250&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=231250&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 range98
Relative range (unbiased)8.41126959013911
Relative range (biased)8.41617555123872
Variance (unbiased)135.746626574515
Variance (biased)135.588413723029
Standard Deviation (unbiased)11.6510354292876
Standard Deviation (biased)11.6442438021122
Coefficient of Variation (unbiased)0.945661564499929
Coefficient of Variation (biased)0.945110319005987
Mean Squared Error (MSE versus 0)287.38344988345
Mean Squared Error (MSE versus Mean)135.588413723029
Mean Absolute Deviation from Mean (MAD Mean)3.58140577371347
Mean Absolute Deviation from Median (MAD Median)3.26923076923077
Median Absolute Deviation from Mean2.32051282051282
Median Absolute Deviation from Median1
Mean Squared Deviation from Mean135.588413723029
Mean Squared Deviation from Median137.332167832168
Interquartile Difference (Weighted Average at Xnp)2
Interquartile Difference (Weighted Average at X(n+1)p)2
Interquartile Difference (Empirical Distribution Function)2
Interquartile Difference (Empirical Distribution Function - Averaging)2
Interquartile Difference (Empirical Distribution Function - Interpolation)2
Interquartile Difference (Closest Observation)2
Interquartile Difference (True Basic - Statistics Graphics Toolkit)2
Interquartile Difference (MS Excel (old versions))2
Semi Interquartile Difference (Weighted Average at Xnp)1
Semi Interquartile Difference (Weighted Average at X(n+1)p)1
Semi Interquartile Difference (Empirical Distribution Function)1
Semi Interquartile Difference (Empirical Distribution Function - Averaging)1
Semi Interquartile Difference (Empirical Distribution Function - Interpolation)1
Semi Interquartile Difference (Closest Observation)1
Semi Interquartile Difference (True Basic - Statistics Graphics Toolkit)1
Semi Interquartile Difference (MS Excel (old versions))1
Coefficient of Quartile Variation (Weighted Average at Xnp)0.0909090909090909
Coefficient of Quartile Variation (Weighted Average at X(n+1)p)0.0909090909090909
Coefficient of Quartile Variation (Empirical Distribution Function)0.0909090909090909
Coefficient of Quartile Variation (Empirical Distribution Function - Averaging)0.0909090909090909
Coefficient of Quartile Variation (Empirical Distribution Function - Interpolation)0.0909090909090909
Coefficient of Quartile Variation (Closest Observation)0.0909090909090909
Coefficient of Quartile Variation (True Basic - Statistics Graphics Toolkit)0.0909090909090909
Coefficient of Quartile Variation (MS Excel (old versions))0.0909090909090909
Number of all Pairs of Observations367653
Squared Differences between all Pairs of Observations271.493253149029
Mean Absolute Differences between all Pairs of Observations5.34460755114197
Gini Mean Difference5.34460755114197
Leik Measure of Dispersion0.522154190583493
Index of Diversity0.997793434131595
Index of Qualitative Variation0.998957720519146
Coefficient of Dispersion0.325582343064861
Observations858



Parameters (Session):
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')