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Author's title

Author

*Unverified author*

R Software Module

co.wasp

Title produced by software

Concentration

Date of computation

Mon, 29 Oct 2007 15:00:17 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Oct/29/mjdoiiiymewvtis1193696425.htm/, Retrieved Tue, 21 Apr 2026 17:24:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2130, Retrieved Tue, 21 Apr 2026 17:24:29 +0000

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Original text written by user:

This is a trial analysis of the iconography of a given subject by Italian artists from the Middle Ages to Modern Times

IsPrivate?

No (this computation is public)

User-defined keywords

artists, artworks

Estimated Impact

467

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Concentration] [Number of Italian...] [2007-10-29 22:00:17] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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Concentration - Ungrouped Data
Entropy	2.287227
Maximum Entropy	2.484907
Normalized Entropy	0.920448
Exponential Index	0.101548
Herfindahl	0.117126
Normalized Herfindahl	0.036865
Gini Coefficient	0.350244
Concentration Coefficient	0.382085
Categories	12

\begin{tabular}{lllllllll}
\hline

Concentration - Ungrouped Data \tabularnewline

Entropy

2.287227 \tabularnewline Maximum Entropy

2.484907 \tabularnewline Normalized Entropy

0.920448 \tabularnewline Exponential Index

0.101548 \tabularnewline Herfindahl

0.117126 \tabularnewline Normalized Herfindahl

0.036865 \tabularnewline Gini Coefficient

0.350244 \tabularnewline Concentration Coefficient

0.382085 \tabularnewline Categories

12 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=2130&T=0

[TABLE]

[ROW][C]Concentration - Ungrouped Data[/C][/ROW]

[ROW][C]Entropy[/C]

2.287227[/C][/ROW] [ROW][C]Maximum Entropy[/C]

2.484907[/C][/ROW] [ROW][C]Normalized Entropy[/C]

0.920448[/C][/ROW] [ROW][C]Exponential Index[/C]

0.101548[/C][/ROW] [ROW][C]Herfindahl[/C]

0.117126[/C][/ROW] [ROW][C]Normalized Herfindahl[/C]

0.036865[/C][/ROW] [ROW][C]Gini Coefficient[/C]

0.350244[/C][/ROW] [ROW][C]Concentration Coefficient[/C]

0.382085[/C][/ROW] [ROW][C]Categories[/C]

12[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=2130&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2130&T=0

As an alternative you can also use a QR Code:

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

Concentration - Ungrouped Data
Entropy	2.287227
Maximum Entropy	2.484907
Normalized Entropy	0.920448
Exponential Index	0.101548
Herfindahl	0.117126
Normalized Herfindahl	0.036865
Gini Coefficient	0.350244
Concentration Coefficient	0.382085
Categories	12

Concentration 2 - Ungrouped Data
Category	Elements (Absolute)	Elements (Relative)	Entropy (Absolute)	Entropy (Relative)
1	11.000000	0.026895	0.097247	0.042517
2	18.000000	0.044010	0.137458	0.060098
3	80.000000	0.195599	0.319157	0.139539
4	63.000000	0.154034	0.288133	0.125975
5	56.000000	0.136919	0.272245	0.119029
6	34.000000	0.083130	0.206773	0.090403
7	36.000000	0.088020	0.213905	0.093521
8	41.000000	0.100244	0.230577	0.100811
9	32.000000	0.078240	0.199353	0.087159
10	11.000000	0.026895	0.097247	0.042517
11	14.000000	0.034230	0.115514	0.050504
12	13.000000	0.031785	0.109618	0.047926

\begin{tabular}{lllllllll}
\hline

Concentration 2 - Ungrouped Data \tabularnewline

Category

Elements (Absolute)

Elements (Relative)

Entropy (Absolute)

Entropy (Relative) \tabularnewline

11.000000

0.026895

0.097247

0.042517 \tabularnewline

18.000000

0.044010

0.137458

0.060098 \tabularnewline

80.000000

0.195599

0.319157

0.139539 \tabularnewline

63.000000

0.154034

0.288133

0.125975 \tabularnewline

56.000000

0.136919

0.272245

0.119029 \tabularnewline

34.000000

0.083130

0.206773

0.090403 \tabularnewline

36.000000

0.088020

0.213905

0.093521 \tabularnewline

41.000000

0.100244

0.230577

0.100811 \tabularnewline

32.000000

0.078240

0.199353

0.087159 \tabularnewline

11.000000

0.026895

0.097247

0.042517 \tabularnewline

14.000000

0.034230

0.115514

0.050504 \tabularnewline

13.000000

0.031785

0.109618

0.047926 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=2130&T=1

[TABLE]

[ROW][C]Concentration 2 - Ungrouped Data[/C][/ROW]

[ROW]

Category[/C]

Elements (Absolute)[/C]

Elements (Relative)[/C]

Entropy (Absolute)[/C]

Entropy (Relative)[/C][/ROW] [ROW]

1[/C]

11.000000[/C]

0.026895[/C]

0.097247[/C]

0.042517[/C][/ROW] [ROW]

2[/C]

18.000000[/C]

0.044010[/C]

0.137458[/C]

0.060098[/C][/ROW] [ROW]

3[/C]

80.000000[/C]

0.195599[/C]

0.319157[/C]

0.139539[/C][/ROW] [ROW]

4[/C]

63.000000[/C]

0.154034[/C]

0.288133[/C]

0.125975[/C][/ROW] [ROW]

5[/C]

56.000000[/C]

0.136919[/C]

0.272245[/C]

0.119029[/C][/ROW] [ROW]

6[/C]

34.000000[/C]

0.083130[/C]

0.206773[/C]

0.090403[/C][/ROW] [ROW]

7[/C]

36.000000[/C]

0.088020[/C]

0.213905[/C]

0.093521[/C][/ROW] [ROW]

8[/C]

41.000000[/C]

0.100244[/C]

0.230577[/C]

0.100811[/C][/ROW] [ROW]

9[/C]

32.000000[/C]

0.078240[/C]

0.199353[/C]

0.087159[/C][/ROW] [ROW]

10[/C]

11.000000[/C]

0.026895[/C]

0.097247[/C]

0.042517[/C][/ROW] [ROW]

11[/C]

14.000000[/C]

0.034230[/C]

0.115514[/C]

0.050504[/C][/ROW] [ROW]

12[/C]

13.000000[/C]

0.031785[/C]

0.109618[/C]

0.047926[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=2130&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2130&T=1

As an alternative you can also use a QR Code:

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

Concentration 2 - Ungrouped Data
Category	Elements (Absolute)	Elements (Relative)	Entropy (Absolute)	Entropy (Relative)
1	11.000000	0.026895	0.097247	0.042517
2	18.000000	0.044010	0.137458	0.060098
3	80.000000	0.195599	0.319157	0.139539
4	63.000000	0.154034	0.288133	0.125975
5	56.000000	0.136919	0.272245	0.119029
6	34.000000	0.083130	0.206773	0.090403
7	36.000000	0.088020	0.213905	0.093521
8	41.000000	0.100244	0.230577	0.100811
9	32.000000	0.078240	0.199353	0.087159
10	11.000000	0.026895	0.097247	0.042517
11	14.000000	0.034230	0.115514	0.050504
12	13.000000	0.031785	0.109618	0.047926

Concentration 3 - Ungrouped Data
Category	Elements (Absolute Cumulated)	Elements (Relative Cumulated)	Entropy (Absolute Cumulated)	Entropy (Relative Cumulated)
1	11.000000	0.026895	0.097247	0.042517
2	29.000000	0.070905	0.234705	0.102615
3	109.000000	0.266504	0.553861	0.242154
4	172.000000	0.420538	0.841995	0.368129
5	228.000000	0.557457	1.114240	0.487158
6	262.000000	0.640587	1.321013	0.577561
7	298.000000	0.728606	1.534918	0.671082
8	339.000000	0.828851	1.765494	0.771893
9	371.000000	0.907090	1.964847	0.859052
10	382.000000	0.933985	2.062094	0.901570
11	396.000000	0.968215	2.177608	0.952074
12	409.000000	1.000000	2.287227	1.000000

\begin{tabular}{lllllllll}
\hline

Concentration 3 - Ungrouped Data \tabularnewline

Category

Elements (Absolute Cumulated)

Elements (Relative Cumulated)

Entropy (Absolute Cumulated)

Entropy (Relative Cumulated) \tabularnewline

11.000000

0.026895

0.097247

0.042517 \tabularnewline

29.000000

0.070905

0.234705

0.102615 \tabularnewline

109.000000

0.266504

0.553861

0.242154 \tabularnewline

172.000000

0.420538

0.841995

0.368129 \tabularnewline

228.000000

0.557457

1.114240

0.487158 \tabularnewline

262.000000

0.640587

1.321013

0.577561 \tabularnewline

298.000000

0.728606

1.534918

0.671082 \tabularnewline

339.000000

0.828851

1.765494

0.771893 \tabularnewline

371.000000

0.907090

1.964847

0.859052 \tabularnewline

382.000000

0.933985

2.062094

0.901570 \tabularnewline

396.000000

0.968215

2.177608

0.952074 \tabularnewline

409.000000

1.000000

2.287227

1.000000 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=2130&T=2

[TABLE]

[ROW][C]Concentration 3 - Ungrouped Data[/C][/ROW]

[ROW]

Category[/C]

Elements (Absolute Cumulated)[/C]

Elements (Relative Cumulated)[/C]

Entropy (Absolute Cumulated)[/C]

Entropy (Relative Cumulated)[/C][/ROW] [ROW]

1[/C]

11.000000[/C]

0.026895[/C]

0.097247[/C]

0.042517[/C][/ROW] [ROW]

2[/C]

29.000000[/C]

0.070905[/C]

0.234705[/C]

0.102615[/C][/ROW] [ROW]

3[/C]

109.000000[/C]

0.266504[/C]

0.553861[/C]

0.242154[/C][/ROW] [ROW]

4[/C]

172.000000[/C]

0.420538[/C]

0.841995[/C]

0.368129[/C][/ROW] [ROW]

5[/C]

228.000000[/C]

0.557457[/C]

1.114240[/C]

0.487158[/C][/ROW] [ROW]

6[/C]

262.000000[/C]

0.640587[/C]

1.321013[/C]

0.577561[/C][/ROW] [ROW]

7[/C]

298.000000[/C]

0.728606[/C]

1.534918[/C]

0.671082[/C][/ROW] [ROW]

8[/C]

339.000000[/C]

0.828851[/C]

1.765494[/C]

0.771893[/C][/ROW] [ROW]

9[/C]

371.000000[/C]

0.907090[/C]

1.964847[/C]

0.859052[/C][/ROW] [ROW]

10[/C]

382.000000[/C]

0.933985[/C]

2.062094[/C]

0.901570[/C][/ROW] [ROW]

11[/C]

396.000000[/C]

0.968215[/C]

2.177608[/C]

0.952074[/C][/ROW] [ROW]

12[/C]

409.000000[/C]

1.000000[/C]

2.287227[/C]

1.000000[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=2130&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2130&T=2

As an alternative you can also use a QR Code:

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

Concentration 3 - Ungrouped Data
Category	Elements (Absolute Cumulated)	Elements (Relative Cumulated)	Entropy (Absolute Cumulated)	Entropy (Relative Cumulated)
1	11.000000	0.026895	0.097247	0.042517
2	29.000000	0.070905	0.234705	0.102615
3	109.000000	0.266504	0.553861	0.242154
4	172.000000	0.420538	0.841995	0.368129
5	228.000000	0.557457	1.114240	0.487158
6	262.000000	0.640587	1.321013	0.577561
7	298.000000	0.728606	1.534918	0.671082
8	339.000000	0.828851	1.765494	0.771893
9	371.000000	0.907090	1.964847	0.859052
10	382.000000	0.933985	2.062094	0.901570
11	396.000000	0.968215	2.177608	0.952074
12	409.000000	1.000000	2.287227	1.000000

Concentration 4 - Lorenz Curve - Ungrouped Data
Cumulative % of population	Cumulative % of variable
	Expected	Observed
0%	0.000000	0.000010
8%	0.083333	0.026895
17%	0.166667	0.053790
25%	0.250000	0.085575
33%	0.333333	0.119804
42%	0.416667	0.163814
50%	0.500000	0.242054
58%	0.583333	0.325183
67%	0.666667	0.413203
75%	0.750000	0.513447
83%	0.833333	0.650367
92%	0.916667	0.804401
100%	1.000000	1.000000

\begin{tabular}{lllllllll}
\hline

Concentration 4 - Lorenz Curve - Ungrouped Data \tabularnewline

Cumulative % of population

Cumulative % of variable \tabularnewline

Expected

Observed \tabularnewline

0.000000

0.000010 \tabularnewline

0.083333

0.026895 \tabularnewline

17%

0.166667

0.053790 \tabularnewline

25%

0.250000

0.085575 \tabularnewline

33%

0.333333

0.119804 \tabularnewline

42%

0.416667

0.163814 \tabularnewline

50%

0.500000

0.242054 \tabularnewline

58%

0.583333

0.325183 \tabularnewline

67%

0.666667

0.413203 \tabularnewline

75%

0.750000

0.513447 \tabularnewline

83%

0.833333

0.650367 \tabularnewline

92%

0.916667

0.804401 \tabularnewline

100%

1.000000

1.000000 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=2130&T=3

[TABLE]

[ROW][C]Concentration 4 - Lorenz Curve - Ungrouped Data[/C][/ROW]

[ROW]

Cumulative % of population[/C]

Cumulative % of variable[/C][/ROW] [ROW]

[/C]

Expected[/C]

Observed[/C][/ROW] [ROW]

0%[/C]

0.000000[/C]

0.000010[/C][/ROW] [ROW]

8%[/C]

0.083333[/C]

0.026895[/C][/ROW] [ROW]

17%[/C]

0.166667[/C]

0.053790[/C][/ROW] [ROW]

25%[/C]

0.250000[/C]

0.085575[/C][/ROW] [ROW]

33%[/C]

0.333333[/C]

0.119804[/C][/ROW] [ROW]

42%[/C]

0.416667[/C]

0.163814[/C][/ROW] [ROW]

50%[/C]

0.500000[/C]

0.242054[/C][/ROW] [ROW]

58%[/C]

0.583333[/C]

0.325183[/C][/ROW] [ROW]

67%[/C]

0.666667[/C]

0.413203[/C][/ROW] [ROW]

75%[/C]

0.750000[/C]

0.513447[/C][/ROW] [ROW]

83%[/C]

0.833333[/C]

0.650367[/C][/ROW] [ROW]

92%[/C]

0.916667[/C]

0.804401[/C][/ROW] [ROW]

100%[/C]

1.000000[/C]

1.000000[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=2130&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2130&T=3

As an alternative you can also use a QR Code:

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

Concentration 4 - Lorenz Curve - Ungrouped Data
Cumulative % of population	Cumulative % of variable
	Expected	Observed
0%	0.000000	0.000010
8%	0.083333	0.026895
17%	0.166667	0.053790
25%	0.250000	0.085575
33%	0.333333	0.119804
42%	0.416667	0.163814
50%	0.500000	0.242054
58%	0.583333	0.325183
67%	0.666667	0.413203
75%	0.750000	0.513447
83%	0.833333	0.650367
92%	0.916667	0.804401
100%	1.000000	1.000000

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code