Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

Author's title

Author

*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Mon, 28 May 2012 11:14:15 -0400

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/2012/May/28/t1338218181f7i6pxx0ht5t1os.htm/, Retrieved Thu, 02 May 2024 10:04:52 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167813, Retrieved Thu, 02 May 2024 10:04:52 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

103

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

-     [Notched Boxplots] [] [2012-02-17 19:34:18] [2e3d5d2fadc43e8101372c775eeeade1]
- RMPD    [Central Tendency] [michelle vandeweyer] [2012-05-28 15:14:15] [09b6c15525a7e41be57b956512900af9] [Current]

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

2,71
2,69
2,67
2,66
2,67
2,67
2,66
2,72
2,63
2,63
2,65
2,66
2,65
2,62
2,61
2,61
2,62
2,61
2,62
2,65
2,64
2,66
2,67
2,68
2,68
2,71
2,72
2,72
2,71
2,7
2,7
2,7
2,68
2,67
2,66
2,64
2,64
2,63
2,61
2,62
2,61
2,6
2,58
2,55
2,53
2,5
2,48
2,47
2,47
2,46
2,46
2,45
2,44
2,42
2,39
2,37
2,34
2,32
2,3
2,29
2,3
2,29
2,29
2,29
2,29
2,28
2,28
2,28
2,29

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167813&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]1 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=167813&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167813&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.55173913043478	0.0180472012100182	141.392512929832
Geometric Mean	2.54725994758009
Harmonic Mean	2.5426446796492
Quadratic Mean	2.55607517296637
Winsorized Mean ( 1 / 23 )	2.55173913043478	0.0180472012100182	141.392512929832
Winsorized Mean ( 2 / 23 )	2.55173913043478	0.0180472012100182	141.392512929832
Winsorized Mean ( 3 / 23 )	2.55173913043478	0.0178942099654402	142.601385328721
Winsorized Mean ( 4 / 23 )	2.55173913043478	0.0178942099654402	142.601385328721
Winsorized Mean ( 5 / 23 )	2.55173913043478	0.0178942099654402	142.601385328721
Winsorized Mean ( 6 / 23 )	2.55086956521739	0.0177840354023854	143.435924833755
Winsorized Mean ( 7 / 23 )	2.55086956521739	0.0177840354023854	143.435924833755
Winsorized Mean ( 8 / 23 )	2.55086956521739	0.0177840354023854	143.435924833755
Winsorized Mean ( 9 / 23 )	2.55086956521739	0.0173472374357158	147.047596176061
Winsorized Mean ( 10 / 23 )	2.54942028985507	0.0171807551810773	148.388139111776
Winsorized Mean ( 11 / 23 )	2.55260869565217	0.0165099006359026	154.610784882693
Winsorized Mean ( 12 / 23 )	2.55608695652174	0.0157995453970346	161.782310331631
Winsorized Mean ( 13 / 23 )	2.55985507246377	0.0144706139503436	176.900239426467
Winsorized Mean ( 14 / 23 )	2.56391304347826	0.0137000155433051	187.146725153257
Winsorized Mean ( 15 / 23 )	2.5704347826087	0.0125133088273808	205.41607484219
Winsorized Mean ( 16 / 23 )	2.57507246376812	0.0117094390492306	219.914246356431
Winsorized Mean ( 17 / 23 )	2.57753623188406	0.0112958468046518	228.18441826093
Winsorized Mean ( 18 / 23 )	2.57753623188406	0.0105585805421398	244.117684341848
Winsorized Mean ( 19 / 23 )	2.57753623188406	0.0105585805421398	244.117684341848
Winsorized Mean ( 20 / 23 )	2.5804347826087	0.0100879229039974	255.794459093873
Winsorized Mean ( 21 / 23 )	2.5804347826087	0.0100879229039974	255.794459093873
Winsorized Mean ( 22 / 23 )	2.5836231884058	0.00957754507985864	269.758394960635
Winsorized Mean ( 23 / 23 )	2.58695652173913	0.00813699923278391	317.925127891902
Trimmed Mean ( 1 / 23 )	2.55328358208955	0.0179569162003298	142.189424598565
Trimmed Mean ( 2 / 23 )	2.55492307692308	0.0178348770737756	143.254313800673
Trimmed Mean ( 3 / 23 )	2.55666666666667	0.0176745917360587	144.652091818941
Trimmed Mean ( 4 / 23 )	2.55852459016393	0.0175350329521346	145.909311784468
Trimmed Mean ( 5 / 23 )	2.56050847457627	0.0173498799993384	147.58075990577
Trimmed Mean ( 6 / 23 )	2.56263157894737	0.0171085402683023	149.786687745375
Trimmed Mean ( 7 / 23 )	2.56509090909091	0.0168252510395423	152.454837259932
Trimmed Mean ( 8 / 23 )	2.5677358490566	0.0164582453372638	156.015164219413
Trimmed Mean ( 9 / 23 )	2.57058823529412	0.0159838442079247	160.824154806241
Trimmed Mean ( 10 / 23 )	2.57367346938776	0.0154790122268717	166.268585596168
Trimmed Mean ( 11 / 23 )	2.57367346938776	0.0148495449419295	173.316655793315
Trimmed Mean ( 12 / 23 )	2.58066666666667	0.0142041393881353	181.684127151153
Trimmed Mean ( 13 / 23 )	2.58395348837209	0.0135426790808544	190.800762016511
Trimmed Mean ( 14 / 23 )	2.58707317073171	0.01301145790766	198.830383888701
Trimmed Mean ( 15 / 23 )	2.59	0.0125010121047747	207.183224709522
Trimmed Mean ( 16 / 23 )	2.59243243243243	0.0121329311722123	213.669095755674
Trimmed Mean ( 17 / 23 )	2.59457142857143	0.0118345943339525	219.236194782598
Trimmed Mean ( 18 / 23 )	2.59666666666667	0.0115114128699576	225.573237273369
Trimmed Mean ( 19 / 23 )	2.59903225806452	0.0112197487054227	231.647991974042
Trimmed Mean ( 20 / 23 )	2.60172413793103	0.0107486849409549	242.050460332861
Trimmed Mean ( 21 / 23 )	2.60444444444444	0.010188163252782	255.634345448212
Trimmed Mean ( 22 / 23 )	2.60444444444444	0.00926066952223219	281.237165217043
Trimmed Mean ( 23 / 23 )	2.61086956521739	0.00797508579700986	327.378241648046
Median	2.62
Midrange	2.5
Midmean - Weighted Average at Xnp	2.59235294117647
Midmean - Weighted Average at X(n+1)p	2.60230769230769
Midmean - Empirical Distribution Function	2.60230769230769
Midmean - Empirical Distribution Function - Averaging	2.60230769230769
Midmean - Empirical Distribution Function - Interpolation	2.60230769230769
Midmean - Closest Observation	2.59825
Midmean - True Basic - Statistics Graphics Toolkit	2.60230769230769
Midmean - MS Excel (old versions)	2.60230769230769
Number of observations	69

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.55173913043478 & 0.0180472012100182 & 141.392512929832 \tabularnewline
Geometric Mean & 2.54725994758009 &  &  \tabularnewline
Harmonic Mean & 2.5426446796492 &  &  \tabularnewline
Quadratic Mean & 2.55607517296637 &  &  \tabularnewline
Winsorized Mean ( 1 / 23 ) & 2.55173913043478 & 0.0180472012100182 & 141.392512929832 \tabularnewline
Winsorized Mean ( 2 / 23 ) & 2.55173913043478 & 0.0180472012100182 & 141.392512929832 \tabularnewline
Winsorized Mean ( 3 / 23 ) & 2.55173913043478 & 0.0178942099654402 & 142.601385328721 \tabularnewline
Winsorized Mean ( 4 / 23 ) & 2.55173913043478 & 0.0178942099654402 & 142.601385328721 \tabularnewline
Winsorized Mean ( 5 / 23 ) & 2.55173913043478 & 0.0178942099654402 & 142.601385328721 \tabularnewline
Winsorized Mean ( 6 / 23 ) & 2.55086956521739 & 0.0177840354023854 & 143.435924833755 \tabularnewline
Winsorized Mean ( 7 / 23 ) & 2.55086956521739 & 0.0177840354023854 & 143.435924833755 \tabularnewline
Winsorized Mean ( 8 / 23 ) & 2.55086956521739 & 0.0177840354023854 & 143.435924833755 \tabularnewline
Winsorized Mean ( 9 / 23 ) & 2.55086956521739 & 0.0173472374357158 & 147.047596176061 \tabularnewline
Winsorized Mean ( 10 / 23 ) & 2.54942028985507 & 0.0171807551810773 & 148.388139111776 \tabularnewline
Winsorized Mean ( 11 / 23 ) & 2.55260869565217 & 0.0165099006359026 & 154.610784882693 \tabularnewline
Winsorized Mean ( 12 / 23 ) & 2.55608695652174 & 0.0157995453970346 & 161.782310331631 \tabularnewline
Winsorized Mean ( 13 / 23 ) & 2.55985507246377 & 0.0144706139503436 & 176.900239426467 \tabularnewline
Winsorized Mean ( 14 / 23 ) & 2.56391304347826 & 0.0137000155433051 & 187.146725153257 \tabularnewline
Winsorized Mean ( 15 / 23 ) & 2.5704347826087 & 0.0125133088273808 & 205.41607484219 \tabularnewline
Winsorized Mean ( 16 / 23 ) & 2.57507246376812 & 0.0117094390492306 & 219.914246356431 \tabularnewline
Winsorized Mean ( 17 / 23 ) & 2.57753623188406 & 0.0112958468046518 & 228.18441826093 \tabularnewline
Winsorized Mean ( 18 / 23 ) & 2.57753623188406 & 0.0105585805421398 & 244.117684341848 \tabularnewline
Winsorized Mean ( 19 / 23 ) & 2.57753623188406 & 0.0105585805421398 & 244.117684341848 \tabularnewline
Winsorized Mean ( 20 / 23 ) & 2.5804347826087 & 0.0100879229039974 & 255.794459093873 \tabularnewline
Winsorized Mean ( 21 / 23 ) & 2.5804347826087 & 0.0100879229039974 & 255.794459093873 \tabularnewline
Winsorized Mean ( 22 / 23 ) & 2.5836231884058 & 0.00957754507985864 & 269.758394960635 \tabularnewline
Winsorized Mean ( 23 / 23 ) & 2.58695652173913 & 0.00813699923278391 & 317.925127891902 \tabularnewline
Trimmed Mean ( 1 / 23 ) & 2.55328358208955 & 0.0179569162003298 & 142.189424598565 \tabularnewline
Trimmed Mean ( 2 / 23 ) & 2.55492307692308 & 0.0178348770737756 & 143.254313800673 \tabularnewline
Trimmed Mean ( 3 / 23 ) & 2.55666666666667 & 0.0176745917360587 & 144.652091818941 \tabularnewline
Trimmed Mean ( 4 / 23 ) & 2.55852459016393 & 0.0175350329521346 & 145.909311784468 \tabularnewline
Trimmed Mean ( 5 / 23 ) & 2.56050847457627 & 0.0173498799993384 & 147.58075990577 \tabularnewline
Trimmed Mean ( 6 / 23 ) & 2.56263157894737 & 0.0171085402683023 & 149.786687745375 \tabularnewline
Trimmed Mean ( 7 / 23 ) & 2.56509090909091 & 0.0168252510395423 & 152.454837259932 \tabularnewline
Trimmed Mean ( 8 / 23 ) & 2.5677358490566 & 0.0164582453372638 & 156.015164219413 \tabularnewline
Trimmed Mean ( 9 / 23 ) & 2.57058823529412 & 0.0159838442079247 & 160.824154806241 \tabularnewline
Trimmed Mean ( 10 / 23 ) & 2.57367346938776 & 0.0154790122268717 & 166.268585596168 \tabularnewline
Trimmed Mean ( 11 / 23 ) & 2.57367346938776 & 0.0148495449419295 & 173.316655793315 \tabularnewline
Trimmed Mean ( 12 / 23 ) & 2.58066666666667 & 0.0142041393881353 & 181.684127151153 \tabularnewline
Trimmed Mean ( 13 / 23 ) & 2.58395348837209 & 0.0135426790808544 & 190.800762016511 \tabularnewline
Trimmed Mean ( 14 / 23 ) & 2.58707317073171 & 0.01301145790766 & 198.830383888701 \tabularnewline
Trimmed Mean ( 15 / 23 ) & 2.59 & 0.0125010121047747 & 207.183224709522 \tabularnewline
Trimmed Mean ( 16 / 23 ) & 2.59243243243243 & 0.0121329311722123 & 213.669095755674 \tabularnewline
Trimmed Mean ( 17 / 23 ) & 2.59457142857143 & 0.0118345943339525 & 219.236194782598 \tabularnewline
Trimmed Mean ( 18 / 23 ) & 2.59666666666667 & 0.0115114128699576 & 225.573237273369 \tabularnewline
Trimmed Mean ( 19 / 23 ) & 2.59903225806452 & 0.0112197487054227 & 231.647991974042 \tabularnewline
Trimmed Mean ( 20 / 23 ) & 2.60172413793103 & 0.0107486849409549 & 242.050460332861 \tabularnewline
Trimmed Mean ( 21 / 23 ) & 2.60444444444444 & 0.010188163252782 & 255.634345448212 \tabularnewline
Trimmed Mean ( 22 / 23 ) & 2.60444444444444 & 0.00926066952223219 & 281.237165217043 \tabularnewline
Trimmed Mean ( 23 / 23 ) & 2.61086956521739 & 0.00797508579700986 & 327.378241648046 \tabularnewline
Median & 2.62 &  &  \tabularnewline
Midrange & 2.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.59235294117647 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.60230769230769 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.60230769230769 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.60230769230769 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.60230769230769 &  &  \tabularnewline
Midmean - Closest Observation & 2.59825 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.60230769230769 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.60230769230769 &  &  \tabularnewline
Number of observations & 69 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167813&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]2.55173913043478[/C][C]0.0180472012100182[/C][C]141.392512929832[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.54725994758009[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.5426446796492[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.55607517296637[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 23 )[/C][C]2.55173913043478[/C][C]0.0180472012100182[/C][C]141.392512929832[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 23 )[/C][C]2.55173913043478[/C][C]0.0180472012100182[/C][C]141.392512929832[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 23 )[/C][C]2.55173913043478[/C][C]0.0178942099654402[/C][C]142.601385328721[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 23 )[/C][C]2.55173913043478[/C][C]0.0178942099654402[/C][C]142.601385328721[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 23 )[/C][C]2.55173913043478[/C][C]0.0178942099654402[/C][C]142.601385328721[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 23 )[/C][C]2.55086956521739[/C][C]0.0177840354023854[/C][C]143.435924833755[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 23 )[/C][C]2.55086956521739[/C][C]0.0177840354023854[/C][C]143.435924833755[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 23 )[/C][C]2.55086956521739[/C][C]0.0177840354023854[/C][C]143.435924833755[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 23 )[/C][C]2.55086956521739[/C][C]0.0173472374357158[/C][C]147.047596176061[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 23 )[/C][C]2.54942028985507[/C][C]0.0171807551810773[/C][C]148.388139111776[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 23 )[/C][C]2.55260869565217[/C][C]0.0165099006359026[/C][C]154.610784882693[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 23 )[/C][C]2.55608695652174[/C][C]0.0157995453970346[/C][C]161.782310331631[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 23 )[/C][C]2.55985507246377[/C][C]0.0144706139503436[/C][C]176.900239426467[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 23 )[/C][C]2.56391304347826[/C][C]0.0137000155433051[/C][C]187.146725153257[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 23 )[/C][C]2.5704347826087[/C][C]0.0125133088273808[/C][C]205.41607484219[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 23 )[/C][C]2.57507246376812[/C][C]0.0117094390492306[/C][C]219.914246356431[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 23 )[/C][C]2.57753623188406[/C][C]0.0112958468046518[/C][C]228.18441826093[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 23 )[/C][C]2.57753623188406[/C][C]0.0105585805421398[/C][C]244.117684341848[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 23 )[/C][C]2.57753623188406[/C][C]0.0105585805421398[/C][C]244.117684341848[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 23 )[/C][C]2.5804347826087[/C][C]0.0100879229039974[/C][C]255.794459093873[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 23 )[/C][C]2.5804347826087[/C][C]0.0100879229039974[/C][C]255.794459093873[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 23 )[/C][C]2.5836231884058[/C][C]0.00957754507985864[/C][C]269.758394960635[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 23 )[/C][C]2.58695652173913[/C][C]0.00813699923278391[/C][C]317.925127891902[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 23 )[/C][C]2.55328358208955[/C][C]0.0179569162003298[/C][C]142.189424598565[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 23 )[/C][C]2.55492307692308[/C][C]0.0178348770737756[/C][C]143.254313800673[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 23 )[/C][C]2.55666666666667[/C][C]0.0176745917360587[/C][C]144.652091818941[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 23 )[/C][C]2.55852459016393[/C][C]0.0175350329521346[/C][C]145.909311784468[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 23 )[/C][C]2.56050847457627[/C][C]0.0173498799993384[/C][C]147.58075990577[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 23 )[/C][C]2.56263157894737[/C][C]0.0171085402683023[/C][C]149.786687745375[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 23 )[/C][C]2.56509090909091[/C][C]0.0168252510395423[/C][C]152.454837259932[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 23 )[/C][C]2.5677358490566[/C][C]0.0164582453372638[/C][C]156.015164219413[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 23 )[/C][C]2.57058823529412[/C][C]0.0159838442079247[/C][C]160.824154806241[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 23 )[/C][C]2.57367346938776[/C][C]0.0154790122268717[/C][C]166.268585596168[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 23 )[/C][C]2.57367346938776[/C][C]0.0148495449419295[/C][C]173.316655793315[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 23 )[/C][C]2.58066666666667[/C][C]0.0142041393881353[/C][C]181.684127151153[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 23 )[/C][C]2.58395348837209[/C][C]0.0135426790808544[/C][C]190.800762016511[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 23 )[/C][C]2.58707317073171[/C][C]0.01301145790766[/C][C]198.830383888701[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 23 )[/C][C]2.59[/C][C]0.0125010121047747[/C][C]207.183224709522[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 23 )[/C][C]2.59243243243243[/C][C]0.0121329311722123[/C][C]213.669095755674[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 23 )[/C][C]2.59457142857143[/C][C]0.0118345943339525[/C][C]219.236194782598[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 23 )[/C][C]2.59666666666667[/C][C]0.0115114128699576[/C][C]225.573237273369[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 23 )[/C][C]2.59903225806452[/C][C]0.0112197487054227[/C][C]231.647991974042[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 23 )[/C][C]2.60172413793103[/C][C]0.0107486849409549[/C][C]242.050460332861[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 23 )[/C][C]2.60444444444444[/C][C]0.010188163252782[/C][C]255.634345448212[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 23 )[/C][C]2.60444444444444[/C][C]0.00926066952223219[/C][C]281.237165217043[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 23 )[/C][C]2.61086956521739[/C][C]0.00797508579700986[/C][C]327.378241648046[/C][/ROW]
[ROW][C]Median[/C][C]2.62[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.59235294117647[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.60230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.60230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.60230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.60230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.59825[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.60230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.60230769230769[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]69[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167813&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167813&T=1

As an alternative you can also use a QR Code:

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

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.55173913043478	0.0180472012100182	141.392512929832
Geometric Mean	2.54725994758009
Harmonic Mean	2.5426446796492
Quadratic Mean	2.55607517296637
Winsorized Mean ( 1 / 23 )	2.55173913043478	0.0180472012100182	141.392512929832
Winsorized Mean ( 2 / 23 )	2.55173913043478	0.0180472012100182	141.392512929832
Winsorized Mean ( 3 / 23 )	2.55173913043478	0.0178942099654402	142.601385328721
Winsorized Mean ( 4 / 23 )	2.55173913043478	0.0178942099654402	142.601385328721
Winsorized Mean ( 5 / 23 )	2.55173913043478	0.0178942099654402	142.601385328721
Winsorized Mean ( 6 / 23 )	2.55086956521739	0.0177840354023854	143.435924833755
Winsorized Mean ( 7 / 23 )	2.55086956521739	0.0177840354023854	143.435924833755
Winsorized Mean ( 8 / 23 )	2.55086956521739	0.0177840354023854	143.435924833755
Winsorized Mean ( 9 / 23 )	2.55086956521739	0.0173472374357158	147.047596176061
Winsorized Mean ( 10 / 23 )	2.54942028985507	0.0171807551810773	148.388139111776
Winsorized Mean ( 11 / 23 )	2.55260869565217	0.0165099006359026	154.610784882693
Winsorized Mean ( 12 / 23 )	2.55608695652174	0.0157995453970346	161.782310331631
Winsorized Mean ( 13 / 23 )	2.55985507246377	0.0144706139503436	176.900239426467
Winsorized Mean ( 14 / 23 )	2.56391304347826	0.0137000155433051	187.146725153257
Winsorized Mean ( 15 / 23 )	2.5704347826087	0.0125133088273808	205.41607484219
Winsorized Mean ( 16 / 23 )	2.57507246376812	0.0117094390492306	219.914246356431
Winsorized Mean ( 17 / 23 )	2.57753623188406	0.0112958468046518	228.18441826093
Winsorized Mean ( 18 / 23 )	2.57753623188406	0.0105585805421398	244.117684341848
Winsorized Mean ( 19 / 23 )	2.57753623188406	0.0105585805421398	244.117684341848
Winsorized Mean ( 20 / 23 )	2.5804347826087	0.0100879229039974	255.794459093873
Winsorized Mean ( 21 / 23 )	2.5804347826087	0.0100879229039974	255.794459093873
Winsorized Mean ( 22 / 23 )	2.5836231884058	0.00957754507985864	269.758394960635
Winsorized Mean ( 23 / 23 )	2.58695652173913	0.00813699923278391	317.925127891902
Trimmed Mean ( 1 / 23 )	2.55328358208955	0.0179569162003298	142.189424598565
Trimmed Mean ( 2 / 23 )	2.55492307692308	0.0178348770737756	143.254313800673
Trimmed Mean ( 3 / 23 )	2.55666666666667	0.0176745917360587	144.652091818941
Trimmed Mean ( 4 / 23 )	2.55852459016393	0.0175350329521346	145.909311784468
Trimmed Mean ( 5 / 23 )	2.56050847457627	0.0173498799993384	147.58075990577
Trimmed Mean ( 6 / 23 )	2.56263157894737	0.0171085402683023	149.786687745375
Trimmed Mean ( 7 / 23 )	2.56509090909091	0.0168252510395423	152.454837259932
Trimmed Mean ( 8 / 23 )	2.5677358490566	0.0164582453372638	156.015164219413
Trimmed Mean ( 9 / 23 )	2.57058823529412	0.0159838442079247	160.824154806241
Trimmed Mean ( 10 / 23 )	2.57367346938776	0.0154790122268717	166.268585596168
Trimmed Mean ( 11 / 23 )	2.57367346938776	0.0148495449419295	173.316655793315
Trimmed Mean ( 12 / 23 )	2.58066666666667	0.0142041393881353	181.684127151153
Trimmed Mean ( 13 / 23 )	2.58395348837209	0.0135426790808544	190.800762016511
Trimmed Mean ( 14 / 23 )	2.58707317073171	0.01301145790766	198.830383888701
Trimmed Mean ( 15 / 23 )	2.59	0.0125010121047747	207.183224709522
Trimmed Mean ( 16 / 23 )	2.59243243243243	0.0121329311722123	213.669095755674
Trimmed Mean ( 17 / 23 )	2.59457142857143	0.0118345943339525	219.236194782598
Trimmed Mean ( 18 / 23 )	2.59666666666667	0.0115114128699576	225.573237273369
Trimmed Mean ( 19 / 23 )	2.59903225806452	0.0112197487054227	231.647991974042
Trimmed Mean ( 20 / 23 )	2.60172413793103	0.0107486849409549	242.050460332861
Trimmed Mean ( 21 / 23 )	2.60444444444444	0.010188163252782	255.634345448212
Trimmed Mean ( 22 / 23 )	2.60444444444444	0.00926066952223219	281.237165217043
Trimmed Mean ( 23 / 23 )	2.61086956521739	0.00797508579700986	327.378241648046
Median	2.62
Midrange	2.5
Midmean - Weighted Average at Xnp	2.59235294117647
Midmean - Weighted Average at X(n+1)p	2.60230769230769
Midmean - Empirical Distribution Function	2.60230769230769
Midmean - Empirical Distribution Function - Averaging	2.60230769230769
Midmean - Empirical Distribution Function - Interpolation	2.60230769230769
Midmean - Closest Observation	2.59825
Midmean - True Basic - Statistics Graphics Toolkit	2.60230769230769
Midmean - MS Excel (old versions)	2.60230769230769
Number of observations	69

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

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

geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
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]
}
}
}
}
midmean <- 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)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code