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*Unverified author*

R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Thu, 18 Oct 2012 08:27:33 -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/Oct/18/t13505632971geqzxac2c35fp0.htm/, Retrieved Mon, 29 Apr 2024 05:59:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=179519, Retrieved Mon, 29 Apr 2024 05:59:00 +0000

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No (this computation is public)

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Estimated Impact

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

-       [Central Tendency] [] [2012-10-18 12:27:33] [be23bcf5581d42dc10000203a523c779] [Current]

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0,68
0,68
0,69
0,69
0,7
0,7
0,7
0,7
0,7
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,71
0,76
0,77
0,78
0,85
0,89
0,9
0,91
0,91
0,91
0,9
0,89
0,88
0,87
0,86
0,87
0,87
0,87
0,85
0,84
0,84
0,84
0,84
0,84
0,82
0,87
0,92
0,92
0,92
0,93
0,94
0,87
0,84
0,83
0,81
0,81
0,81
0,8
0,8
0,8
0,8
0,8
0,8
0,79
0,8
0,8
0,8
0,81
0,83
0,83
0,83
0,83
0,82
0,82
0,82

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179519&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]2 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=179519&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179519&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	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	0.808888888888889	0.00868856828933565	93.0980642555022
Geometric Mean	0.805505349492587
Harmonic Mean	0.80205851558656
Quadratic Mean	0.812195241989949
Winsorized Mean ( 1 / 24 )	0.80875	0.00866011286145181	93.3879284183392
Winsorized Mean ( 2 / 24 )	0.80875	0.0085510011402632	94.5795687234708
Winsorized Mean ( 3 / 24 )	0.80875	0.0085510011402632	94.5795687234708
Winsorized Mean ( 4 / 24 )	0.809305555555556	0.00844601374821813	95.8210085469369
Winsorized Mean ( 5 / 24 )	0.808611111111111	0.00832230621485328	97.1619032315752
Winsorized Mean ( 6 / 24 )	0.808611111111111	0.00832230621485328	97.1619032315752
Winsorized Mean ( 7 / 24 )	0.808611111111111	0.00832230621485328	97.1619032315752
Winsorized Mean ( 8 / 24 )	0.8075	0.0081379681629751	99.2262422054982
Winsorized Mean ( 9 / 24 )	0.80875	0.00791172319092151	102.221725973429
Winsorized Mean ( 10 / 24 )	0.807361111111111	0.00769374950958621	104.937275395457
Winsorized Mean ( 11 / 24 )	0.807361111111111	0.00769374950958621	104.937275395457
Winsorized Mean ( 12 / 24 )	0.805694444444444	0.00745047915424846	108.139950164818
Winsorized Mean ( 13 / 24 )	0.803888888888889	0.00720685737706438	111.544997608423
Winsorized Mean ( 14 / 24 )	0.803888888888889	0.00720685737706438	111.544997608423
Winsorized Mean ( 15 / 24 )	0.803888888888889	0.00720685737706438	111.544997608423
Winsorized Mean ( 16 / 24 )	0.803888888888889	0.00720685737706438	111.544997608423
Winsorized Mean ( 17 / 24 )	0.803888888888889	0.00720685737706438	111.544997608423
Winsorized Mean ( 18 / 24 )	0.816388888888889	0.00504791422379389	161.727963807458
Winsorized Mean ( 19 / 24 )	0.816388888888889	0.00424828767657331	192.168928057949
Winsorized Mean ( 20 / 24 )	0.816388888888889	0.00343339005579856	237.779243144865
Winsorized Mean ( 21 / 24 )	0.819305555555556	0.00301487177744984	271.754693411397
Winsorized Mean ( 22 / 24 )	0.819305555555556	0.00218765912802741	374.512438916531
Winsorized Mean ( 23 / 24 )	0.819305555555556	0.00218765912802741	374.512438916531
Winsorized Mean ( 24 / 24 )	0.819305555555556	0.00218765912802741	374.512438916531
Trimmed Mean ( 1 / 24 )	0.808857142857143	0.00853816873501164	94.7342653864804
Trimmed Mean ( 2 / 24 )	0.808970588235294	0.00839158956930475	96.4025446614303
Trimmed Mean ( 3 / 24 )	0.809090909090909	0.00828323572443399	97.6781219329836
Trimmed Mean ( 4 / 24 )	0.80921875	0.00815069102965587	99.2822261395628
Trimmed Mean ( 5 / 24 )	0.809193548387097	0.00802658982473445	100.814114842833
Trimmed Mean ( 6 / 24 )	0.809333333333333	0.0079114687068718	102.298746708099
Trimmed Mean ( 7 / 24 )	0.80948275862069	0.00776789121485217	104.208817583975
Trimmed Mean ( 8 / 24 )	0.809642857142857	0.00758914247382012	106.684366505945
Trimmed Mean ( 9 / 24 )	0.81	0.00741124987690643	109.293305913753
Trimmed Mean ( 10 / 24 )	0.810192307692308	0.00724225484569751	111.870173717185
Trimmed Mean ( 11 / 24 )	0.8106	0.00707631865550766	114.551087855419
Trimmed Mean ( 12 / 24 )	0.811041666666667	0.00686263125501559	118.182317616718
Trimmed Mean ( 13 / 24 )	0.811739130434783	0.00663983257330742	122.252951632851
Trimmed Mean ( 14 / 24 )	0.812727272727273	0.00639902572826501	127.007970781769
Trimmed Mean ( 15 / 24 )	0.813809523809524	0.0060768632732567	133.919340820283
Trimmed Mean ( 16 / 24 )	0.815	0.00563869415688347	144.537011110114
Trimmed Mean ( 17 / 24 )	0.816315789473684	0.00502371407198282	162.492486191892
Trimmed Mean ( 18 / 24 )	0.817777777777778	0.00410402649963425	199.262304434598
Trimmed Mean ( 19 / 24 )	0.817941176470588	0.00367531176032703	222.55014807174
Trimmed Mean ( 20 / 24 )	0.818125	0.00334318939376467	244.713925428775
Trimmed Mean ( 21 / 24 )	0.818333333333333	0.00314709621069756	260.028063505548
Trimmed Mean ( 22 / 24 )	0.818214285714286	0.00300147985672232	272.603623803024
Trimmed Mean ( 23 / 24 )	0.818076923076923	0.00303919173309821	269.175818744071
Trimmed Mean ( 24 / 24 )	0.817916666666667	0.00306801915670253	266.594380572824
Median	0.82
Midrange	0.81
Midmean - Weighted Average at Xnp	0.8036
Midmean - Weighted Average at X(n+1)p	0.824146341463414
Midmean - Empirical Distribution Function	0.8036
Midmean - Empirical Distribution Function - Averaging	0.824146341463414
Midmean - Empirical Distribution Function - Interpolation	0.824146341463414
Midmean - Closest Observation	0.8036
Midmean - True Basic - Statistics Graphics Toolkit	0.824146341463414
Midmean - MS Excel (old versions)	0.8036
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.808888888888889 & 0.00868856828933565 & 93.0980642555022 \tabularnewline
Geometric Mean & 0.805505349492587 &  &  \tabularnewline
Harmonic Mean & 0.80205851558656 &  &  \tabularnewline
Quadratic Mean & 0.812195241989949 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 0.80875 & 0.00866011286145181 & 93.3879284183392 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 0.80875 & 0.0085510011402632 & 94.5795687234708 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 0.80875 & 0.0085510011402632 & 94.5795687234708 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 0.809305555555556 & 0.00844601374821813 & 95.8210085469369 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 0.808611111111111 & 0.00832230621485328 & 97.1619032315752 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 0.808611111111111 & 0.00832230621485328 & 97.1619032315752 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 0.808611111111111 & 0.00832230621485328 & 97.1619032315752 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 0.8075 & 0.0081379681629751 & 99.2262422054982 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 0.80875 & 0.00791172319092151 & 102.221725973429 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 0.807361111111111 & 0.00769374950958621 & 104.937275395457 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 0.807361111111111 & 0.00769374950958621 & 104.937275395457 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 0.805694444444444 & 0.00745047915424846 & 108.139950164818 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 0.803888888888889 & 0.00720685737706438 & 111.544997608423 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 0.803888888888889 & 0.00720685737706438 & 111.544997608423 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 0.803888888888889 & 0.00720685737706438 & 111.544997608423 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 0.803888888888889 & 0.00720685737706438 & 111.544997608423 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 0.803888888888889 & 0.00720685737706438 & 111.544997608423 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 0.816388888888889 & 0.00504791422379389 & 161.727963807458 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 0.816388888888889 & 0.00424828767657331 & 192.168928057949 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 0.816388888888889 & 0.00343339005579856 & 237.779243144865 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 0.819305555555556 & 0.00301487177744984 & 271.754693411397 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 0.819305555555556 & 0.00218765912802741 & 374.512438916531 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 0.819305555555556 & 0.00218765912802741 & 374.512438916531 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 0.819305555555556 & 0.00218765912802741 & 374.512438916531 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 0.808857142857143 & 0.00853816873501164 & 94.7342653864804 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 0.808970588235294 & 0.00839158956930475 & 96.4025446614303 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 0.809090909090909 & 0.00828323572443399 & 97.6781219329836 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 0.80921875 & 0.00815069102965587 & 99.2822261395628 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 0.809193548387097 & 0.00802658982473445 & 100.814114842833 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 0.809333333333333 & 0.0079114687068718 & 102.298746708099 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 0.80948275862069 & 0.00776789121485217 & 104.208817583975 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 0.809642857142857 & 0.00758914247382012 & 106.684366505945 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 0.81 & 0.00741124987690643 & 109.293305913753 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 0.810192307692308 & 0.00724225484569751 & 111.870173717185 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 0.8106 & 0.00707631865550766 & 114.551087855419 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 0.811041666666667 & 0.00686263125501559 & 118.182317616718 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 0.811739130434783 & 0.00663983257330742 & 122.252951632851 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 0.812727272727273 & 0.00639902572826501 & 127.007970781769 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 0.813809523809524 & 0.0060768632732567 & 133.919340820283 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 0.815 & 0.00563869415688347 & 144.537011110114 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 0.816315789473684 & 0.00502371407198282 & 162.492486191892 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 0.817777777777778 & 0.00410402649963425 & 199.262304434598 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 0.817941176470588 & 0.00367531176032703 & 222.55014807174 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 0.818125 & 0.00334318939376467 & 244.713925428775 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 0.818333333333333 & 0.00314709621069756 & 260.028063505548 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 0.818214285714286 & 0.00300147985672232 & 272.603623803024 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 0.818076923076923 & 0.00303919173309821 & 269.175818744071 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 0.817916666666667 & 0.00306801915670253 & 266.594380572824 \tabularnewline
Median & 0.82 &  &  \tabularnewline
Midrange & 0.81 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.8036 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.824146341463414 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.8036 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.824146341463414 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.824146341463414 &  &  \tabularnewline
Midmean - Closest Observation & 0.8036 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.824146341463414 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.8036 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179519&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]0.808888888888889[/C][C]0.00868856828933565[/C][C]93.0980642555022[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.805505349492587[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.80205851558656[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.812195241989949[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]0.80875[/C][C]0.00866011286145181[/C][C]93.3879284183392[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]0.80875[/C][C]0.0085510011402632[/C][C]94.5795687234708[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]0.80875[/C][C]0.0085510011402632[/C][C]94.5795687234708[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]0.809305555555556[/C][C]0.00844601374821813[/C][C]95.8210085469369[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]0.808611111111111[/C][C]0.00832230621485328[/C][C]97.1619032315752[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]0.808611111111111[/C][C]0.00832230621485328[/C][C]97.1619032315752[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]0.808611111111111[/C][C]0.00832230621485328[/C][C]97.1619032315752[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]0.8075[/C][C]0.0081379681629751[/C][C]99.2262422054982[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]0.80875[/C][C]0.00791172319092151[/C][C]102.221725973429[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]0.807361111111111[/C][C]0.00769374950958621[/C][C]104.937275395457[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]0.807361111111111[/C][C]0.00769374950958621[/C][C]104.937275395457[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]0.805694444444444[/C][C]0.00745047915424846[/C][C]108.139950164818[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]0.803888888888889[/C][C]0.00720685737706438[/C][C]111.544997608423[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]0.803888888888889[/C][C]0.00720685737706438[/C][C]111.544997608423[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]0.803888888888889[/C][C]0.00720685737706438[/C][C]111.544997608423[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]0.803888888888889[/C][C]0.00720685737706438[/C][C]111.544997608423[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]0.803888888888889[/C][C]0.00720685737706438[/C][C]111.544997608423[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]0.816388888888889[/C][C]0.00504791422379389[/C][C]161.727963807458[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]0.816388888888889[/C][C]0.00424828767657331[/C][C]192.168928057949[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]0.816388888888889[/C][C]0.00343339005579856[/C][C]237.779243144865[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]0.819305555555556[/C][C]0.00301487177744984[/C][C]271.754693411397[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]0.819305555555556[/C][C]0.00218765912802741[/C][C]374.512438916531[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]0.819305555555556[/C][C]0.00218765912802741[/C][C]374.512438916531[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]0.819305555555556[/C][C]0.00218765912802741[/C][C]374.512438916531[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]0.808857142857143[/C][C]0.00853816873501164[/C][C]94.7342653864804[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]0.808970588235294[/C][C]0.00839158956930475[/C][C]96.4025446614303[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]0.809090909090909[/C][C]0.00828323572443399[/C][C]97.6781219329836[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]0.80921875[/C][C]0.00815069102965587[/C][C]99.2822261395628[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]0.809193548387097[/C][C]0.00802658982473445[/C][C]100.814114842833[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]0.809333333333333[/C][C]0.0079114687068718[/C][C]102.298746708099[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]0.80948275862069[/C][C]0.00776789121485217[/C][C]104.208817583975[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]0.809642857142857[/C][C]0.00758914247382012[/C][C]106.684366505945[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]0.81[/C][C]0.00741124987690643[/C][C]109.293305913753[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]0.810192307692308[/C][C]0.00724225484569751[/C][C]111.870173717185[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]0.8106[/C][C]0.00707631865550766[/C][C]114.551087855419[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]0.811041666666667[/C][C]0.00686263125501559[/C][C]118.182317616718[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]0.811739130434783[/C][C]0.00663983257330742[/C][C]122.252951632851[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]0.812727272727273[/C][C]0.00639902572826501[/C][C]127.007970781769[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]0.813809523809524[/C][C]0.0060768632732567[/C][C]133.919340820283[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]0.815[/C][C]0.00563869415688347[/C][C]144.537011110114[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]0.816315789473684[/C][C]0.00502371407198282[/C][C]162.492486191892[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]0.817777777777778[/C][C]0.00410402649963425[/C][C]199.262304434598[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]0.817941176470588[/C][C]0.00367531176032703[/C][C]222.55014807174[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]0.818125[/C][C]0.00334318939376467[/C][C]244.713925428775[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]0.818333333333333[/C][C]0.00314709621069756[/C][C]260.028063505548[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]0.818214285714286[/C][C]0.00300147985672232[/C][C]272.603623803024[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]0.818076923076923[/C][C]0.00303919173309821[/C][C]269.175818744071[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]0.817916666666667[/C][C]0.00306801915670253[/C][C]266.594380572824[/C][/ROW]
[ROW][C]Median[/C][C]0.82[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.81[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.8036[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.824146341463414[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.8036[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.824146341463414[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.824146341463414[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.8036[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.824146341463414[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.8036[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=179519&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179519&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	0.808888888888889	0.00868856828933565	93.0980642555022
Geometric Mean	0.805505349492587
Harmonic Mean	0.80205851558656
Quadratic Mean	0.812195241989949
Winsorized Mean ( 1 / 24 )	0.80875	0.00866011286145181	93.3879284183392
Winsorized Mean ( 2 / 24 )	0.80875	0.0085510011402632	94.5795687234708
Winsorized Mean ( 3 / 24 )	0.80875	0.0085510011402632	94.5795687234708
Winsorized Mean ( 4 / 24 )	0.809305555555556	0.00844601374821813	95.8210085469369
Winsorized Mean ( 5 / 24 )	0.808611111111111	0.00832230621485328	97.1619032315752
Winsorized Mean ( 6 / 24 )	0.808611111111111	0.00832230621485328	97.1619032315752
Winsorized Mean ( 7 / 24 )	0.808611111111111	0.00832230621485328	97.1619032315752
Winsorized Mean ( 8 / 24 )	0.8075	0.0081379681629751	99.2262422054982
Winsorized Mean ( 9 / 24 )	0.80875	0.00791172319092151	102.221725973429
Winsorized Mean ( 10 / 24 )	0.807361111111111	0.00769374950958621	104.937275395457
Winsorized Mean ( 11 / 24 )	0.807361111111111	0.00769374950958621	104.937275395457
Winsorized Mean ( 12 / 24 )	0.805694444444444	0.00745047915424846	108.139950164818
Winsorized Mean ( 13 / 24 )	0.803888888888889	0.00720685737706438	111.544997608423
Winsorized Mean ( 14 / 24 )	0.803888888888889	0.00720685737706438	111.544997608423
Winsorized Mean ( 15 / 24 )	0.803888888888889	0.00720685737706438	111.544997608423
Winsorized Mean ( 16 / 24 )	0.803888888888889	0.00720685737706438	111.544997608423
Winsorized Mean ( 17 / 24 )	0.803888888888889	0.00720685737706438	111.544997608423
Winsorized Mean ( 18 / 24 )	0.816388888888889	0.00504791422379389	161.727963807458
Winsorized Mean ( 19 / 24 )	0.816388888888889	0.00424828767657331	192.168928057949
Winsorized Mean ( 20 / 24 )	0.816388888888889	0.00343339005579856	237.779243144865
Winsorized Mean ( 21 / 24 )	0.819305555555556	0.00301487177744984	271.754693411397
Winsorized Mean ( 22 / 24 )	0.819305555555556	0.00218765912802741	374.512438916531
Winsorized Mean ( 23 / 24 )	0.819305555555556	0.00218765912802741	374.512438916531
Winsorized Mean ( 24 / 24 )	0.819305555555556	0.00218765912802741	374.512438916531
Trimmed Mean ( 1 / 24 )	0.808857142857143	0.00853816873501164	94.7342653864804
Trimmed Mean ( 2 / 24 )	0.808970588235294	0.00839158956930475	96.4025446614303
Trimmed Mean ( 3 / 24 )	0.809090909090909	0.00828323572443399	97.6781219329836
Trimmed Mean ( 4 / 24 )	0.80921875	0.00815069102965587	99.2822261395628
Trimmed Mean ( 5 / 24 )	0.809193548387097	0.00802658982473445	100.814114842833
Trimmed Mean ( 6 / 24 )	0.809333333333333	0.0079114687068718	102.298746708099
Trimmed Mean ( 7 / 24 )	0.80948275862069	0.00776789121485217	104.208817583975
Trimmed Mean ( 8 / 24 )	0.809642857142857	0.00758914247382012	106.684366505945
Trimmed Mean ( 9 / 24 )	0.81	0.00741124987690643	109.293305913753
Trimmed Mean ( 10 / 24 )	0.810192307692308	0.00724225484569751	111.870173717185
Trimmed Mean ( 11 / 24 )	0.8106	0.00707631865550766	114.551087855419
Trimmed Mean ( 12 / 24 )	0.811041666666667	0.00686263125501559	118.182317616718
Trimmed Mean ( 13 / 24 )	0.811739130434783	0.00663983257330742	122.252951632851
Trimmed Mean ( 14 / 24 )	0.812727272727273	0.00639902572826501	127.007970781769
Trimmed Mean ( 15 / 24 )	0.813809523809524	0.0060768632732567	133.919340820283
Trimmed Mean ( 16 / 24 )	0.815	0.00563869415688347	144.537011110114
Trimmed Mean ( 17 / 24 )	0.816315789473684	0.00502371407198282	162.492486191892
Trimmed Mean ( 18 / 24 )	0.817777777777778	0.00410402649963425	199.262304434598
Trimmed Mean ( 19 / 24 )	0.817941176470588	0.00367531176032703	222.55014807174
Trimmed Mean ( 20 / 24 )	0.818125	0.00334318939376467	244.713925428775
Trimmed Mean ( 21 / 24 )	0.818333333333333	0.00314709621069756	260.028063505548
Trimmed Mean ( 22 / 24 )	0.818214285714286	0.00300147985672232	272.603623803024
Trimmed Mean ( 23 / 24 )	0.818076923076923	0.00303919173309821	269.175818744071
Trimmed Mean ( 24 / 24 )	0.817916666666667	0.00306801915670253	266.594380572824
Median	0.82
Midrange	0.81
Midmean - Weighted Average at Xnp	0.8036
Midmean - Weighted Average at X(n+1)p	0.824146341463414
Midmean - Empirical Distribution Function	0.8036
Midmean - Empirical Distribution Function - Averaging	0.824146341463414
Midmean - Empirical Distribution Function - Interpolation	0.824146341463414
Midmean - Closest Observation	0.8036
Midmean - True Basic - Statistics Graphics Toolkit	0.824146341463414
Midmean - MS Excel (old versions)	0.8036
Number of observations	72

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