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R Software Module

rwasp_centraltendency.wasp

Title produced by software

Central Tendency

Date of computation

Sat, 04 Dec 2010 09:51:15 +0000

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/2010/Dec/04/t1291456199hpluf9285wk24hv.htm/, Retrieved Mon, 29 Apr 2024 13:00:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105058, Retrieved Mon, 29 Apr 2024 13:00:29 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

171

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

-     [Central Tendency] [SHW_WS3_Yt=c+Xt] [2009-10-16 08:10:06] [8b1aef4e7013bd33fbc2a5833375c5f5]
-  M D    [Central Tendency] [paper univariate] [2010-12-04 09:51:15] [da925928e5a77063c5ecc7b801d712e1] [Current]
- R  D      [Central Tendency] [] [2011-12-01 18:07:24] [74be16979710d4c4e7c6647856088456] 
-    D      [Central Tendency] [Central Tendancy] [2011-12-18 12:40:51] [c505444e07acba7694d29053ca5d114e] 
- RMPD      [Univariate Data Series] [Aantal seconden i...] [2011-12-18 13:06:11] [c505444e07acba7694d29053ca5d114e] 
- RMPD      [Univariate Data Series] [aantal characters] [2011-12-18 13:10:30] [c505444e07acba7694d29053ca5d114e] 
- RMPD      [Univariate Data Series] [] [2011-12-18 13:16:44] [c505444e07acba7694d29053ca5d114e] 
- RMPD      [Univariate Data Series] [] [2011-12-18 13:17:37] [c505444e07acba7694d29053ca5d114e] 
- RM D      [Pearson Correlation] [] [2011-12-18 13:23:29] [c505444e07acba7694d29053ca5d114e] 
- RM D      [Kendall tau Rank Correlation] [] [2011-12-18 13:38:06] [c505444e07acba7694d29053ca5d114e] 

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1,79
1,95
2,26
2,04
2,16
2,75
2,79
2,88
3,36
2,97
3,1
2,49
2,2
2,25
2,09
2,79
3,14
2,93
2,65
2,67
2,26
2,35
2,13
2,18
2,9
2,63
2,67
1,81
1,33
0,88
1,28
1,26
1,26
1,29
1,1
1,37
1,21
1,74
1,76
1,48
1,04
1,62
1,49
1,79
1,8
1,58
1,86
1,74
1,59
1,26
1,13
1,92
2,61
2,26
2,41
2,26
2,03
2,86
2,55
2,27
2,26
2,57
3,07
2,76
2,51
2,87
3,14
3,11
3,16
2,47
2,57
2,89

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' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105058&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105058&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105058&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' @ 72.249.127.135

Central Tendency - Ungrouped Data
Measure	Value	S.E.	Value/S.E.
Arithmetic Mean	2.18888888888889	0.0750780906851099	29.1548289109996
Geometric Mean	2.08657236970492
Harmonic Mean	1.97447077267891
Quadratic Mean	2.27847353872426
Winsorized Mean ( 1 / 24 )	2.18833333333333	0.0739998519644926	29.5721312305241
Winsorized Mean ( 2 / 24 )	2.18944444444444	0.0735418740142282	29.7713985915133
Winsorized Mean ( 3 / 24 )	2.19069444444444	0.073284054716027	29.8931937231544
Winsorized Mean ( 4 / 24 )	2.19347222222222	0.0721026588716559	30.4215164398673
Winsorized Mean ( 5 / 24 )	2.19625	0.0713239533289228	30.7926004868464
Winsorized Mean ( 6 / 24 )	2.19375	0.0708832156587744	30.9487934430136
Winsorized Mean ( 7 / 24 )	2.18402777777778	0.0692590620281086	31.5341807096867
Winsorized Mean ( 8 / 24 )	2.18180555555556	0.0681442265912429	32.0174674318768
Winsorized Mean ( 9 / 24 )	2.17930555555556	0.0673388432613144	32.3632757856942
Winsorized Mean ( 10 / 24 )	2.18347222222222	0.0661077390777444	33.0289955863473
Winsorized Mean ( 11 / 24 )	2.18805555555556	0.0647786162796669	33.7774358456365
Winsorized Mean ( 12 / 24 )	2.20472222222222	0.06136806662922	35.9262128224267
Winsorized Mean ( 13 / 24 )	2.20472222222222	0.0607935178154806	36.2657451229251
Winsorized Mean ( 14 / 24 )	2.20861111111111	0.0559255966559899	39.4919543674562
Winsorized Mean ( 15 / 24 )	2.21069444444444	0.0555968914100741	39.7629145870531
Winsorized Mean ( 16 / 24 )	2.21069444444444	0.0535844755932576	41.2562485676843
Winsorized Mean ( 17 / 24 )	2.23666666666667	0.0490105542592103	45.6364287340485
Winsorized Mean ( 18 / 24 )	2.21666666666667	0.046149040719298	48.0327788425672
Winsorized Mean ( 19 / 24 )	2.22194444444444	0.0453868086325075	48.9557321034689
Winsorized Mean ( 20 / 24 )	2.22472222222222	0.0434325211075561	51.2224979229949
Winsorized Mean ( 21 / 24 )	2.21888888888889	0.0426341001169705	52.0449331122545
Winsorized Mean ( 22 / 24 )	2.21583333333333	0.0413763359144925	53.5531550670057
Winsorized Mean ( 23 / 24 )	2.20625	0.039230887066188	56.2375761801599
Winsorized Mean ( 24 / 24 )	2.22291666666667	0.0368897595856197	60.2583668648576
Trimmed Mean ( 1 / 24 )	2.19085714285714	0.0729870639597987	30.0170608871713
Trimmed Mean ( 2 / 24 )	2.19352941176471	0.0717670986518013	30.5645546911022
Trimmed Mean ( 3 / 24 )	2.19575757575758	0.0705849884018913	31.1079965509882
Trimmed Mean ( 4 / 24 )	2.19765625	0.069268693464084	31.7265439854079
Trimmed Mean ( 5 / 24 )	2.19887096774194	0.0680976314238408	32.2899772248484
Trimmed Mean ( 6 / 24 )	2.1995	0.0669021652677559	32.8763649307486
Trimmed Mean ( 7 / 24 )	2.20068965517241	0.0655475619972625	33.5739360567571
Trimmed Mean ( 8 / 24 )	2.20375	0.064281524935645	34.2827896850031
Trimmed Mean ( 9 / 24 )	2.20740740740741	0.0629616064309	35.0595788852691
Trimmed Mean ( 10 / 24 )	2.21173076923077	0.0614773629099807	35.9763442109469
Trimmed Mean ( 11 / 24 )	2.2158	0.0598802137604735	37.0038759190708
Trimmed Mean ( 12 / 24 )	2.21958333333333	0.0581465792195972	38.1722082902043
Trimmed Mean ( 13 / 24 )	2.22152173913043	0.0567109523381672	39.1727108704419
Trimmed Mean ( 14 / 24 )	2.22363636363636	0.0549573070021372	40.4611594878528
Trimmed Mean ( 15 / 24 )	2.22547619047619	0.0537730879900023	41.3864309018288
Trimmed Mean ( 16 / 24 )	2.22725	0.0522358893963302	42.6383091345713
Trimmed Mean ( 17 / 24 )	2.22921052631579	0.0506281756869851	44.0310261246259
Trimmed Mean ( 18 / 24 )	2.22833333333333	0.04954795656735	44.9732640397467
Trimmed Mean ( 19 / 24 )	2.22970588235294	0.0486877447348406	45.7960395269116
Trimmed Mean ( 20 / 24 )	2.230625	0.047574088018652	46.8873938082734
Trimmed Mean ( 21 / 24 )	2.23133333333333	0.0464256501965086	48.0625112171533
Trimmed Mean ( 22 / 24 )	2.23285714285714	0.0448597377337287	49.7741907478501
Trimmed Mean ( 23 / 24 )	2.235	0.042817142505166	52.1987192333151
Trimmed Mean ( 24 / 24 )	2.23875	0.0403441378210235	55.4913333364972
Median	2.26
Midrange	2.12
Midmean - Weighted Average at Xnp	2.21513513513513
Midmean - Weighted Average at X(n+1)p	2.21513513513513
Midmean - Empirical Distribution Function	2.21513513513513
Midmean - Empirical Distribution Function - Averaging	2.21513513513513
Midmean - Empirical Distribution Function - Interpolation	2.21513513513513
Midmean - Closest Observation	2.21513513513513
Midmean - True Basic - Statistics Graphics Toolkit	2.21513513513513
Midmean - MS Excel (old versions)	2.22921052631579
Number of observations	72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2.18888888888889 & 0.0750780906851099 & 29.1548289109996 \tabularnewline
Geometric Mean & 2.08657236970492 &  &  \tabularnewline
Harmonic Mean & 1.97447077267891 &  &  \tabularnewline
Quadratic Mean & 2.27847353872426 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 2.18833333333333 & 0.0739998519644926 & 29.5721312305241 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 2.18944444444444 & 0.0735418740142282 & 29.7713985915133 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 2.19069444444444 & 0.073284054716027 & 29.8931937231544 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 2.19347222222222 & 0.0721026588716559 & 30.4215164398673 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 2.19625 & 0.0713239533289228 & 30.7926004868464 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 2.19375 & 0.0708832156587744 & 30.9487934430136 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 2.18402777777778 & 0.0692590620281086 & 31.5341807096867 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 2.18180555555556 & 0.0681442265912429 & 32.0174674318768 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 2.17930555555556 & 0.0673388432613144 & 32.3632757856942 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 2.18347222222222 & 0.0661077390777444 & 33.0289955863473 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 2.18805555555556 & 0.0647786162796669 & 33.7774358456365 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 2.20472222222222 & 0.06136806662922 & 35.9262128224267 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 2.20472222222222 & 0.0607935178154806 & 36.2657451229251 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 2.20861111111111 & 0.0559255966559899 & 39.4919543674562 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 2.21069444444444 & 0.0555968914100741 & 39.7629145870531 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 2.21069444444444 & 0.0535844755932576 & 41.2562485676843 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 2.23666666666667 & 0.0490105542592103 & 45.6364287340485 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 2.21666666666667 & 0.046149040719298 & 48.0327788425672 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 2.22194444444444 & 0.0453868086325075 & 48.9557321034689 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 2.22472222222222 & 0.0434325211075561 & 51.2224979229949 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 2.21888888888889 & 0.0426341001169705 & 52.0449331122545 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 2.21583333333333 & 0.0413763359144925 & 53.5531550670057 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 2.20625 & 0.039230887066188 & 56.2375761801599 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 2.22291666666667 & 0.0368897595856197 & 60.2583668648576 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 2.19085714285714 & 0.0729870639597987 & 30.0170608871713 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 2.19352941176471 & 0.0717670986518013 & 30.5645546911022 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 2.19575757575758 & 0.0705849884018913 & 31.1079965509882 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 2.19765625 & 0.069268693464084 & 31.7265439854079 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 2.19887096774194 & 0.0680976314238408 & 32.2899772248484 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 2.1995 & 0.0669021652677559 & 32.8763649307486 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 2.20068965517241 & 0.0655475619972625 & 33.5739360567571 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 2.20375 & 0.064281524935645 & 34.2827896850031 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 2.20740740740741 & 0.0629616064309 & 35.0595788852691 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 2.21173076923077 & 0.0614773629099807 & 35.9763442109469 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 2.2158 & 0.0598802137604735 & 37.0038759190708 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 2.21958333333333 & 0.0581465792195972 & 38.1722082902043 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 2.22152173913043 & 0.0567109523381672 & 39.1727108704419 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 2.22363636363636 & 0.0549573070021372 & 40.4611594878528 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 2.22547619047619 & 0.0537730879900023 & 41.3864309018288 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 2.22725 & 0.0522358893963302 & 42.6383091345713 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 2.22921052631579 & 0.0506281756869851 & 44.0310261246259 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 2.22833333333333 & 0.04954795656735 & 44.9732640397467 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 2.22970588235294 & 0.0486877447348406 & 45.7960395269116 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 2.230625 & 0.047574088018652 & 46.8873938082734 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 2.23133333333333 & 0.0464256501965086 & 48.0625112171533 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 2.23285714285714 & 0.0448597377337287 & 49.7741907478501 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 2.235 & 0.042817142505166 & 52.1987192333151 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 2.23875 & 0.0403441378210235 & 55.4913333364972 \tabularnewline
Median & 2.26 &  &  \tabularnewline
Midrange & 2.12 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2.21513513513513 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2.21513513513513 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2.21513513513513 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2.21513513513513 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2.21513513513513 &  &  \tabularnewline
Midmean - Closest Observation & 2.21513513513513 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2.21513513513513 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2.22921052631579 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105058&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]2.18888888888889[/C][C]0.0750780906851099[/C][C]29.1548289109996[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.08657236970492[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.97447077267891[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2.27847353872426[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]2.18833333333333[/C][C]0.0739998519644926[/C][C]29.5721312305241[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]2.18944444444444[/C][C]0.0735418740142282[/C][C]29.7713985915133[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]2.19069444444444[/C][C]0.073284054716027[/C][C]29.8931937231544[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]2.19347222222222[/C][C]0.0721026588716559[/C][C]30.4215164398673[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]2.19625[/C][C]0.0713239533289228[/C][C]30.7926004868464[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]2.19375[/C][C]0.0708832156587744[/C][C]30.9487934430136[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]2.18402777777778[/C][C]0.0692590620281086[/C][C]31.5341807096867[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]2.18180555555556[/C][C]0.0681442265912429[/C][C]32.0174674318768[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]2.17930555555556[/C][C]0.0673388432613144[/C][C]32.3632757856942[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]2.18347222222222[/C][C]0.0661077390777444[/C][C]33.0289955863473[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]2.18805555555556[/C][C]0.0647786162796669[/C][C]33.7774358456365[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]2.20472222222222[/C][C]0.06136806662922[/C][C]35.9262128224267[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]2.20472222222222[/C][C]0.0607935178154806[/C][C]36.2657451229251[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]2.20861111111111[/C][C]0.0559255966559899[/C][C]39.4919543674562[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]2.21069444444444[/C][C]0.0555968914100741[/C][C]39.7629145870531[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]2.21069444444444[/C][C]0.0535844755932576[/C][C]41.2562485676843[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]2.23666666666667[/C][C]0.0490105542592103[/C][C]45.6364287340485[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]2.21666666666667[/C][C]0.046149040719298[/C][C]48.0327788425672[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]2.22194444444444[/C][C]0.0453868086325075[/C][C]48.9557321034689[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]2.22472222222222[/C][C]0.0434325211075561[/C][C]51.2224979229949[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]2.21888888888889[/C][C]0.0426341001169705[/C][C]52.0449331122545[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]2.21583333333333[/C][C]0.0413763359144925[/C][C]53.5531550670057[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]2.20625[/C][C]0.039230887066188[/C][C]56.2375761801599[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]2.22291666666667[/C][C]0.0368897595856197[/C][C]60.2583668648576[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]2.19085714285714[/C][C]0.0729870639597987[/C][C]30.0170608871713[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]2.19352941176471[/C][C]0.0717670986518013[/C][C]30.5645546911022[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]2.19575757575758[/C][C]0.0705849884018913[/C][C]31.1079965509882[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]2.19765625[/C][C]0.069268693464084[/C][C]31.7265439854079[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]2.19887096774194[/C][C]0.0680976314238408[/C][C]32.2899772248484[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]2.1995[/C][C]0.0669021652677559[/C][C]32.8763649307486[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]2.20068965517241[/C][C]0.0655475619972625[/C][C]33.5739360567571[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]2.20375[/C][C]0.064281524935645[/C][C]34.2827896850031[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]2.20740740740741[/C][C]0.0629616064309[/C][C]35.0595788852691[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]2.21173076923077[/C][C]0.0614773629099807[/C][C]35.9763442109469[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]2.2158[/C][C]0.0598802137604735[/C][C]37.0038759190708[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]2.21958333333333[/C][C]0.0581465792195972[/C][C]38.1722082902043[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]2.22152173913043[/C][C]0.0567109523381672[/C][C]39.1727108704419[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]2.22363636363636[/C][C]0.0549573070021372[/C][C]40.4611594878528[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]2.22547619047619[/C][C]0.0537730879900023[/C][C]41.3864309018288[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]2.22725[/C][C]0.0522358893963302[/C][C]42.6383091345713[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]2.22921052631579[/C][C]0.0506281756869851[/C][C]44.0310261246259[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]2.22833333333333[/C][C]0.04954795656735[/C][C]44.9732640397467[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]2.22970588235294[/C][C]0.0486877447348406[/C][C]45.7960395269116[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]2.230625[/C][C]0.047574088018652[/C][C]46.8873938082734[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]2.23133333333333[/C][C]0.0464256501965086[/C][C]48.0625112171533[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]2.23285714285714[/C][C]0.0448597377337287[/C][C]49.7741907478501[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]2.235[/C][C]0.042817142505166[/C][C]52.1987192333151[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]2.23875[/C][C]0.0403441378210235[/C][C]55.4913333364972[/C][/ROW]
[ROW][C]Median[/C][C]2.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2.12[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2.21513513513513[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2.21513513513513[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2.21513513513513[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2.21513513513513[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2.21513513513513[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2.21513513513513[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2.21513513513513[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2.22921052631579[/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=105058&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105058&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	2.18888888888889	0.0750780906851099	29.1548289109996
Geometric Mean	2.08657236970492
Harmonic Mean	1.97447077267891
Quadratic Mean	2.27847353872426
Winsorized Mean ( 1 / 24 )	2.18833333333333	0.0739998519644926	29.5721312305241
Winsorized Mean ( 2 / 24 )	2.18944444444444	0.0735418740142282	29.7713985915133
Winsorized Mean ( 3 / 24 )	2.19069444444444	0.073284054716027	29.8931937231544
Winsorized Mean ( 4 / 24 )	2.19347222222222	0.0721026588716559	30.4215164398673
Winsorized Mean ( 5 / 24 )	2.19625	0.0713239533289228	30.7926004868464
Winsorized Mean ( 6 / 24 )	2.19375	0.0708832156587744	30.9487934430136
Winsorized Mean ( 7 / 24 )	2.18402777777778	0.0692590620281086	31.5341807096867
Winsorized Mean ( 8 / 24 )	2.18180555555556	0.0681442265912429	32.0174674318768
Winsorized Mean ( 9 / 24 )	2.17930555555556	0.0673388432613144	32.3632757856942
Winsorized Mean ( 10 / 24 )	2.18347222222222	0.0661077390777444	33.0289955863473
Winsorized Mean ( 11 / 24 )	2.18805555555556	0.0647786162796669	33.7774358456365
Winsorized Mean ( 12 / 24 )	2.20472222222222	0.06136806662922	35.9262128224267
Winsorized Mean ( 13 / 24 )	2.20472222222222	0.0607935178154806	36.2657451229251
Winsorized Mean ( 14 / 24 )	2.20861111111111	0.0559255966559899	39.4919543674562
Winsorized Mean ( 15 / 24 )	2.21069444444444	0.0555968914100741	39.7629145870531
Winsorized Mean ( 16 / 24 )	2.21069444444444	0.0535844755932576	41.2562485676843
Winsorized Mean ( 17 / 24 )	2.23666666666667	0.0490105542592103	45.6364287340485
Winsorized Mean ( 18 / 24 )	2.21666666666667	0.046149040719298	48.0327788425672
Winsorized Mean ( 19 / 24 )	2.22194444444444	0.0453868086325075	48.9557321034689
Winsorized Mean ( 20 / 24 )	2.22472222222222	0.0434325211075561	51.2224979229949
Winsorized Mean ( 21 / 24 )	2.21888888888889	0.0426341001169705	52.0449331122545
Winsorized Mean ( 22 / 24 )	2.21583333333333	0.0413763359144925	53.5531550670057
Winsorized Mean ( 23 / 24 )	2.20625	0.039230887066188	56.2375761801599
Winsorized Mean ( 24 / 24 )	2.22291666666667	0.0368897595856197	60.2583668648576
Trimmed Mean ( 1 / 24 )	2.19085714285714	0.0729870639597987	30.0170608871713
Trimmed Mean ( 2 / 24 )	2.19352941176471	0.0717670986518013	30.5645546911022
Trimmed Mean ( 3 / 24 )	2.19575757575758	0.0705849884018913	31.1079965509882
Trimmed Mean ( 4 / 24 )	2.19765625	0.069268693464084	31.7265439854079
Trimmed Mean ( 5 / 24 )	2.19887096774194	0.0680976314238408	32.2899772248484
Trimmed Mean ( 6 / 24 )	2.1995	0.0669021652677559	32.8763649307486
Trimmed Mean ( 7 / 24 )	2.20068965517241	0.0655475619972625	33.5739360567571
Trimmed Mean ( 8 / 24 )	2.20375	0.064281524935645	34.2827896850031
Trimmed Mean ( 9 / 24 )	2.20740740740741	0.0629616064309	35.0595788852691
Trimmed Mean ( 10 / 24 )	2.21173076923077	0.0614773629099807	35.9763442109469
Trimmed Mean ( 11 / 24 )	2.2158	0.0598802137604735	37.0038759190708
Trimmed Mean ( 12 / 24 )	2.21958333333333	0.0581465792195972	38.1722082902043
Trimmed Mean ( 13 / 24 )	2.22152173913043	0.0567109523381672	39.1727108704419
Trimmed Mean ( 14 / 24 )	2.22363636363636	0.0549573070021372	40.4611594878528
Trimmed Mean ( 15 / 24 )	2.22547619047619	0.0537730879900023	41.3864309018288
Trimmed Mean ( 16 / 24 )	2.22725	0.0522358893963302	42.6383091345713
Trimmed Mean ( 17 / 24 )	2.22921052631579	0.0506281756869851	44.0310261246259
Trimmed Mean ( 18 / 24 )	2.22833333333333	0.04954795656735	44.9732640397467
Trimmed Mean ( 19 / 24 )	2.22970588235294	0.0486877447348406	45.7960395269116
Trimmed Mean ( 20 / 24 )	2.230625	0.047574088018652	46.8873938082734
Trimmed Mean ( 21 / 24 )	2.23133333333333	0.0464256501965086	48.0625112171533
Trimmed Mean ( 22 / 24 )	2.23285714285714	0.0448597377337287	49.7741907478501
Trimmed Mean ( 23 / 24 )	2.235	0.042817142505166	52.1987192333151
Trimmed Mean ( 24 / 24 )	2.23875	0.0403441378210235	55.4913333364972
Median	2.26
Midrange	2.12
Midmean - Weighted Average at Xnp	2.21513513513513
Midmean - Weighted Average at X(n+1)p	2.21513513513513
Midmean - Empirical Distribution Function	2.21513513513513
Midmean - Empirical Distribution Function - Averaging	2.21513513513513
Midmean - Empirical Distribution Function - Interpolation	2.21513513513513
Midmean - Closest Observation	2.21513513513513
Midmean - True Basic - Statistics Graphics Toolkit	2.21513513513513
Midmean - MS Excel (old versions)	2.22921052631579
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