Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 30 Nov 2007 07:18:06 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/30/t1196431624wzfp6taqg2bzym6.htm/, Retrieved Sat, 27 Apr 2024 15:01:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7693, Retrieved Sat, 27 Apr 2024 15:01:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact185
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2007-11-30 14:18:06] [2467046df5c61f7ccf2ce4e184abae94] [Current]
Feedback Forum

Post a new message
Dataseries X:
103,1
103,1
103,3
103,5
103,3
103,5
103,8
103,9
103,9
104,2
104,6
104,9
105,2
105,2
105,6
105,6
106,2
106,3
106,4
106,9
107,2
107,3
107,3
107,4
107,55
107,87
108,37
108,38
107,92
108,03
108,14
108,3
108,64
108,66
109,04
109,03
109,03
109,54
109,75
109,83
109,65
109,82
109,95
110,12
110,15
110,2
109,99
110,14
110,14
110,81
110,97
110,99
109,73
109,81
110,02
110,18
110,21
110,25
110,36
110,51
110,64
110,95
111,18
111,19
111,69
111,7
111,83
111,77
111,73
112,01
111,86
112,04




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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=7693&T=0

[TABLE]
[ROW][C]Summary of compuational 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=7693&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7693&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean108.366250.317491108491322341.320582220216
Geometric Mean108.332892116852
Harmonic Mean108.299201416288
Quadratic Mean108.399266519402
Winsorized Mean ( 1 / 24 )108.3658333333330.317423468651428341.392001649169
Winsorized Mean ( 2 / 24 )108.3672222222220.315484215745069343.494909773204
Winsorized Mean ( 3 / 24 )108.3659722222220.315290043314458343.702487661947
Winsorized Mean ( 4 / 24 )108.373750.312298287794647347.019994138622
Winsorized Mean ( 5 / 24 )108.3709722222220.311874862030586347.48222898322
Winsorized Mean ( 6 / 24 )108.3934722222220.30610239470718354.108540463763
Winsorized Mean ( 7 / 24 )108.4022222222220.303912619627141356.688782305969
Winsorized Mean ( 8 / 24 )108.3466666666670.295914605645135366.141665871665
Winsorized Mean ( 9 / 24 )108.3829166666670.287937965893108376.410649184422
Winsorized Mean ( 10 / 24 )108.4120833333330.273230037270471396.779521081775
Winsorized Mean ( 11 / 24 )108.4548611111110.263969339005273410.861585363687
Winsorized Mean ( 12 / 24 )108.5015277777780.254201368347780426.832980809663
Winsorized Mean ( 13 / 24 )108.476250.250830111462159432.469010070847
Winsorized Mean ( 14 / 24 )108.5209722222220.232494817930893466.767273301029
Winsorized Mean ( 15 / 24 )108.4938888888890.229077430816930473.612300006948
Winsorized Mean ( 16 / 24 )108.5938888888890.201917505462864537.813146215107
Winsorized Mean ( 17 / 24 )108.5915277777780.194832766028707557.357625163407
Winsorized Mean ( 18 / 24 )108.6065277777780.189516636590796573.071207528239
Winsorized Mean ( 19 / 24 )108.7358333333330.168197285002809646.477934120741
Winsorized Mean ( 20 / 24 )108.8136111111110.154984514542163702.093440964443
Winsorized Mean ( 21 / 24 )108.8340277777780.149654879410026727.23340666757
Winsorized Mean ( 22 / 24 )108.8309722222220.149276968912359729.054006221934
Winsorized Mean ( 23 / 24 )108.8629166666670.144694843416300752.362102866779
Winsorized Mean ( 24 / 24 )108.906250.136811505395589796.031369475094
Trimmed Mean ( 1 / 24 )108.3890.313276490372785345.985106865254
Trimmed Mean ( 2 / 24 )108.4135294117650.308249380580078351.707209298351
Trimmed Mean ( 3 / 24 )108.4387878787880.303373458383918357.443226762306
Trimmed Mean ( 4 / 24 )108.466093750.297508221273918364.581836715479
Trimmed Mean ( 5 / 24 )108.4929032258060.291449847479477372.252393213025
Trimmed Mean ( 6 / 24 )108.5221666666670.284135729051347381.937769772894
Trimmed Mean ( 7 / 24 )108.5487931034480.276830986150932392.112149773097
Trimmed Mean ( 8 / 24 )108.5757142857140.268375083658593404.567044024982
Trimmed Mean ( 9 / 24 )108.6138888888890.2597249548618418.188113447483
Trimmed Mean ( 10 / 24 )108.6494230769230.250887626870793433.060109149494
Trimmed Mean ( 11 / 24 )108.68360.243272377790653446.756845092898
Trimmed Mean ( 12 / 24 )108.7147916666670.235769261072362461.106724312547
Trimmed Mean ( 13 / 24 )108.7426086956520.228436279507921476.0303789306
Trimmed Mean ( 14 / 24 )108.7761363636360.219486045805392495.594769883836
Trimmed Mean ( 15 / 24 )108.8073809523810.212204035753851512.748876645275
Trimmed Mean ( 16 / 24 )108.8450.203021724238616536.124892093184
Trimmed Mean ( 17 / 24 )108.8747368421050.197737824053634550.601471231798
Trimmed Mean ( 18 / 24 )108.9080555555560.191929145095823567.438861363041
Trimmed Mean ( 19 / 24 )108.9435294117650.184965614356522588.993417997012
Trimmed Mean ( 20 / 24 )108.9681250.181314886883690600.988296509272
Trimmed Mean ( 21 / 24 )108.9866666666670.179420736723166607.436290013823
Trimmed Mean ( 22 / 24 )109.0053571428570.177426102169085614.370466409595
Trimmed Mean ( 23 / 24 )109.0273076923080.173607477411020628.010436636799
Trimmed Mean ( 24 / 24 )109.048750.168612531231833646.741669811386
Median109.035
Midrange107.57
Midmean - Weighted Average at Xnp108.837567567568
Midmean - Weighted Average at X(n+1)p108.908055555556
Midmean - Empirical Distribution Function108.837567567568
Midmean - Empirical Distribution Function - Averaging108.908055555556
Midmean - Empirical Distribution Function - Interpolation108.908055555556
Midmean - Closest Observation108.837567567568
Midmean - True Basic - Statistics Graphics Toolkit108.908055555556
Midmean - MS Excel (old versions)108.874736842105
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 108.36625 & 0.317491108491322 & 341.320582220216 \tabularnewline
Geometric Mean & 108.332892116852 &  &  \tabularnewline
Harmonic Mean & 108.299201416288 &  &  \tabularnewline
Quadratic Mean & 108.399266519402 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 108.365833333333 & 0.317423468651428 & 341.392001649169 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 108.367222222222 & 0.315484215745069 & 343.494909773204 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 108.365972222222 & 0.315290043314458 & 343.702487661947 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 108.37375 & 0.312298287794647 & 347.019994138622 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 108.370972222222 & 0.311874862030586 & 347.48222898322 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 108.393472222222 & 0.30610239470718 & 354.108540463763 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 108.402222222222 & 0.303912619627141 & 356.688782305969 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 108.346666666667 & 0.295914605645135 & 366.141665871665 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 108.382916666667 & 0.287937965893108 & 376.410649184422 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 108.412083333333 & 0.273230037270471 & 396.779521081775 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 108.454861111111 & 0.263969339005273 & 410.861585363687 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 108.501527777778 & 0.254201368347780 & 426.832980809663 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 108.47625 & 0.250830111462159 & 432.469010070847 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 108.520972222222 & 0.232494817930893 & 466.767273301029 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 108.493888888889 & 0.229077430816930 & 473.612300006948 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 108.593888888889 & 0.201917505462864 & 537.813146215107 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 108.591527777778 & 0.194832766028707 & 557.357625163407 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 108.606527777778 & 0.189516636590796 & 573.071207528239 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 108.735833333333 & 0.168197285002809 & 646.477934120741 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 108.813611111111 & 0.154984514542163 & 702.093440964443 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 108.834027777778 & 0.149654879410026 & 727.23340666757 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 108.830972222222 & 0.149276968912359 & 729.054006221934 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 108.862916666667 & 0.144694843416300 & 752.362102866779 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 108.90625 & 0.136811505395589 & 796.031369475094 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 108.389 & 0.313276490372785 & 345.985106865254 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 108.413529411765 & 0.308249380580078 & 351.707209298351 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 108.438787878788 & 0.303373458383918 & 357.443226762306 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 108.46609375 & 0.297508221273918 & 364.581836715479 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 108.492903225806 & 0.291449847479477 & 372.252393213025 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 108.522166666667 & 0.284135729051347 & 381.937769772894 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 108.548793103448 & 0.276830986150932 & 392.112149773097 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 108.575714285714 & 0.268375083658593 & 404.567044024982 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 108.613888888889 & 0.2597249548618 & 418.188113447483 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 108.649423076923 & 0.250887626870793 & 433.060109149494 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 108.6836 & 0.243272377790653 & 446.756845092898 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 108.714791666667 & 0.235769261072362 & 461.106724312547 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 108.742608695652 & 0.228436279507921 & 476.0303789306 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 108.776136363636 & 0.219486045805392 & 495.594769883836 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 108.807380952381 & 0.212204035753851 & 512.748876645275 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 108.845 & 0.203021724238616 & 536.124892093184 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 108.874736842105 & 0.197737824053634 & 550.601471231798 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 108.908055555556 & 0.191929145095823 & 567.438861363041 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 108.943529411765 & 0.184965614356522 & 588.993417997012 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 108.968125 & 0.181314886883690 & 600.988296509272 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 108.986666666667 & 0.179420736723166 & 607.436290013823 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 109.005357142857 & 0.177426102169085 & 614.370466409595 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 109.027307692308 & 0.173607477411020 & 628.010436636799 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 109.04875 & 0.168612531231833 & 646.741669811386 \tabularnewline
Median & 109.035 &  &  \tabularnewline
Midrange & 107.57 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 108.837567567568 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 108.908055555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 108.837567567568 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 108.908055555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 108.908055555556 &  &  \tabularnewline
Midmean - Closest Observation & 108.837567567568 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 108.908055555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 108.874736842105 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7693&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]108.36625[/C][C]0.317491108491322[/C][C]341.320582220216[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]108.332892116852[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]108.299201416288[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]108.399266519402[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]108.365833333333[/C][C]0.317423468651428[/C][C]341.392001649169[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]108.367222222222[/C][C]0.315484215745069[/C][C]343.494909773204[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]108.365972222222[/C][C]0.315290043314458[/C][C]343.702487661947[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]108.37375[/C][C]0.312298287794647[/C][C]347.019994138622[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]108.370972222222[/C][C]0.311874862030586[/C][C]347.48222898322[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]108.393472222222[/C][C]0.30610239470718[/C][C]354.108540463763[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]108.402222222222[/C][C]0.303912619627141[/C][C]356.688782305969[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]108.346666666667[/C][C]0.295914605645135[/C][C]366.141665871665[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]108.382916666667[/C][C]0.287937965893108[/C][C]376.410649184422[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]108.412083333333[/C][C]0.273230037270471[/C][C]396.779521081775[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]108.454861111111[/C][C]0.263969339005273[/C][C]410.861585363687[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]108.501527777778[/C][C]0.254201368347780[/C][C]426.832980809663[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]108.47625[/C][C]0.250830111462159[/C][C]432.469010070847[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]108.520972222222[/C][C]0.232494817930893[/C][C]466.767273301029[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]108.493888888889[/C][C]0.229077430816930[/C][C]473.612300006948[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]108.593888888889[/C][C]0.201917505462864[/C][C]537.813146215107[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]108.591527777778[/C][C]0.194832766028707[/C][C]557.357625163407[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]108.606527777778[/C][C]0.189516636590796[/C][C]573.071207528239[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]108.735833333333[/C][C]0.168197285002809[/C][C]646.477934120741[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]108.813611111111[/C][C]0.154984514542163[/C][C]702.093440964443[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]108.834027777778[/C][C]0.149654879410026[/C][C]727.23340666757[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]108.830972222222[/C][C]0.149276968912359[/C][C]729.054006221934[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]108.862916666667[/C][C]0.144694843416300[/C][C]752.362102866779[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]108.90625[/C][C]0.136811505395589[/C][C]796.031369475094[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]108.389[/C][C]0.313276490372785[/C][C]345.985106865254[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]108.413529411765[/C][C]0.308249380580078[/C][C]351.707209298351[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]108.438787878788[/C][C]0.303373458383918[/C][C]357.443226762306[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]108.46609375[/C][C]0.297508221273918[/C][C]364.581836715479[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]108.492903225806[/C][C]0.291449847479477[/C][C]372.252393213025[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]108.522166666667[/C][C]0.284135729051347[/C][C]381.937769772894[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]108.548793103448[/C][C]0.276830986150932[/C][C]392.112149773097[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]108.575714285714[/C][C]0.268375083658593[/C][C]404.567044024982[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]108.613888888889[/C][C]0.2597249548618[/C][C]418.188113447483[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]108.649423076923[/C][C]0.250887626870793[/C][C]433.060109149494[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]108.6836[/C][C]0.243272377790653[/C][C]446.756845092898[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]108.714791666667[/C][C]0.235769261072362[/C][C]461.106724312547[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]108.742608695652[/C][C]0.228436279507921[/C][C]476.0303789306[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]108.776136363636[/C][C]0.219486045805392[/C][C]495.594769883836[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]108.807380952381[/C][C]0.212204035753851[/C][C]512.748876645275[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]108.845[/C][C]0.203021724238616[/C][C]536.124892093184[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]108.874736842105[/C][C]0.197737824053634[/C][C]550.601471231798[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]108.908055555556[/C][C]0.191929145095823[/C][C]567.438861363041[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]108.943529411765[/C][C]0.184965614356522[/C][C]588.993417997012[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]108.968125[/C][C]0.181314886883690[/C][C]600.988296509272[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]108.986666666667[/C][C]0.179420736723166[/C][C]607.436290013823[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]109.005357142857[/C][C]0.177426102169085[/C][C]614.370466409595[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]109.027307692308[/C][C]0.173607477411020[/C][C]628.010436636799[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]109.04875[/C][C]0.168612531231833[/C][C]646.741669811386[/C][/ROW]
[ROW][C]Median[/C][C]109.035[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]107.57[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]108.837567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]108.908055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]108.837567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]108.908055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]108.908055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]108.837567567568[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]108.908055555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]108.874736842105[/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=7693&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7693&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
MeasureValueS.E.Value/S.E.
Arithmetic Mean108.366250.317491108491322341.320582220216
Geometric Mean108.332892116852
Harmonic Mean108.299201416288
Quadratic Mean108.399266519402
Winsorized Mean ( 1 / 24 )108.3658333333330.317423468651428341.392001649169
Winsorized Mean ( 2 / 24 )108.3672222222220.315484215745069343.494909773204
Winsorized Mean ( 3 / 24 )108.3659722222220.315290043314458343.702487661947
Winsorized Mean ( 4 / 24 )108.373750.312298287794647347.019994138622
Winsorized Mean ( 5 / 24 )108.3709722222220.311874862030586347.48222898322
Winsorized Mean ( 6 / 24 )108.3934722222220.30610239470718354.108540463763
Winsorized Mean ( 7 / 24 )108.4022222222220.303912619627141356.688782305969
Winsorized Mean ( 8 / 24 )108.3466666666670.295914605645135366.141665871665
Winsorized Mean ( 9 / 24 )108.3829166666670.287937965893108376.410649184422
Winsorized Mean ( 10 / 24 )108.4120833333330.273230037270471396.779521081775
Winsorized Mean ( 11 / 24 )108.4548611111110.263969339005273410.861585363687
Winsorized Mean ( 12 / 24 )108.5015277777780.254201368347780426.832980809663
Winsorized Mean ( 13 / 24 )108.476250.250830111462159432.469010070847
Winsorized Mean ( 14 / 24 )108.5209722222220.232494817930893466.767273301029
Winsorized Mean ( 15 / 24 )108.4938888888890.229077430816930473.612300006948
Winsorized Mean ( 16 / 24 )108.5938888888890.201917505462864537.813146215107
Winsorized Mean ( 17 / 24 )108.5915277777780.194832766028707557.357625163407
Winsorized Mean ( 18 / 24 )108.6065277777780.189516636590796573.071207528239
Winsorized Mean ( 19 / 24 )108.7358333333330.168197285002809646.477934120741
Winsorized Mean ( 20 / 24 )108.8136111111110.154984514542163702.093440964443
Winsorized Mean ( 21 / 24 )108.8340277777780.149654879410026727.23340666757
Winsorized Mean ( 22 / 24 )108.8309722222220.149276968912359729.054006221934
Winsorized Mean ( 23 / 24 )108.8629166666670.144694843416300752.362102866779
Winsorized Mean ( 24 / 24 )108.906250.136811505395589796.031369475094
Trimmed Mean ( 1 / 24 )108.3890.313276490372785345.985106865254
Trimmed Mean ( 2 / 24 )108.4135294117650.308249380580078351.707209298351
Trimmed Mean ( 3 / 24 )108.4387878787880.303373458383918357.443226762306
Trimmed Mean ( 4 / 24 )108.466093750.297508221273918364.581836715479
Trimmed Mean ( 5 / 24 )108.4929032258060.291449847479477372.252393213025
Trimmed Mean ( 6 / 24 )108.5221666666670.284135729051347381.937769772894
Trimmed Mean ( 7 / 24 )108.5487931034480.276830986150932392.112149773097
Trimmed Mean ( 8 / 24 )108.5757142857140.268375083658593404.567044024982
Trimmed Mean ( 9 / 24 )108.6138888888890.2597249548618418.188113447483
Trimmed Mean ( 10 / 24 )108.6494230769230.250887626870793433.060109149494
Trimmed Mean ( 11 / 24 )108.68360.243272377790653446.756845092898
Trimmed Mean ( 12 / 24 )108.7147916666670.235769261072362461.106724312547
Trimmed Mean ( 13 / 24 )108.7426086956520.228436279507921476.0303789306
Trimmed Mean ( 14 / 24 )108.7761363636360.219486045805392495.594769883836
Trimmed Mean ( 15 / 24 )108.8073809523810.212204035753851512.748876645275
Trimmed Mean ( 16 / 24 )108.8450.203021724238616536.124892093184
Trimmed Mean ( 17 / 24 )108.8747368421050.197737824053634550.601471231798
Trimmed Mean ( 18 / 24 )108.9080555555560.191929145095823567.438861363041
Trimmed Mean ( 19 / 24 )108.9435294117650.184965614356522588.993417997012
Trimmed Mean ( 20 / 24 )108.9681250.181314886883690600.988296509272
Trimmed Mean ( 21 / 24 )108.9866666666670.179420736723166607.436290013823
Trimmed Mean ( 22 / 24 )109.0053571428570.177426102169085614.370466409595
Trimmed Mean ( 23 / 24 )109.0273076923080.173607477411020628.010436636799
Trimmed Mean ( 24 / 24 )109.048750.168612531231833646.741669811386
Median109.035
Midrange107.57
Midmean - Weighted Average at Xnp108.837567567568
Midmean - Weighted Average at X(n+1)p108.908055555556
Midmean - Empirical Distribution Function108.837567567568
Midmean - Empirical Distribution Function - Averaging108.908055555556
Midmean - Empirical Distribution Function - Interpolation108.908055555556
Midmean - Closest Observation108.837567567568
Midmean - True Basic - Statistics Graphics Toolkit108.908055555556
Midmean - MS Excel (old versions)108.874736842105
Number of observations72



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')