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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 11 Dec 2007 15:15:49 -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/Dec/11/t11974104652tqesdkp6s3bjbs.htm/, Retrieved Mon, 29 Apr 2024 04:35:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3171, Retrieved Mon, 29 Apr 2024 04:35:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact214
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Workshop2: the se...] [2007-11-22 16:20:38] [74be16979710d4c4e7c6647856088456]
-    D    [Central Tendency] [Tijdreeks 3: afze...] [2007-12-11 22:15:49] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
99,7
99,7
99,7
99,8
99,7
99,6
99,4
99,6
99,6
98,9
98,7
98,8
98,5
98,7
99,4
100,8
100,5
100,9
100,8
101,0
101,4
101,6
101,3
100,9
99,4
99,6
99,7
99,8
99,7
99,9
100,2
100,4
101,0
101,4
101,7
101,7
102,3
102,4
102,6
103,0
103,1
103,0
103,2
103,4
103,3
103,0
102,9
102,6
102,7
102,6
102,9
102,8
103,5
103,9
104,4
104,6
104,7
104,5
104,3
104,4
105,0
105,0
105,2
105,8
107,4
107,7
107,7
108,6
109,4
109,2
109,1
109,6
110,4
109,7
110,1
110,4
110,6
110,8
111,6
112,0
113,4
114,7




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3171&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]1 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=3171&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3171&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean103.50.447105852657823231.488806028245
Geometric Mean103.423501952263
Harmonic Mean103.348714193157
Quadratic Mean103.578193627433
Winsorized Mean ( 1 / 27 )103.4865853658540.442127300468653234.065132951886
Winsorized Mean ( 2 / 27 )103.4524390243900.433236823419229238.789579814371
Winsorized Mean ( 3 / 27 )103.4414634146340.429245366336394240.984461399097
Winsorized Mean ( 4 / 27 )103.4073170731710.419771738232368246.341779722028
Winsorized Mean ( 5 / 27 )103.4256097560980.413283686500302250.253308162024
Winsorized Mean ( 6 / 27 )103.4109756097560.410176209729290252.113538418052
Winsorized Mean ( 7 / 27 )103.4109756097560.410176209729290252.113538418052
Winsorized Mean ( 8 / 27 )103.4012195121950.401767001612352257.366132851205
Winsorized Mean ( 9 / 27 )103.3573170731710.392871708994692263.081598157446
Winsorized Mean ( 10 / 27 )103.3451219512190.390450416788821264.681807234732
Winsorized Mean ( 11 / 27 )103.3182926829270.38518221128335268.232253869385
Winsorized Mean ( 12 / 27 )103.3036585365850.377775566396968273.45246152853
Winsorized Mean ( 13 / 27 )103.2878048780490.374730216089728275.632442870091
Winsorized Mean ( 14 / 27 )103.2024390243900.358620662138596287.776053975679
Winsorized Mean ( 15 / 27 )103.0378048780490.328880100610915313.298994638623
Winsorized Mean ( 16 / 27 )103.0378048780490.328880100610915313.298994638623
Winsorized Mean ( 17 / 27 )102.9756097560980.318096003868699323.724939966876
Winsorized Mean ( 18 / 27 )102.6463414634150.258200027510489397.545819235998
Winsorized Mean ( 19 / 27 )102.5073170731710.237976644087186430.745283707823
Winsorized Mean ( 20 / 27 )102.4829268292680.227821100236312449.839486873541
Winsorized Mean ( 21 / 27 )102.5597560975610.217288453616316471.998186699138
Winsorized Mean ( 22 / 27 )102.5329268292680.199147950748708514.858056253103
Winsorized Mean ( 23 / 27 )102.5329268292680.191705878539110534.84498029282
Winsorized Mean ( 24 / 27 )102.5914634146340.176547242104506581.099212832256
Winsorized Mean ( 25 / 27 )102.5609756097560.172506157216228594.535159004216
Winsorized Mean ( 26 / 27 )102.5926829268290.168542117321059608.706503499055
Winsorized Mean ( 27 / 27 )102.5597560975610.164208243865832624.571298511411
Trimmed Mean ( 1 / 27 )103.42250.431519155595171239.670704438033
Trimmed Mean ( 2 / 27 )103.3551282051280.419042434078101246.645971385955
Trimmed Mean ( 3 / 27 )103.3026315789470.409967793703875251.977431313944
Trimmed Mean ( 4 / 27 )103.2513513513510.401013355610718257.476091274082
Trimmed Mean ( 5 / 27 )103.2069444444440.393771570881871262.098516186192
Trimmed Mean ( 6 / 27 )103.1557142857140.386980858896563266.565417679449
Trimmed Mean ( 7 / 27 )103.1044117647060.379613463956759271.603674669585
Trimmed Mean ( 8 / 27 )103.050.370662168140266278.015964016602
Trimmed Mean ( 9 / 27 )102.993750.361735475953758284.721175683543
Trimmed Mean ( 10 / 27 )102.9403225806450.352871874625538291.721528358937
Trimmed Mean ( 11 / 27 )102.8850.34248860758817300.404152781968
Trimmed Mean ( 12 / 27 )102.8293103448280.330822442298631310.829306592218
Trimmed Mean ( 13 / 27 )102.7714285714290.317893985899186323.288370117265
Trimmed Mean ( 14 / 27 )102.7111111111110.302316547125252339.746904652748
Trimmed Mean ( 15 / 27 )102.6557692307690.286490880477583358.321245896696
Trimmed Mean ( 16 / 27 )102.6140.273600483350808375.050507014014
Trimmed Mean ( 17 / 27 )102.568750.256945303014347399.18515262477
Trimmed Mean ( 18 / 27 )102.5260869565220.238036143535114430.716467818247
Trimmed Mean ( 19 / 27 )102.5136363636360.228900093356915447.853187214698
Trimmed Mean ( 20 / 27 )102.5142857142860.22158680794694462.637133790172
Trimmed Mean ( 21 / 27 )102.51750.214143718215786478.732231111707
Trimmed Mean ( 22 / 27 )102.5131578947370.206583364242314496.231428269767
Trimmed Mean ( 23 / 27 )102.5111111111110.200704227531095510.757109464618
Trimmed Mean ( 24 / 27 )102.5088235294120.194274905241909527.648300236044
Trimmed Mean ( 25 / 27 )102.50.189066040689320542.138607368585
Trimmed Mean ( 26 / 27 )102.4933333333330.182444029101501561.77959803942
Trimmed Mean ( 27 / 27 )102.4821428571430.173590588356153590.366930762872
Median102.65
Midrange106.6
Midmean - Weighted Average at Xnp102.514285714286
Midmean - Weighted Average at X(n+1)p102.514285714286
Midmean - Empirical Distribution Function102.514285714286
Midmean - Empirical Distribution Function - Averaging102.514285714286
Midmean - Empirical Distribution Function - Interpolation102.578048780488
Midmean - Closest Observation102.514285714286
Midmean - True Basic - Statistics Graphics Toolkit102.514285714286
Midmean - MS Excel (old versions)102.514285714286
Number of observations82

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 103.5 & 0.447105852657823 & 231.488806028245 \tabularnewline
Geometric Mean & 103.423501952263 &  &  \tabularnewline
Harmonic Mean & 103.348714193157 &  &  \tabularnewline
Quadratic Mean & 103.578193627433 &  &  \tabularnewline
Winsorized Mean ( 1 / 27 ) & 103.486585365854 & 0.442127300468653 & 234.065132951886 \tabularnewline
Winsorized Mean ( 2 / 27 ) & 103.452439024390 & 0.433236823419229 & 238.789579814371 \tabularnewline
Winsorized Mean ( 3 / 27 ) & 103.441463414634 & 0.429245366336394 & 240.984461399097 \tabularnewline
Winsorized Mean ( 4 / 27 ) & 103.407317073171 & 0.419771738232368 & 246.341779722028 \tabularnewline
Winsorized Mean ( 5 / 27 ) & 103.425609756098 & 0.413283686500302 & 250.253308162024 \tabularnewline
Winsorized Mean ( 6 / 27 ) & 103.410975609756 & 0.410176209729290 & 252.113538418052 \tabularnewline
Winsorized Mean ( 7 / 27 ) & 103.410975609756 & 0.410176209729290 & 252.113538418052 \tabularnewline
Winsorized Mean ( 8 / 27 ) & 103.401219512195 & 0.401767001612352 & 257.366132851205 \tabularnewline
Winsorized Mean ( 9 / 27 ) & 103.357317073171 & 0.392871708994692 & 263.081598157446 \tabularnewline
Winsorized Mean ( 10 / 27 ) & 103.345121951219 & 0.390450416788821 & 264.681807234732 \tabularnewline
Winsorized Mean ( 11 / 27 ) & 103.318292682927 & 0.38518221128335 & 268.232253869385 \tabularnewline
Winsorized Mean ( 12 / 27 ) & 103.303658536585 & 0.377775566396968 & 273.45246152853 \tabularnewline
Winsorized Mean ( 13 / 27 ) & 103.287804878049 & 0.374730216089728 & 275.632442870091 \tabularnewline
Winsorized Mean ( 14 / 27 ) & 103.202439024390 & 0.358620662138596 & 287.776053975679 \tabularnewline
Winsorized Mean ( 15 / 27 ) & 103.037804878049 & 0.328880100610915 & 313.298994638623 \tabularnewline
Winsorized Mean ( 16 / 27 ) & 103.037804878049 & 0.328880100610915 & 313.298994638623 \tabularnewline
Winsorized Mean ( 17 / 27 ) & 102.975609756098 & 0.318096003868699 & 323.724939966876 \tabularnewline
Winsorized Mean ( 18 / 27 ) & 102.646341463415 & 0.258200027510489 & 397.545819235998 \tabularnewline
Winsorized Mean ( 19 / 27 ) & 102.507317073171 & 0.237976644087186 & 430.745283707823 \tabularnewline
Winsorized Mean ( 20 / 27 ) & 102.482926829268 & 0.227821100236312 & 449.839486873541 \tabularnewline
Winsorized Mean ( 21 / 27 ) & 102.559756097561 & 0.217288453616316 & 471.998186699138 \tabularnewline
Winsorized Mean ( 22 / 27 ) & 102.532926829268 & 0.199147950748708 & 514.858056253103 \tabularnewline
Winsorized Mean ( 23 / 27 ) & 102.532926829268 & 0.191705878539110 & 534.84498029282 \tabularnewline
Winsorized Mean ( 24 / 27 ) & 102.591463414634 & 0.176547242104506 & 581.099212832256 \tabularnewline
Winsorized Mean ( 25 / 27 ) & 102.560975609756 & 0.172506157216228 & 594.535159004216 \tabularnewline
Winsorized Mean ( 26 / 27 ) & 102.592682926829 & 0.168542117321059 & 608.706503499055 \tabularnewline
Winsorized Mean ( 27 / 27 ) & 102.559756097561 & 0.164208243865832 & 624.571298511411 \tabularnewline
Trimmed Mean ( 1 / 27 ) & 103.4225 & 0.431519155595171 & 239.670704438033 \tabularnewline
Trimmed Mean ( 2 / 27 ) & 103.355128205128 & 0.419042434078101 & 246.645971385955 \tabularnewline
Trimmed Mean ( 3 / 27 ) & 103.302631578947 & 0.409967793703875 & 251.977431313944 \tabularnewline
Trimmed Mean ( 4 / 27 ) & 103.251351351351 & 0.401013355610718 & 257.476091274082 \tabularnewline
Trimmed Mean ( 5 / 27 ) & 103.206944444444 & 0.393771570881871 & 262.098516186192 \tabularnewline
Trimmed Mean ( 6 / 27 ) & 103.155714285714 & 0.386980858896563 & 266.565417679449 \tabularnewline
Trimmed Mean ( 7 / 27 ) & 103.104411764706 & 0.379613463956759 & 271.603674669585 \tabularnewline
Trimmed Mean ( 8 / 27 ) & 103.05 & 0.370662168140266 & 278.015964016602 \tabularnewline
Trimmed Mean ( 9 / 27 ) & 102.99375 & 0.361735475953758 & 284.721175683543 \tabularnewline
Trimmed Mean ( 10 / 27 ) & 102.940322580645 & 0.352871874625538 & 291.721528358937 \tabularnewline
Trimmed Mean ( 11 / 27 ) & 102.885 & 0.34248860758817 & 300.404152781968 \tabularnewline
Trimmed Mean ( 12 / 27 ) & 102.829310344828 & 0.330822442298631 & 310.829306592218 \tabularnewline
Trimmed Mean ( 13 / 27 ) & 102.771428571429 & 0.317893985899186 & 323.288370117265 \tabularnewline
Trimmed Mean ( 14 / 27 ) & 102.711111111111 & 0.302316547125252 & 339.746904652748 \tabularnewline
Trimmed Mean ( 15 / 27 ) & 102.655769230769 & 0.286490880477583 & 358.321245896696 \tabularnewline
Trimmed Mean ( 16 / 27 ) & 102.614 & 0.273600483350808 & 375.050507014014 \tabularnewline
Trimmed Mean ( 17 / 27 ) & 102.56875 & 0.256945303014347 & 399.18515262477 \tabularnewline
Trimmed Mean ( 18 / 27 ) & 102.526086956522 & 0.238036143535114 & 430.716467818247 \tabularnewline
Trimmed Mean ( 19 / 27 ) & 102.513636363636 & 0.228900093356915 & 447.853187214698 \tabularnewline
Trimmed Mean ( 20 / 27 ) & 102.514285714286 & 0.22158680794694 & 462.637133790172 \tabularnewline
Trimmed Mean ( 21 / 27 ) & 102.5175 & 0.214143718215786 & 478.732231111707 \tabularnewline
Trimmed Mean ( 22 / 27 ) & 102.513157894737 & 0.206583364242314 & 496.231428269767 \tabularnewline
Trimmed Mean ( 23 / 27 ) & 102.511111111111 & 0.200704227531095 & 510.757109464618 \tabularnewline
Trimmed Mean ( 24 / 27 ) & 102.508823529412 & 0.194274905241909 & 527.648300236044 \tabularnewline
Trimmed Mean ( 25 / 27 ) & 102.5 & 0.189066040689320 & 542.138607368585 \tabularnewline
Trimmed Mean ( 26 / 27 ) & 102.493333333333 & 0.182444029101501 & 561.77959803942 \tabularnewline
Trimmed Mean ( 27 / 27 ) & 102.482142857143 & 0.173590588356153 & 590.366930762872 \tabularnewline
Median & 102.65 &  &  \tabularnewline
Midrange & 106.6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 102.514285714286 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 102.514285714286 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 102.514285714286 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 102.514285714286 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 102.578048780488 &  &  \tabularnewline
Midmean - Closest Observation & 102.514285714286 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 102.514285714286 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 102.514285714286 &  &  \tabularnewline
Number of observations & 82 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3171&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]103.5[/C][C]0.447105852657823[/C][C]231.488806028245[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]103.423501952263[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]103.348714193157[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]103.578193627433[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 27 )[/C][C]103.486585365854[/C][C]0.442127300468653[/C][C]234.065132951886[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 27 )[/C][C]103.452439024390[/C][C]0.433236823419229[/C][C]238.789579814371[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 27 )[/C][C]103.441463414634[/C][C]0.429245366336394[/C][C]240.984461399097[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 27 )[/C][C]103.407317073171[/C][C]0.419771738232368[/C][C]246.341779722028[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 27 )[/C][C]103.425609756098[/C][C]0.413283686500302[/C][C]250.253308162024[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 27 )[/C][C]103.410975609756[/C][C]0.410176209729290[/C][C]252.113538418052[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 27 )[/C][C]103.410975609756[/C][C]0.410176209729290[/C][C]252.113538418052[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 27 )[/C][C]103.401219512195[/C][C]0.401767001612352[/C][C]257.366132851205[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 27 )[/C][C]103.357317073171[/C][C]0.392871708994692[/C][C]263.081598157446[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 27 )[/C][C]103.345121951219[/C][C]0.390450416788821[/C][C]264.681807234732[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 27 )[/C][C]103.318292682927[/C][C]0.38518221128335[/C][C]268.232253869385[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 27 )[/C][C]103.303658536585[/C][C]0.377775566396968[/C][C]273.45246152853[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 27 )[/C][C]103.287804878049[/C][C]0.374730216089728[/C][C]275.632442870091[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 27 )[/C][C]103.202439024390[/C][C]0.358620662138596[/C][C]287.776053975679[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 27 )[/C][C]103.037804878049[/C][C]0.328880100610915[/C][C]313.298994638623[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 27 )[/C][C]103.037804878049[/C][C]0.328880100610915[/C][C]313.298994638623[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 27 )[/C][C]102.975609756098[/C][C]0.318096003868699[/C][C]323.724939966876[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 27 )[/C][C]102.646341463415[/C][C]0.258200027510489[/C][C]397.545819235998[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 27 )[/C][C]102.507317073171[/C][C]0.237976644087186[/C][C]430.745283707823[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 27 )[/C][C]102.482926829268[/C][C]0.227821100236312[/C][C]449.839486873541[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 27 )[/C][C]102.559756097561[/C][C]0.217288453616316[/C][C]471.998186699138[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 27 )[/C][C]102.532926829268[/C][C]0.199147950748708[/C][C]514.858056253103[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 27 )[/C][C]102.532926829268[/C][C]0.191705878539110[/C][C]534.84498029282[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 27 )[/C][C]102.591463414634[/C][C]0.176547242104506[/C][C]581.099212832256[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 27 )[/C][C]102.560975609756[/C][C]0.172506157216228[/C][C]594.535159004216[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 27 )[/C][C]102.592682926829[/C][C]0.168542117321059[/C][C]608.706503499055[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 27 )[/C][C]102.559756097561[/C][C]0.164208243865832[/C][C]624.571298511411[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 27 )[/C][C]103.4225[/C][C]0.431519155595171[/C][C]239.670704438033[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 27 )[/C][C]103.355128205128[/C][C]0.419042434078101[/C][C]246.645971385955[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 27 )[/C][C]103.302631578947[/C][C]0.409967793703875[/C][C]251.977431313944[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 27 )[/C][C]103.251351351351[/C][C]0.401013355610718[/C][C]257.476091274082[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 27 )[/C][C]103.206944444444[/C][C]0.393771570881871[/C][C]262.098516186192[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 27 )[/C][C]103.155714285714[/C][C]0.386980858896563[/C][C]266.565417679449[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 27 )[/C][C]103.104411764706[/C][C]0.379613463956759[/C][C]271.603674669585[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 27 )[/C][C]103.05[/C][C]0.370662168140266[/C][C]278.015964016602[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 27 )[/C][C]102.99375[/C][C]0.361735475953758[/C][C]284.721175683543[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 27 )[/C][C]102.940322580645[/C][C]0.352871874625538[/C][C]291.721528358937[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 27 )[/C][C]102.885[/C][C]0.34248860758817[/C][C]300.404152781968[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 27 )[/C][C]102.829310344828[/C][C]0.330822442298631[/C][C]310.829306592218[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 27 )[/C][C]102.771428571429[/C][C]0.317893985899186[/C][C]323.288370117265[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 27 )[/C][C]102.711111111111[/C][C]0.302316547125252[/C][C]339.746904652748[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 27 )[/C][C]102.655769230769[/C][C]0.286490880477583[/C][C]358.321245896696[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 27 )[/C][C]102.614[/C][C]0.273600483350808[/C][C]375.050507014014[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 27 )[/C][C]102.56875[/C][C]0.256945303014347[/C][C]399.18515262477[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 27 )[/C][C]102.526086956522[/C][C]0.238036143535114[/C][C]430.716467818247[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 27 )[/C][C]102.513636363636[/C][C]0.228900093356915[/C][C]447.853187214698[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 27 )[/C][C]102.514285714286[/C][C]0.22158680794694[/C][C]462.637133790172[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 27 )[/C][C]102.5175[/C][C]0.214143718215786[/C][C]478.732231111707[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 27 )[/C][C]102.513157894737[/C][C]0.206583364242314[/C][C]496.231428269767[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 27 )[/C][C]102.511111111111[/C][C]0.200704227531095[/C][C]510.757109464618[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 27 )[/C][C]102.508823529412[/C][C]0.194274905241909[/C][C]527.648300236044[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 27 )[/C][C]102.5[/C][C]0.189066040689320[/C][C]542.138607368585[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 27 )[/C][C]102.493333333333[/C][C]0.182444029101501[/C][C]561.77959803942[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 27 )[/C][C]102.482142857143[/C][C]0.173590588356153[/C][C]590.366930762872[/C][/ROW]
[ROW][C]Median[/C][C]102.65[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]106.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]102.514285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]102.514285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]102.514285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]102.514285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]102.578048780488[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]102.514285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]102.514285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]102.514285714286[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]82[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3171&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3171&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 Mean103.50.447105852657823231.488806028245
Geometric Mean103.423501952263
Harmonic Mean103.348714193157
Quadratic Mean103.578193627433
Winsorized Mean ( 1 / 27 )103.4865853658540.442127300468653234.065132951886
Winsorized Mean ( 2 / 27 )103.4524390243900.433236823419229238.789579814371
Winsorized Mean ( 3 / 27 )103.4414634146340.429245366336394240.984461399097
Winsorized Mean ( 4 / 27 )103.4073170731710.419771738232368246.341779722028
Winsorized Mean ( 5 / 27 )103.4256097560980.413283686500302250.253308162024
Winsorized Mean ( 6 / 27 )103.4109756097560.410176209729290252.113538418052
Winsorized Mean ( 7 / 27 )103.4109756097560.410176209729290252.113538418052
Winsorized Mean ( 8 / 27 )103.4012195121950.401767001612352257.366132851205
Winsorized Mean ( 9 / 27 )103.3573170731710.392871708994692263.081598157446
Winsorized Mean ( 10 / 27 )103.3451219512190.390450416788821264.681807234732
Winsorized Mean ( 11 / 27 )103.3182926829270.38518221128335268.232253869385
Winsorized Mean ( 12 / 27 )103.3036585365850.377775566396968273.45246152853
Winsorized Mean ( 13 / 27 )103.2878048780490.374730216089728275.632442870091
Winsorized Mean ( 14 / 27 )103.2024390243900.358620662138596287.776053975679
Winsorized Mean ( 15 / 27 )103.0378048780490.328880100610915313.298994638623
Winsorized Mean ( 16 / 27 )103.0378048780490.328880100610915313.298994638623
Winsorized Mean ( 17 / 27 )102.9756097560980.318096003868699323.724939966876
Winsorized Mean ( 18 / 27 )102.6463414634150.258200027510489397.545819235998
Winsorized Mean ( 19 / 27 )102.5073170731710.237976644087186430.745283707823
Winsorized Mean ( 20 / 27 )102.4829268292680.227821100236312449.839486873541
Winsorized Mean ( 21 / 27 )102.5597560975610.217288453616316471.998186699138
Winsorized Mean ( 22 / 27 )102.5329268292680.199147950748708514.858056253103
Winsorized Mean ( 23 / 27 )102.5329268292680.191705878539110534.84498029282
Winsorized Mean ( 24 / 27 )102.5914634146340.176547242104506581.099212832256
Winsorized Mean ( 25 / 27 )102.5609756097560.172506157216228594.535159004216
Winsorized Mean ( 26 / 27 )102.5926829268290.168542117321059608.706503499055
Winsorized Mean ( 27 / 27 )102.5597560975610.164208243865832624.571298511411
Trimmed Mean ( 1 / 27 )103.42250.431519155595171239.670704438033
Trimmed Mean ( 2 / 27 )103.3551282051280.419042434078101246.645971385955
Trimmed Mean ( 3 / 27 )103.3026315789470.409967793703875251.977431313944
Trimmed Mean ( 4 / 27 )103.2513513513510.401013355610718257.476091274082
Trimmed Mean ( 5 / 27 )103.2069444444440.393771570881871262.098516186192
Trimmed Mean ( 6 / 27 )103.1557142857140.386980858896563266.565417679449
Trimmed Mean ( 7 / 27 )103.1044117647060.379613463956759271.603674669585
Trimmed Mean ( 8 / 27 )103.050.370662168140266278.015964016602
Trimmed Mean ( 9 / 27 )102.993750.361735475953758284.721175683543
Trimmed Mean ( 10 / 27 )102.9403225806450.352871874625538291.721528358937
Trimmed Mean ( 11 / 27 )102.8850.34248860758817300.404152781968
Trimmed Mean ( 12 / 27 )102.8293103448280.330822442298631310.829306592218
Trimmed Mean ( 13 / 27 )102.7714285714290.317893985899186323.288370117265
Trimmed Mean ( 14 / 27 )102.7111111111110.302316547125252339.746904652748
Trimmed Mean ( 15 / 27 )102.6557692307690.286490880477583358.321245896696
Trimmed Mean ( 16 / 27 )102.6140.273600483350808375.050507014014
Trimmed Mean ( 17 / 27 )102.568750.256945303014347399.18515262477
Trimmed Mean ( 18 / 27 )102.5260869565220.238036143535114430.716467818247
Trimmed Mean ( 19 / 27 )102.5136363636360.228900093356915447.853187214698
Trimmed Mean ( 20 / 27 )102.5142857142860.22158680794694462.637133790172
Trimmed Mean ( 21 / 27 )102.51750.214143718215786478.732231111707
Trimmed Mean ( 22 / 27 )102.5131578947370.206583364242314496.231428269767
Trimmed Mean ( 23 / 27 )102.5111111111110.200704227531095510.757109464618
Trimmed Mean ( 24 / 27 )102.5088235294120.194274905241909527.648300236044
Trimmed Mean ( 25 / 27 )102.50.189066040689320542.138607368585
Trimmed Mean ( 26 / 27 )102.4933333333330.182444029101501561.77959803942
Trimmed Mean ( 27 / 27 )102.4821428571430.173590588356153590.366930762872
Median102.65
Midrange106.6
Midmean - Weighted Average at Xnp102.514285714286
Midmean - Weighted Average at X(n+1)p102.514285714286
Midmean - Empirical Distribution Function102.514285714286
Midmean - Empirical Distribution Function - Averaging102.514285714286
Midmean - Empirical Distribution Function - Interpolation102.578048780488
Midmean - Closest Observation102.514285714286
Midmean - True Basic - Statistics Graphics Toolkit102.514285714286
Midmean - MS Excel (old versions)102.514285714286
Number of observations82



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')