Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 20 Oct 2007 07:51:07 -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/Oct/20/j9i5dls60c9ddoi1192891633.htm/, Retrieved Thu, 02 May 2024 20:23:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1139, Retrieved Thu, 02 May 2024 20:23:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsWS2CTOM
Estimated Impact220
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [WS2 Central tende...] [2007-10-20 14:51:07] [e51d7ab0e549b3dc96ac85a81d9bd259] [Current]
-    D    [Central Tendency] [Robuustheid Centr...] [2008-12-26 17:06:34] [c29178f7f550574a75dc881e636e0923]
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Dataseries X:
93,5
94,7
112,9
99,2
105,6
113,0
83,1
81,1
96,9
104,3
97,7
102,6
89,9
96,0
112,7
107,1
106,2
121,0
101,2
83,2
105,1
113,3
99,1
100,3
93,5
98,8
106,2
98,3
102,1
117,1
101,5
80,5
105,9
109,5
97,2
114,5
93,5
100,9
121,1
116,5
109,3
118,1
108,3
105,4
116,2
111,2
105,8
122,7
99,5
107,9
124,6
115,0
110,3
132,7
99,7
96,5
118,7
112,9
130,5
137,9
115,0
116,8
140,9
120,7
134,2
147,3
112,4
107,1
128,4
137,7
135,0
151,0
137,4
132,4
161,3
139,8
146,0
154,6
142,1
120,5




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=1139&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=1139&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1139&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 Mean113.00751.9695295774192257.3779146531427
Geometric Mean111.701951852900
Harmonic Mean110.442586594646
Quadratic Mean114.355322350995
Winsorized Mean ( 1 / 26 )112.931251.9435967520686758.1042594765613
Winsorized Mean ( 2 / 26 )112.891251.9098903091224259.1087610952236
Winsorized Mean ( 3 / 26 )112.756251.8754365261895260.1226692694826
Winsorized Mean ( 4 / 26 )113.026251.7995303041806662.8087505597531
Winsorized Mean ( 5 / 26 )113.00751.7103748710055066.0717728702157
Winsorized Mean ( 6 / 26 )112.91751.6912598994443066.7653150394574
Winsorized Mean ( 7 / 26 )112.821251.6713460937315367.5032241515638
Winsorized Mean ( 8 / 26 )112.751251.6159391925107869.7744386190742
Winsorized Mean ( 9 / 26 )112.8751.5913417831773570.9307084079877
Winsorized Mean ( 10 / 26 )112.91.5756362990346071.6535916754232
Winsorized Mean ( 11 / 26 )112.6251.5048113763794574.8432672478685
Winsorized Mean ( 12 / 26 )112.551.4764426542850976.2305259017987
Winsorized Mean ( 13 / 26 )112.38751.4210971147299179.085024404796
Winsorized Mean ( 14 / 26 )112.441.3980123774827480.4284724592063
Winsorized Mean ( 15 / 26 )112.17751.3225538382475484.818853309323
Winsorized Mean ( 16 / 26 )111.81751.2424808978996789.9953473643095
Winsorized Mean ( 17 / 26 )111.031251.10858644420368100.155698800517
Winsorized Mean ( 18 / 26 )110.671251.03479068046316106.950373722408
Winsorized Mean ( 19 / 26 )110.338750.973681344161607113.321211977218
Winsorized Mean ( 20 / 26 )110.463750.949640577827718116.321640607106
Winsorized Mean ( 21 / 26 )110.54250.917443087946197120.489762746442
Winsorized Mean ( 22 / 26 )110.570.89881145148271123.018014309453
Winsorized Mean ( 23 / 26 )110.138750.816744257863601134.850963370218
Winsorized Mean ( 24 / 26 )110.138750.769042009992244143.215518227815
Winsorized Mean ( 25 / 26 )109.98250.708009723794343155.340380652663
Winsorized Mean ( 26 / 26 )110.43750.624569155295741176.821892441529
Trimmed Mean ( 1 / 26 )112.8051282051281.8753833196240560.1504380596398
Trimmed Mean ( 2 / 26 )112.6723684210531.7952232903039862.762314320228
Trimmed Mean ( 3 / 26 )112.5540540540541.7223804906493265.347961536433
Trimmed Mean ( 4 / 26 )112.4791666666671.6522971365540768.0744184434321
Trimmed Mean ( 5 / 26 )112.3228571428571.5971651535312670.3263885356603
Trimmed Mean ( 6 / 26 )112.1617647058821.5593525780714971.92841842388
Trimmed Mean ( 7 / 26 )112.0090909090911.5193080980639073.7237503386096
Trimmed Mean ( 8 / 26 )111.86406251.4761939732851575.7787015286722
Trimmed Mean ( 9 / 26 )111.7209677419351.4372640166300777.7316946985745
Trimmed Mean ( 10 / 26 )111.551.3949839518749779.9650776269276
Trimmed Mean ( 11 / 26 )111.3637931034481.3462809750786882.7195772390229
Trimmed Mean ( 12 / 26 )111.21.3021784943581485.3953589940156
Trimmed Mean ( 13 / 26 )111.0333333333331.2533895344016588.5864532021475
Trimmed Mean ( 14 / 26 )110.8730769230771.2045042269601392.0487238163481
Trimmed Mean ( 15 / 26 )110.6941.1472252594492496.488461257506
Trimmed Mean ( 16 / 26 )110.5291666666671.09184987770176101.23110230073
Trimmed Mean ( 17 / 26 )110.3891304347831.03991930317205106.151631283374
Trimmed Mean ( 18 / 26 )110.3204545454551.00506423566688109.764580840204
Trimmed Mean ( 19 / 26 )110.2833333333330.97614352171713112.978604969210
Trimmed Mean ( 20 / 26 )110.27750.951318164443421115.920734115824
Trimmed Mean ( 21 / 26 )110.2578947368420.922792098562036119.482920268449
Trimmed Mean ( 22 / 26 )110.2277777777780.89115237603859123.691279675166
Trimmed Mean ( 23 / 26 )110.1911764705880.851530734993867129.40363975398
Trimmed Mean ( 24 / 26 )110.1968750.819144473735132134.526788049396
Trimmed Mean ( 25 / 26 )110.2033333333330.786092962437567140.191222411670
Trimmed Mean ( 26 / 26 )110.2285714285710.756118904293553145.782059941430
Median109.9
Midrange120.9
Midmean - Weighted Average at Xnp110.019512195122
Midmean - Weighted Average at X(n+1)p110.2775
Midmean - Empirical Distribution Function110.019512195122
Midmean - Empirical Distribution Function - Averaging110.2775
Midmean - Empirical Distribution Function - Interpolation110.2775
Midmean - Closest Observation110.019512195122
Midmean - True Basic - Statistics Graphics Toolkit110.2775
Midmean - MS Excel (old versions)110.283333333333
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 113.0075 & 1.96952957741922 & 57.3779146531427 \tabularnewline
Geometric Mean & 111.701951852900 &  &  \tabularnewline
Harmonic Mean & 110.442586594646 &  &  \tabularnewline
Quadratic Mean & 114.355322350995 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 112.93125 & 1.94359675206867 & 58.1042594765613 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 112.89125 & 1.90989030912242 & 59.1087610952236 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 112.75625 & 1.87543652618952 & 60.1226692694826 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 113.02625 & 1.79953030418066 & 62.8087505597531 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 113.0075 & 1.71037487100550 & 66.0717728702157 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 112.9175 & 1.69125989944430 & 66.7653150394574 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 112.82125 & 1.67134609373153 & 67.5032241515638 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 112.75125 & 1.61593919251078 & 69.7744386190742 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 112.875 & 1.59134178317735 & 70.9307084079877 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 112.9 & 1.57563629903460 & 71.6535916754232 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 112.625 & 1.50481137637945 & 74.8432672478685 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 112.55 & 1.47644265428509 & 76.2305259017987 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 112.3875 & 1.42109711472991 & 79.085024404796 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 112.44 & 1.39801237748274 & 80.4284724592063 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 112.1775 & 1.32255383824754 & 84.818853309323 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 111.8175 & 1.24248089789967 & 89.9953473643095 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 111.03125 & 1.10858644420368 & 100.155698800517 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 110.67125 & 1.03479068046316 & 106.950373722408 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 110.33875 & 0.973681344161607 & 113.321211977218 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 110.46375 & 0.949640577827718 & 116.321640607106 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 110.5425 & 0.917443087946197 & 120.489762746442 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 110.57 & 0.89881145148271 & 123.018014309453 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 110.13875 & 0.816744257863601 & 134.850963370218 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 110.13875 & 0.769042009992244 & 143.215518227815 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 109.9825 & 0.708009723794343 & 155.340380652663 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 110.4375 & 0.624569155295741 & 176.821892441529 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 112.805128205128 & 1.87538331962405 & 60.1504380596398 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 112.672368421053 & 1.79522329030398 & 62.762314320228 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 112.554054054054 & 1.72238049064932 & 65.347961536433 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 112.479166666667 & 1.65229713655407 & 68.0744184434321 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 112.322857142857 & 1.59716515353126 & 70.3263885356603 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 112.161764705882 & 1.55935257807149 & 71.92841842388 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 112.009090909091 & 1.51930809806390 & 73.7237503386096 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 111.8640625 & 1.47619397328515 & 75.7787015286722 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 111.720967741935 & 1.43726401663007 & 77.7316946985745 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 111.55 & 1.39498395187497 & 79.9650776269276 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 111.363793103448 & 1.34628097507868 & 82.7195772390229 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 111.2 & 1.30217849435814 & 85.3953589940156 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 111.033333333333 & 1.25338953440165 & 88.5864532021475 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 110.873076923077 & 1.20450422696013 & 92.0487238163481 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 110.694 & 1.14722525944924 & 96.488461257506 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 110.529166666667 & 1.09184987770176 & 101.23110230073 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 110.389130434783 & 1.03991930317205 & 106.151631283374 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 110.320454545455 & 1.00506423566688 & 109.764580840204 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 110.283333333333 & 0.97614352171713 & 112.978604969210 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 110.2775 & 0.951318164443421 & 115.920734115824 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 110.257894736842 & 0.922792098562036 & 119.482920268449 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 110.227777777778 & 0.89115237603859 & 123.691279675166 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 110.191176470588 & 0.851530734993867 & 129.40363975398 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 110.196875 & 0.819144473735132 & 134.526788049396 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 110.203333333333 & 0.786092962437567 & 140.191222411670 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 110.228571428571 & 0.756118904293553 & 145.782059941430 \tabularnewline
Median & 109.9 &  &  \tabularnewline
Midrange & 120.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 110.019512195122 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 110.2775 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 110.019512195122 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 110.2775 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 110.2775 &  &  \tabularnewline
Midmean - Closest Observation & 110.019512195122 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 110.2775 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 110.283333333333 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1139&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]113.0075[/C][C]1.96952957741922[/C][C]57.3779146531427[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]111.701951852900[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]110.442586594646[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]114.355322350995[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]112.93125[/C][C]1.94359675206867[/C][C]58.1042594765613[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]112.89125[/C][C]1.90989030912242[/C][C]59.1087610952236[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]112.75625[/C][C]1.87543652618952[/C][C]60.1226692694826[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]113.02625[/C][C]1.79953030418066[/C][C]62.8087505597531[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]113.0075[/C][C]1.71037487100550[/C][C]66.0717728702157[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]112.9175[/C][C]1.69125989944430[/C][C]66.7653150394574[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]112.82125[/C][C]1.67134609373153[/C][C]67.5032241515638[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]112.75125[/C][C]1.61593919251078[/C][C]69.7744386190742[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]112.875[/C][C]1.59134178317735[/C][C]70.9307084079877[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]112.9[/C][C]1.57563629903460[/C][C]71.6535916754232[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]112.625[/C][C]1.50481137637945[/C][C]74.8432672478685[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]112.55[/C][C]1.47644265428509[/C][C]76.2305259017987[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]112.3875[/C][C]1.42109711472991[/C][C]79.085024404796[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]112.44[/C][C]1.39801237748274[/C][C]80.4284724592063[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]112.1775[/C][C]1.32255383824754[/C][C]84.818853309323[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]111.8175[/C][C]1.24248089789967[/C][C]89.9953473643095[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]111.03125[/C][C]1.10858644420368[/C][C]100.155698800517[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]110.67125[/C][C]1.03479068046316[/C][C]106.950373722408[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]110.33875[/C][C]0.973681344161607[/C][C]113.321211977218[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]110.46375[/C][C]0.949640577827718[/C][C]116.321640607106[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]110.5425[/C][C]0.917443087946197[/C][C]120.489762746442[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]110.57[/C][C]0.89881145148271[/C][C]123.018014309453[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]110.13875[/C][C]0.816744257863601[/C][C]134.850963370218[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]110.13875[/C][C]0.769042009992244[/C][C]143.215518227815[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]109.9825[/C][C]0.708009723794343[/C][C]155.340380652663[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]110.4375[/C][C]0.624569155295741[/C][C]176.821892441529[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]112.805128205128[/C][C]1.87538331962405[/C][C]60.1504380596398[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]112.672368421053[/C][C]1.79522329030398[/C][C]62.762314320228[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]112.554054054054[/C][C]1.72238049064932[/C][C]65.347961536433[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]112.479166666667[/C][C]1.65229713655407[/C][C]68.0744184434321[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]112.322857142857[/C][C]1.59716515353126[/C][C]70.3263885356603[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]112.161764705882[/C][C]1.55935257807149[/C][C]71.92841842388[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]112.009090909091[/C][C]1.51930809806390[/C][C]73.7237503386096[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]111.8640625[/C][C]1.47619397328515[/C][C]75.7787015286722[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]111.720967741935[/C][C]1.43726401663007[/C][C]77.7316946985745[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]111.55[/C][C]1.39498395187497[/C][C]79.9650776269276[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]111.363793103448[/C][C]1.34628097507868[/C][C]82.7195772390229[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]111.2[/C][C]1.30217849435814[/C][C]85.3953589940156[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]111.033333333333[/C][C]1.25338953440165[/C][C]88.5864532021475[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]110.873076923077[/C][C]1.20450422696013[/C][C]92.0487238163481[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]110.694[/C][C]1.14722525944924[/C][C]96.488461257506[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]110.529166666667[/C][C]1.09184987770176[/C][C]101.23110230073[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]110.389130434783[/C][C]1.03991930317205[/C][C]106.151631283374[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]110.320454545455[/C][C]1.00506423566688[/C][C]109.764580840204[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]110.283333333333[/C][C]0.97614352171713[/C][C]112.978604969210[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]110.2775[/C][C]0.951318164443421[/C][C]115.920734115824[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]110.257894736842[/C][C]0.922792098562036[/C][C]119.482920268449[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]110.227777777778[/C][C]0.89115237603859[/C][C]123.691279675166[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]110.191176470588[/C][C]0.851530734993867[/C][C]129.40363975398[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]110.196875[/C][C]0.819144473735132[/C][C]134.526788049396[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]110.203333333333[/C][C]0.786092962437567[/C][C]140.191222411670[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]110.228571428571[/C][C]0.756118904293553[/C][C]145.782059941430[/C][/ROW]
[ROW][C]Median[/C][C]109.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]120.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]110.019512195122[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]110.2775[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]110.019512195122[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]110.2775[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]110.2775[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]110.019512195122[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]110.2775[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]110.283333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]80[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=1139&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1139&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 Mean113.00751.9695295774192257.3779146531427
Geometric Mean111.701951852900
Harmonic Mean110.442586594646
Quadratic Mean114.355322350995
Winsorized Mean ( 1 / 26 )112.931251.9435967520686758.1042594765613
Winsorized Mean ( 2 / 26 )112.891251.9098903091224259.1087610952236
Winsorized Mean ( 3 / 26 )112.756251.8754365261895260.1226692694826
Winsorized Mean ( 4 / 26 )113.026251.7995303041806662.8087505597531
Winsorized Mean ( 5 / 26 )113.00751.7103748710055066.0717728702157
Winsorized Mean ( 6 / 26 )112.91751.6912598994443066.7653150394574
Winsorized Mean ( 7 / 26 )112.821251.6713460937315367.5032241515638
Winsorized Mean ( 8 / 26 )112.751251.6159391925107869.7744386190742
Winsorized Mean ( 9 / 26 )112.8751.5913417831773570.9307084079877
Winsorized Mean ( 10 / 26 )112.91.5756362990346071.6535916754232
Winsorized Mean ( 11 / 26 )112.6251.5048113763794574.8432672478685
Winsorized Mean ( 12 / 26 )112.551.4764426542850976.2305259017987
Winsorized Mean ( 13 / 26 )112.38751.4210971147299179.085024404796
Winsorized Mean ( 14 / 26 )112.441.3980123774827480.4284724592063
Winsorized Mean ( 15 / 26 )112.17751.3225538382475484.818853309323
Winsorized Mean ( 16 / 26 )111.81751.2424808978996789.9953473643095
Winsorized Mean ( 17 / 26 )111.031251.10858644420368100.155698800517
Winsorized Mean ( 18 / 26 )110.671251.03479068046316106.950373722408
Winsorized Mean ( 19 / 26 )110.338750.973681344161607113.321211977218
Winsorized Mean ( 20 / 26 )110.463750.949640577827718116.321640607106
Winsorized Mean ( 21 / 26 )110.54250.917443087946197120.489762746442
Winsorized Mean ( 22 / 26 )110.570.89881145148271123.018014309453
Winsorized Mean ( 23 / 26 )110.138750.816744257863601134.850963370218
Winsorized Mean ( 24 / 26 )110.138750.769042009992244143.215518227815
Winsorized Mean ( 25 / 26 )109.98250.708009723794343155.340380652663
Winsorized Mean ( 26 / 26 )110.43750.624569155295741176.821892441529
Trimmed Mean ( 1 / 26 )112.8051282051281.8753833196240560.1504380596398
Trimmed Mean ( 2 / 26 )112.6723684210531.7952232903039862.762314320228
Trimmed Mean ( 3 / 26 )112.5540540540541.7223804906493265.347961536433
Trimmed Mean ( 4 / 26 )112.4791666666671.6522971365540768.0744184434321
Trimmed Mean ( 5 / 26 )112.3228571428571.5971651535312670.3263885356603
Trimmed Mean ( 6 / 26 )112.1617647058821.5593525780714971.92841842388
Trimmed Mean ( 7 / 26 )112.0090909090911.5193080980639073.7237503386096
Trimmed Mean ( 8 / 26 )111.86406251.4761939732851575.7787015286722
Trimmed Mean ( 9 / 26 )111.7209677419351.4372640166300777.7316946985745
Trimmed Mean ( 10 / 26 )111.551.3949839518749779.9650776269276
Trimmed Mean ( 11 / 26 )111.3637931034481.3462809750786882.7195772390229
Trimmed Mean ( 12 / 26 )111.21.3021784943581485.3953589940156
Trimmed Mean ( 13 / 26 )111.0333333333331.2533895344016588.5864532021475
Trimmed Mean ( 14 / 26 )110.8730769230771.2045042269601392.0487238163481
Trimmed Mean ( 15 / 26 )110.6941.1472252594492496.488461257506
Trimmed Mean ( 16 / 26 )110.5291666666671.09184987770176101.23110230073
Trimmed Mean ( 17 / 26 )110.3891304347831.03991930317205106.151631283374
Trimmed Mean ( 18 / 26 )110.3204545454551.00506423566688109.764580840204
Trimmed Mean ( 19 / 26 )110.2833333333330.97614352171713112.978604969210
Trimmed Mean ( 20 / 26 )110.27750.951318164443421115.920734115824
Trimmed Mean ( 21 / 26 )110.2578947368420.922792098562036119.482920268449
Trimmed Mean ( 22 / 26 )110.2277777777780.89115237603859123.691279675166
Trimmed Mean ( 23 / 26 )110.1911764705880.851530734993867129.40363975398
Trimmed Mean ( 24 / 26 )110.1968750.819144473735132134.526788049396
Trimmed Mean ( 25 / 26 )110.2033333333330.786092962437567140.191222411670
Trimmed Mean ( 26 / 26 )110.2285714285710.756118904293553145.782059941430
Median109.9
Midrange120.9
Midmean - Weighted Average at Xnp110.019512195122
Midmean - Weighted Average at X(n+1)p110.2775
Midmean - Empirical Distribution Function110.019512195122
Midmean - Empirical Distribution Function - Averaging110.2775
Midmean - Empirical Distribution Function - Interpolation110.2775
Midmean - Closest Observation110.019512195122
Midmean - True Basic - Statistics Graphics Toolkit110.2775
Midmean - MS Excel (old versions)110.283333333333
Number of observations80



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')