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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 computationMon, 12 Nov 2007 03:08:37 -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/12/t1194861822780xv3baab5h9x3.htm/, Retrieved Sun, 28 Apr 2024 20:35:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5154, Retrieved Sun, 28 Apr 2024 20:35:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact207
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2007-11-12 10:08:37] [addc65c5fbfb06e42e5fd21f3a753dae] [Current]
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Dataseries X:
93,5
94,7
112,9
99,2
105,6
113
83,1
81,1
96,9
104,3
97,7
102,6
89,9
96
112,7
107,1
106,2
121
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
110,3
132,7
99,7
96,5
118,7
112,9
130,5
137,9
115
116,8
140,9
120,7
134,2
147,3
112,4
107,1
128,4
137,7
135
151
137,4
132,4
161,3
139,8
146
154,6
142,1
120,5




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=5154&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=5154&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5154&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 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=5154&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=5154&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5154&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')