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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, 20 Nov 2007 12:53:14 -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/20/t1195587975h5qx3pm90s49828.htm/, Retrieved Sun, 05 May 2024 10:03:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5810, Retrieved Sun, 05 May 2024 10:03:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsConsumptiegoederen
Estimated Impact247
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central tendency] [2007-11-20 19:53:14] [6dd0685065b0babfa744248f2bd1b94f] [Current]
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Dataseries X:
115,9
112,9
126,3
116,8
112
129,7
113,6
115,7
119,5
125,8
129,6
128
112,8
101,6
123,9
118,8
109,1
130,6
112,4
111
116,2
119,8
117,2
127,3
107,7
97,5
120,1
110,6
111,3
119,8
105,5
108,7
128,7
119,5
121,1
128,4
108,8
107,5
125,6
102,9
107,5
120,4
104,3
100,6
121,9
112,7
124,9
123,9
102,2
104,9
109,8
98,9
107,3
112,6
104
110,6
100,8
103,8
117
108,4
95,5
96,9
103,9
101,1
100,6
104,3
98
99,5
97,4
105,6
117,5
107,4
97,8
91,5
107,7
100,1
96,6
106,8
98
98,6




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=5810&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=5810&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5810&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 Mean111.143751.1248499812070698.8076204444022
Geometric Mean110.697511362123
Harmonic Mean110.255563217667
Quadratic Mean111.592521590831
Winsorized Mean ( 1 / 26 )111.18251.1124394095290899.9447691691052
Winsorized Mean ( 2 / 26 )111.20751.10716277690183100.443676684283
Winsorized Mean ( 3 / 26 )111.1851.09834181693835101.229870597052
Winsorized Mean ( 4 / 26 )111.1951.09127277333524101.894780770674
Winsorized Mean ( 5 / 26 )111.176251.08532682435502102.435734108082
Winsorized Mean ( 6 / 26 )111.146251.07159815546864103.720083347281
Winsorized Mean ( 7 / 26 )111.076251.05248086026976105.537548655783
Winsorized Mean ( 8 / 26 )111.026251.04342235060425106.405857547238
Winsorized Mean ( 9 / 26 )111.071251.02888226459529107.953313826135
Winsorized Mean ( 10 / 26 )111.021251.00770087633726110.172822716533
Winsorized Mean ( 11 / 26 )110.966250.97167958422452114.20045434891
Winsorized Mean ( 12 / 26 )111.056250.958444883206943115.871295205216
Winsorized Mean ( 13 / 26 )110.81250.89352873024439124.016717369224
Winsorized Mean ( 14 / 26 )110.67250.871932189835245126.927875000133
Winsorized Mean ( 15 / 26 )110.578750.84687753689657130.572302584884
Winsorized Mean ( 16 / 26 )110.578750.829388393217434133.325654065442
Winsorized Mean ( 17 / 26 )110.621250.804930796911421137.429516207433
Winsorized Mean ( 18 / 26 )110.756250.786050944797127140.902126933497
Winsorized Mean ( 19 / 26 )110.851250.753113776243905147.190575311026
Winsorized Mean ( 20 / 26 )111.076250.723747813774272153.473693303125
Winsorized Mean ( 21 / 26 )110.918750.693639944514863159.908250493817
Winsorized Mean ( 22 / 26 )110.588750.639889710013384172.824704428654
Winsorized Mean ( 23 / 26 )110.588750.616957094270652179.248688485760
Winsorized Mean ( 24 / 26 )110.528750.608851361353097181.536507948941
Winsorized Mean ( 25 / 26 )110.653750.576435862005764191.961946321260
Winsorized Mean ( 26 / 26 )110.653750.525826485525165210.437764255038
Trimmed Mean ( 1 / 26 )111.1461538461541.09734291793682101.28661882206
Trimmed Mean ( 2 / 26 )111.1078947368421.07955767933453102.919831764183
Trimmed Mean ( 3 / 26 )111.0540540540541.06180567040654104.589810686860
Trimmed Mean ( 4 / 26 )111.0055555555561.04463172163093106.262861118413
Trimmed Mean ( 5 / 26 )110.9514285714291.02662433604448108.074029297725
Trimmed Mean ( 6 / 26 )110.8985294117651.00687167678732110.141671444781
Trimmed Mean ( 7 / 26 )110.8484848484850.986870078629589112.323280692038
Trimmed Mean ( 8 / 26 )110.80781250.96749580791384114.530535009686
Trimmed Mean ( 9 / 26 )110.7725806451610.946096574044374117.083798508677
Trimmed Mean ( 10 / 26 )110.7283333333330.923197867849307119.939979488132
Trimmed Mean ( 11 / 26 )110.6879310344830.89973471114033123.022852918719
Trimmed Mean ( 12 / 26 )110.6517857142860.87839874635992125.969881187588
Trimmed Mean ( 13 / 26 )110.6018518518520.854447364486212129.442557199949
Trimmed Mean ( 14 / 26 )110.5769230769230.837869773323028131.973877800091
Trimmed Mean ( 15 / 26 )110.5660.82102280661355134.668609823457
Trimmed Mean ( 16 / 26 )110.5645833333330.80430187330277137.466524700873
Trimmed Mean ( 17 / 26 )110.5630434782610.78602134361288140.661630090180
Trimmed Mean ( 18 / 26 )110.5568181818180.767070687080084144.128592115365
Trimmed Mean ( 19 / 26 )110.5357142857140.745858261473805148.19935635934
Trimmed Mean ( 20 / 26 )110.50250.724679305730367152.484690988423
Trimmed Mean ( 21 / 26 )110.4421052631580.702177385552691157.285192510476
Trimmed Mean ( 22 / 26 )110.3916666666670.678752064512047162.639161541302
Trimmed Mean ( 23 / 26 )110.3705882352940.660234515292083167.168764550982
Trimmed Mean ( 24 / 26 )110.3468750.639414178315942172.574958050862
Trimmed Mean ( 25 / 26 )110.3266666666670.610952400149997180.581444052892
Trimmed Mean ( 26 / 26 )110.2892857142860.578891005214598190.518223155671
Median110.2
Midrange111.05
Midmean - Weighted Average at Xnp110.535714285714
Midmean - Weighted Average at X(n+1)p110.721951219512
Midmean - Empirical Distribution Function110.535714285714
Midmean - Empirical Distribution Function - Averaging110.721951219512
Midmean - Empirical Distribution Function - Interpolation110.721951219512
Midmean - Closest Observation110.535714285714
Midmean - True Basic - Statistics Graphics Toolkit110.721951219512
Midmean - MS Excel (old versions)110.535714285714
Number of observations80

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 111.14375 & 1.12484998120706 & 98.8076204444022 \tabularnewline
Geometric Mean & 110.697511362123 &  &  \tabularnewline
Harmonic Mean & 110.255563217667 &  &  \tabularnewline
Quadratic Mean & 111.592521590831 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 111.1825 & 1.11243940952908 & 99.9447691691052 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 111.2075 & 1.10716277690183 & 100.443676684283 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 111.185 & 1.09834181693835 & 101.229870597052 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 111.195 & 1.09127277333524 & 101.894780770674 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 111.17625 & 1.08532682435502 & 102.435734108082 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 111.14625 & 1.07159815546864 & 103.720083347281 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 111.07625 & 1.05248086026976 & 105.537548655783 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 111.02625 & 1.04342235060425 & 106.405857547238 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 111.07125 & 1.02888226459529 & 107.953313826135 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 111.02125 & 1.00770087633726 & 110.172822716533 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 110.96625 & 0.97167958422452 & 114.20045434891 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 111.05625 & 0.958444883206943 & 115.871295205216 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 110.8125 & 0.89352873024439 & 124.016717369224 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 110.6725 & 0.871932189835245 & 126.927875000133 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 110.57875 & 0.84687753689657 & 130.572302584884 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 110.57875 & 0.829388393217434 & 133.325654065442 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 110.62125 & 0.804930796911421 & 137.429516207433 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 110.75625 & 0.786050944797127 & 140.902126933497 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 110.85125 & 0.753113776243905 & 147.190575311026 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 111.07625 & 0.723747813774272 & 153.473693303125 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 110.91875 & 0.693639944514863 & 159.908250493817 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 110.58875 & 0.639889710013384 & 172.824704428654 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 110.58875 & 0.616957094270652 & 179.248688485760 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 110.52875 & 0.608851361353097 & 181.536507948941 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 110.65375 & 0.576435862005764 & 191.961946321260 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 110.65375 & 0.525826485525165 & 210.437764255038 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 111.146153846154 & 1.09734291793682 & 101.28661882206 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 111.107894736842 & 1.07955767933453 & 102.919831764183 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 111.054054054054 & 1.06180567040654 & 104.589810686860 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 111.005555555556 & 1.04463172163093 & 106.262861118413 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 110.951428571429 & 1.02662433604448 & 108.074029297725 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 110.898529411765 & 1.00687167678732 & 110.141671444781 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 110.848484848485 & 0.986870078629589 & 112.323280692038 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 110.8078125 & 0.96749580791384 & 114.530535009686 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 110.772580645161 & 0.946096574044374 & 117.083798508677 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 110.728333333333 & 0.923197867849307 & 119.939979488132 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 110.687931034483 & 0.89973471114033 & 123.022852918719 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 110.651785714286 & 0.87839874635992 & 125.969881187588 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 110.601851851852 & 0.854447364486212 & 129.442557199949 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 110.576923076923 & 0.837869773323028 & 131.973877800091 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 110.566 & 0.82102280661355 & 134.668609823457 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 110.564583333333 & 0.80430187330277 & 137.466524700873 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 110.563043478261 & 0.78602134361288 & 140.661630090180 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 110.556818181818 & 0.767070687080084 & 144.128592115365 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 110.535714285714 & 0.745858261473805 & 148.19935635934 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 110.5025 & 0.724679305730367 & 152.484690988423 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 110.442105263158 & 0.702177385552691 & 157.285192510476 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 110.391666666667 & 0.678752064512047 & 162.639161541302 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 110.370588235294 & 0.660234515292083 & 167.168764550982 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 110.346875 & 0.639414178315942 & 172.574958050862 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 110.326666666667 & 0.610952400149997 & 180.581444052892 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 110.289285714286 & 0.578891005214598 & 190.518223155671 \tabularnewline
Median & 110.2 &  &  \tabularnewline
Midrange & 111.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 110.535714285714 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 110.721951219512 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 110.535714285714 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 110.721951219512 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 110.721951219512 &  &  \tabularnewline
Midmean - Closest Observation & 110.535714285714 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 110.721951219512 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 110.535714285714 &  &  \tabularnewline
Number of observations & 80 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5810&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]111.14375[/C][C]1.12484998120706[/C][C]98.8076204444022[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]110.697511362123[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]110.255563217667[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]111.592521590831[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]111.1825[/C][C]1.11243940952908[/C][C]99.9447691691052[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]111.2075[/C][C]1.10716277690183[/C][C]100.443676684283[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]111.185[/C][C]1.09834181693835[/C][C]101.229870597052[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]111.195[/C][C]1.09127277333524[/C][C]101.894780770674[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]111.17625[/C][C]1.08532682435502[/C][C]102.435734108082[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]111.14625[/C][C]1.07159815546864[/C][C]103.720083347281[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]111.07625[/C][C]1.05248086026976[/C][C]105.537548655783[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]111.02625[/C][C]1.04342235060425[/C][C]106.405857547238[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]111.07125[/C][C]1.02888226459529[/C][C]107.953313826135[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]111.02125[/C][C]1.00770087633726[/C][C]110.172822716533[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]110.96625[/C][C]0.97167958422452[/C][C]114.20045434891[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]111.05625[/C][C]0.958444883206943[/C][C]115.871295205216[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]110.8125[/C][C]0.89352873024439[/C][C]124.016717369224[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]110.6725[/C][C]0.871932189835245[/C][C]126.927875000133[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]110.57875[/C][C]0.84687753689657[/C][C]130.572302584884[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]110.57875[/C][C]0.829388393217434[/C][C]133.325654065442[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]110.62125[/C][C]0.804930796911421[/C][C]137.429516207433[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]110.75625[/C][C]0.786050944797127[/C][C]140.902126933497[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]110.85125[/C][C]0.753113776243905[/C][C]147.190575311026[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]111.07625[/C][C]0.723747813774272[/C][C]153.473693303125[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]110.91875[/C][C]0.693639944514863[/C][C]159.908250493817[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]110.58875[/C][C]0.639889710013384[/C][C]172.824704428654[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]110.58875[/C][C]0.616957094270652[/C][C]179.248688485760[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]110.52875[/C][C]0.608851361353097[/C][C]181.536507948941[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]110.65375[/C][C]0.576435862005764[/C][C]191.961946321260[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]110.65375[/C][C]0.525826485525165[/C][C]210.437764255038[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]111.146153846154[/C][C]1.09734291793682[/C][C]101.28661882206[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]111.107894736842[/C][C]1.07955767933453[/C][C]102.919831764183[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]111.054054054054[/C][C]1.06180567040654[/C][C]104.589810686860[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]111.005555555556[/C][C]1.04463172163093[/C][C]106.262861118413[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]110.951428571429[/C][C]1.02662433604448[/C][C]108.074029297725[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]110.898529411765[/C][C]1.00687167678732[/C][C]110.141671444781[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]110.848484848485[/C][C]0.986870078629589[/C][C]112.323280692038[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]110.8078125[/C][C]0.96749580791384[/C][C]114.530535009686[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]110.772580645161[/C][C]0.946096574044374[/C][C]117.083798508677[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]110.728333333333[/C][C]0.923197867849307[/C][C]119.939979488132[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]110.687931034483[/C][C]0.89973471114033[/C][C]123.022852918719[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]110.651785714286[/C][C]0.87839874635992[/C][C]125.969881187588[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]110.601851851852[/C][C]0.854447364486212[/C][C]129.442557199949[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]110.576923076923[/C][C]0.837869773323028[/C][C]131.973877800091[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]110.566[/C][C]0.82102280661355[/C][C]134.668609823457[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]110.564583333333[/C][C]0.80430187330277[/C][C]137.466524700873[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]110.563043478261[/C][C]0.78602134361288[/C][C]140.661630090180[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]110.556818181818[/C][C]0.767070687080084[/C][C]144.128592115365[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]110.535714285714[/C][C]0.745858261473805[/C][C]148.19935635934[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]110.5025[/C][C]0.724679305730367[/C][C]152.484690988423[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]110.442105263158[/C][C]0.702177385552691[/C][C]157.285192510476[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]110.391666666667[/C][C]0.678752064512047[/C][C]162.639161541302[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]110.370588235294[/C][C]0.660234515292083[/C][C]167.168764550982[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]110.346875[/C][C]0.639414178315942[/C][C]172.574958050862[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]110.326666666667[/C][C]0.610952400149997[/C][C]180.581444052892[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]110.289285714286[/C][C]0.578891005214598[/C][C]190.518223155671[/C][/ROW]
[ROW][C]Median[/C][C]110.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]111.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]110.535714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]110.721951219512[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]110.535714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]110.721951219512[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]110.721951219512[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]110.535714285714[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]110.721951219512[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]110.535714285714[/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=5810&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5810&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 Mean111.143751.1248499812070698.8076204444022
Geometric Mean110.697511362123
Harmonic Mean110.255563217667
Quadratic Mean111.592521590831
Winsorized Mean ( 1 / 26 )111.18251.1124394095290899.9447691691052
Winsorized Mean ( 2 / 26 )111.20751.10716277690183100.443676684283
Winsorized Mean ( 3 / 26 )111.1851.09834181693835101.229870597052
Winsorized Mean ( 4 / 26 )111.1951.09127277333524101.894780770674
Winsorized Mean ( 5 / 26 )111.176251.08532682435502102.435734108082
Winsorized Mean ( 6 / 26 )111.146251.07159815546864103.720083347281
Winsorized Mean ( 7 / 26 )111.076251.05248086026976105.537548655783
Winsorized Mean ( 8 / 26 )111.026251.04342235060425106.405857547238
Winsorized Mean ( 9 / 26 )111.071251.02888226459529107.953313826135
Winsorized Mean ( 10 / 26 )111.021251.00770087633726110.172822716533
Winsorized Mean ( 11 / 26 )110.966250.97167958422452114.20045434891
Winsorized Mean ( 12 / 26 )111.056250.958444883206943115.871295205216
Winsorized Mean ( 13 / 26 )110.81250.89352873024439124.016717369224
Winsorized Mean ( 14 / 26 )110.67250.871932189835245126.927875000133
Winsorized Mean ( 15 / 26 )110.578750.84687753689657130.572302584884
Winsorized Mean ( 16 / 26 )110.578750.829388393217434133.325654065442
Winsorized Mean ( 17 / 26 )110.621250.804930796911421137.429516207433
Winsorized Mean ( 18 / 26 )110.756250.786050944797127140.902126933497
Winsorized Mean ( 19 / 26 )110.851250.753113776243905147.190575311026
Winsorized Mean ( 20 / 26 )111.076250.723747813774272153.473693303125
Winsorized Mean ( 21 / 26 )110.918750.693639944514863159.908250493817
Winsorized Mean ( 22 / 26 )110.588750.639889710013384172.824704428654
Winsorized Mean ( 23 / 26 )110.588750.616957094270652179.248688485760
Winsorized Mean ( 24 / 26 )110.528750.608851361353097181.536507948941
Winsorized Mean ( 25 / 26 )110.653750.576435862005764191.961946321260
Winsorized Mean ( 26 / 26 )110.653750.525826485525165210.437764255038
Trimmed Mean ( 1 / 26 )111.1461538461541.09734291793682101.28661882206
Trimmed Mean ( 2 / 26 )111.1078947368421.07955767933453102.919831764183
Trimmed Mean ( 3 / 26 )111.0540540540541.06180567040654104.589810686860
Trimmed Mean ( 4 / 26 )111.0055555555561.04463172163093106.262861118413
Trimmed Mean ( 5 / 26 )110.9514285714291.02662433604448108.074029297725
Trimmed Mean ( 6 / 26 )110.8985294117651.00687167678732110.141671444781
Trimmed Mean ( 7 / 26 )110.8484848484850.986870078629589112.323280692038
Trimmed Mean ( 8 / 26 )110.80781250.96749580791384114.530535009686
Trimmed Mean ( 9 / 26 )110.7725806451610.946096574044374117.083798508677
Trimmed Mean ( 10 / 26 )110.7283333333330.923197867849307119.939979488132
Trimmed Mean ( 11 / 26 )110.6879310344830.89973471114033123.022852918719
Trimmed Mean ( 12 / 26 )110.6517857142860.87839874635992125.969881187588
Trimmed Mean ( 13 / 26 )110.6018518518520.854447364486212129.442557199949
Trimmed Mean ( 14 / 26 )110.5769230769230.837869773323028131.973877800091
Trimmed Mean ( 15 / 26 )110.5660.82102280661355134.668609823457
Trimmed Mean ( 16 / 26 )110.5645833333330.80430187330277137.466524700873
Trimmed Mean ( 17 / 26 )110.5630434782610.78602134361288140.661630090180
Trimmed Mean ( 18 / 26 )110.5568181818180.767070687080084144.128592115365
Trimmed Mean ( 19 / 26 )110.5357142857140.745858261473805148.19935635934
Trimmed Mean ( 20 / 26 )110.50250.724679305730367152.484690988423
Trimmed Mean ( 21 / 26 )110.4421052631580.702177385552691157.285192510476
Trimmed Mean ( 22 / 26 )110.3916666666670.678752064512047162.639161541302
Trimmed Mean ( 23 / 26 )110.3705882352940.660234515292083167.168764550982
Trimmed Mean ( 24 / 26 )110.3468750.639414178315942172.574958050862
Trimmed Mean ( 25 / 26 )110.3266666666670.610952400149997180.581444052892
Trimmed Mean ( 26 / 26 )110.2892857142860.578891005214598190.518223155671
Median110.2
Midrange111.05
Midmean - Weighted Average at Xnp110.535714285714
Midmean - Weighted Average at X(n+1)p110.721951219512
Midmean - Empirical Distribution Function110.535714285714
Midmean - Empirical Distribution Function - Averaging110.721951219512
Midmean - Empirical Distribution Function - Interpolation110.721951219512
Midmean - Closest Observation110.535714285714
Midmean - True Basic - Statistics Graphics Toolkit110.721951219512
Midmean - MS Excel (old versions)110.535714285714
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')