Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 14 Dec 2007 13:04:55 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/14/t1197661805a4785e9oxs662sp.htm/, Retrieved Thu, 02 May 2024 18:26:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3959, Retrieved Thu, 02 May 2024 18:26:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact184
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2007-12-14 20:04:55] [ba3202e2798d2e4685d19d988e9c69df] [Current]
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Dataseries X:
88
88.4
95
101.8
107.6
118.9
126.9
106.3
109.2
104.6
100.8
92.1
86.4
96
98.5
112
113.9
120
126.7
112.8
116.2
110.6
105
101.2
99.3
101.9
106.4
118.9
121.9
132
121.4
117
122.7
113
104
101.2
100.8
98.9
103
117.8
126.6
127.6
115.8
114.8
119.2
109.9
98.9
98.6
96.6
96.7
103.5
115.3
122.5
125.3
111.2
110.7
114.2
105.6
95.5
97.3
95.5
96.3
100.2
113.4
121.4
122.1
119.3
110.8
110.1
99.7
104.8
105.4
106.5




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=3959&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=3959&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3959&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 Mean108.6356164383561.2551027807898186.5551555626334
Geometric Mean108.112481811640
Harmonic Mean107.588923139812
Quadratic Mean109.156390258411
Winsorized Mean ( 1 / 24 )108.5972602739731.2356281449090687.888302578253
Winsorized Mean ( 2 / 24 )108.5890410958901.2290768857294488.3500799312845
Winsorized Mean ( 3 / 24 )108.7328767123291.1952930497852890.9675470227668
Winsorized Mean ( 4 / 24 )108.8863013698631.1656132149762693.415465757293
Winsorized Mean ( 5 / 24 )108.8315068493151.1416810429923995.3256669341408
Winsorized Mean ( 6 / 24 )108.6178082191781.1012538558591998.63103556122
Winsorized Mean ( 7 / 24 )108.6465753424661.0900286295371999.6731392170819
Winsorized Mean ( 8 / 24 )108.6356164383561.07709014153632100.860282950323
Winsorized Mean ( 9 / 24 )108.6479452054791.06698074283933101.827465898174
Winsorized Mean ( 10 / 24 )108.5931506849321.05313970094545103.113718519435
Winsorized Mean ( 11 / 24 )108.6835616438361.03917009259766104.586883723871
Winsorized Mean ( 12 / 24 )108.6506849315070.971572975126267111.829669734676
Winsorized Mean ( 13 / 24 )108.5438356164380.94905822561444114.37004884096
Winsorized Mean ( 14 / 24 )108.5821917808220.937728850740169115.792738695323
Winsorized Mean ( 15 / 24 )108.5205479452050.92809390209802116.928413924375
Winsorized Mean ( 16 / 24 )108.6082191780820.915592466122766118.620699925593
Winsorized Mean ( 17 / 24 )108.4452054794520.863164775015517125.636736598180
Winsorized Mean ( 18 / 24 )108.3712328767120.81658857014542132.712159879256
Winsorized Mean ( 19 / 24 )108.3191780821920.764879437416958141.616015261166
Winsorized Mean ( 20 / 24 )108.2095890410960.74932786824136144.408867769804
Winsorized Mean ( 21 / 24 )108.1808219178080.713518244965719151.616055624486
Winsorized Mean ( 22 / 24 )108.0301369863010.692849664815285155.921468209272
Winsorized Mean ( 23 / 24 )108.0301369863010.641697606238332168.350537599135
Winsorized Mean ( 24 / 24 )107.9643835616440.624162665468132172.974754074194
Trimmed Mean ( 1 / 24 )108.6197183098591.2069010480198989.9988598800762
Trimmed Mean ( 2 / 24 )108.6434782608701.1728210797045992.6343157885894
Trimmed Mean ( 3 / 24 )108.6731343283581.1364138212319895.6281350138333
Trimmed Mean ( 4 / 24 )108.6507692307691.1084316776525698.022071564095
Trimmed Mean ( 5 / 24 )108.5825396825401.08547298965830100.032465770264
Trimmed Mean ( 6 / 24 )108.5229508196721.06501851863789101.897712500312
Trimmed Mean ( 7 / 24 )108.5033898305081.05111881641825103.226569761391
Trimmed Mean ( 8 / 24 )108.4771929824561.03638692305762104.668623820937
Trimmed Mean ( 9 / 24 )108.4509090909091.02076380172114106.244861845656
Trimmed Mean ( 10 / 24 )108.4207547169811.00312414196778108.083087806358
Trimmed Mean ( 11 / 24 )108.3960784313730.983666453848046110.195969383050
Trimmed Mean ( 12 / 24 )108.3571428571430.961654257810272112.677858988403
Trimmed Mean ( 13 / 24 )108.3191489361700.94782792878719114.281448822438
Trimmed Mean ( 14 / 24 )108.2911111111110.93398690440402115.944999443233
Trimmed Mean ( 15 / 24 )108.2558139534880.917398594283154118.00303012027
Trimmed Mean ( 16 / 24 )108.2243902439020.896842567742351120.672673372696
Trimmed Mean ( 17 / 24 )108.1794871794870.871425062471293124.140894998703
Trimmed Mean ( 18 / 24 )108.1486486486490.849356067885771127.330165448578
Trimmed Mean ( 19 / 24 )108.1228571428570.829782655701046130.302623705130
Trimmed Mean ( 20 / 24 )108.10.814452781524708132.72715429571
Trimmed Mean ( 21 / 24 )108.0870967741940.7950754604815135.945708484998
Trimmed Mean ( 22 / 24 )108.0758620689660.775576302052711139.349103090079
Trimmed Mean ( 23 / 24 )108.0814814814810.751011417491994143.914565030742
Trimmed Mean ( 24 / 24 )108.0880.729207789316598148.226611925386
Median107.6
Midrange109.2
Midmean - Weighted Average at Xnp107.902777777778
Midmean - Weighted Average at X(n+1)p108.148648648649
Midmean - Empirical Distribution Function108.148648648649
Midmean - Empirical Distribution Function - Averaging108.148648648649
Midmean - Empirical Distribution Function - Interpolation108.148648648649
Midmean - Closest Observation107.926315789474
Midmean - True Basic - Statistics Graphics Toolkit108.148648648649
Midmean - MS Excel (old versions)108.148648648649
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 108.635616438356 & 1.25510278078981 & 86.5551555626334 \tabularnewline
Geometric Mean & 108.112481811640 &  &  \tabularnewline
Harmonic Mean & 107.588923139812 &  &  \tabularnewline
Quadratic Mean & 109.156390258411 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 108.597260273973 & 1.23562814490906 & 87.888302578253 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 108.589041095890 & 1.22907688572944 & 88.3500799312845 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 108.732876712329 & 1.19529304978528 & 90.9675470227668 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 108.886301369863 & 1.16561321497626 & 93.415465757293 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 108.831506849315 & 1.14168104299239 & 95.3256669341408 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 108.617808219178 & 1.10125385585919 & 98.63103556122 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 108.646575342466 & 1.09002862953719 & 99.6731392170819 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 108.635616438356 & 1.07709014153632 & 100.860282950323 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 108.647945205479 & 1.06698074283933 & 101.827465898174 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 108.593150684932 & 1.05313970094545 & 103.113718519435 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 108.683561643836 & 1.03917009259766 & 104.586883723871 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 108.650684931507 & 0.971572975126267 & 111.829669734676 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 108.543835616438 & 0.94905822561444 & 114.37004884096 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 108.582191780822 & 0.937728850740169 & 115.792738695323 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 108.520547945205 & 0.92809390209802 & 116.928413924375 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 108.608219178082 & 0.915592466122766 & 118.620699925593 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 108.445205479452 & 0.863164775015517 & 125.636736598180 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 108.371232876712 & 0.81658857014542 & 132.712159879256 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 108.319178082192 & 0.764879437416958 & 141.616015261166 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 108.209589041096 & 0.74932786824136 & 144.408867769804 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 108.180821917808 & 0.713518244965719 & 151.616055624486 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 108.030136986301 & 0.692849664815285 & 155.921468209272 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 108.030136986301 & 0.641697606238332 & 168.350537599135 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 107.964383561644 & 0.624162665468132 & 172.974754074194 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 108.619718309859 & 1.20690104801989 & 89.9988598800762 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 108.643478260870 & 1.17282107970459 & 92.6343157885894 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 108.673134328358 & 1.13641382123198 & 95.6281350138333 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 108.650769230769 & 1.10843167765256 & 98.022071564095 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 108.582539682540 & 1.08547298965830 & 100.032465770264 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 108.522950819672 & 1.06501851863789 & 101.897712500312 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 108.503389830508 & 1.05111881641825 & 103.226569761391 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 108.477192982456 & 1.03638692305762 & 104.668623820937 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 108.450909090909 & 1.02076380172114 & 106.244861845656 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 108.420754716981 & 1.00312414196778 & 108.083087806358 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 108.396078431373 & 0.983666453848046 & 110.195969383050 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 108.357142857143 & 0.961654257810272 & 112.677858988403 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 108.319148936170 & 0.94782792878719 & 114.281448822438 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 108.291111111111 & 0.93398690440402 & 115.944999443233 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 108.255813953488 & 0.917398594283154 & 118.00303012027 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 108.224390243902 & 0.896842567742351 & 120.672673372696 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 108.179487179487 & 0.871425062471293 & 124.140894998703 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 108.148648648649 & 0.849356067885771 & 127.330165448578 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 108.122857142857 & 0.829782655701046 & 130.302623705130 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 108.1 & 0.814452781524708 & 132.72715429571 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 108.087096774194 & 0.7950754604815 & 135.945708484998 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 108.075862068966 & 0.775576302052711 & 139.349103090079 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 108.081481481481 & 0.751011417491994 & 143.914565030742 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 108.088 & 0.729207789316598 & 148.226611925386 \tabularnewline
Median & 107.6 &  &  \tabularnewline
Midrange & 109.2 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 107.902777777778 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 108.148648648649 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 108.148648648649 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 108.148648648649 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 108.148648648649 &  &  \tabularnewline
Midmean - Closest Observation & 107.926315789474 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 108.148648648649 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 108.148648648649 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3959&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]108.635616438356[/C][C]1.25510278078981[/C][C]86.5551555626334[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]108.112481811640[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]107.588923139812[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]109.156390258411[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]108.597260273973[/C][C]1.23562814490906[/C][C]87.888302578253[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]108.589041095890[/C][C]1.22907688572944[/C][C]88.3500799312845[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]108.732876712329[/C][C]1.19529304978528[/C][C]90.9675470227668[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]108.886301369863[/C][C]1.16561321497626[/C][C]93.415465757293[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]108.831506849315[/C][C]1.14168104299239[/C][C]95.3256669341408[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]108.617808219178[/C][C]1.10125385585919[/C][C]98.63103556122[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]108.646575342466[/C][C]1.09002862953719[/C][C]99.6731392170819[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]108.635616438356[/C][C]1.07709014153632[/C][C]100.860282950323[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]108.647945205479[/C][C]1.06698074283933[/C][C]101.827465898174[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]108.593150684932[/C][C]1.05313970094545[/C][C]103.113718519435[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]108.683561643836[/C][C]1.03917009259766[/C][C]104.586883723871[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]108.650684931507[/C][C]0.971572975126267[/C][C]111.829669734676[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]108.543835616438[/C][C]0.94905822561444[/C][C]114.37004884096[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]108.582191780822[/C][C]0.937728850740169[/C][C]115.792738695323[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]108.520547945205[/C][C]0.92809390209802[/C][C]116.928413924375[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]108.608219178082[/C][C]0.915592466122766[/C][C]118.620699925593[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]108.445205479452[/C][C]0.863164775015517[/C][C]125.636736598180[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]108.371232876712[/C][C]0.81658857014542[/C][C]132.712159879256[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]108.319178082192[/C][C]0.764879437416958[/C][C]141.616015261166[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]108.209589041096[/C][C]0.74932786824136[/C][C]144.408867769804[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]108.180821917808[/C][C]0.713518244965719[/C][C]151.616055624486[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]108.030136986301[/C][C]0.692849664815285[/C][C]155.921468209272[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]108.030136986301[/C][C]0.641697606238332[/C][C]168.350537599135[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]107.964383561644[/C][C]0.624162665468132[/C][C]172.974754074194[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]108.619718309859[/C][C]1.20690104801989[/C][C]89.9988598800762[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]108.643478260870[/C][C]1.17282107970459[/C][C]92.6343157885894[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]108.673134328358[/C][C]1.13641382123198[/C][C]95.6281350138333[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]108.650769230769[/C][C]1.10843167765256[/C][C]98.022071564095[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]108.582539682540[/C][C]1.08547298965830[/C][C]100.032465770264[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]108.522950819672[/C][C]1.06501851863789[/C][C]101.897712500312[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]108.503389830508[/C][C]1.05111881641825[/C][C]103.226569761391[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]108.477192982456[/C][C]1.03638692305762[/C][C]104.668623820937[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]108.450909090909[/C][C]1.02076380172114[/C][C]106.244861845656[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]108.420754716981[/C][C]1.00312414196778[/C][C]108.083087806358[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]108.396078431373[/C][C]0.983666453848046[/C][C]110.195969383050[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]108.357142857143[/C][C]0.961654257810272[/C][C]112.677858988403[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]108.319148936170[/C][C]0.94782792878719[/C][C]114.281448822438[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]108.291111111111[/C][C]0.93398690440402[/C][C]115.944999443233[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]108.255813953488[/C][C]0.917398594283154[/C][C]118.00303012027[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]108.224390243902[/C][C]0.896842567742351[/C][C]120.672673372696[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]108.179487179487[/C][C]0.871425062471293[/C][C]124.140894998703[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]108.148648648649[/C][C]0.849356067885771[/C][C]127.330165448578[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]108.122857142857[/C][C]0.829782655701046[/C][C]130.302623705130[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]108.1[/C][C]0.814452781524708[/C][C]132.72715429571[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]108.087096774194[/C][C]0.7950754604815[/C][C]135.945708484998[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]108.075862068966[/C][C]0.775576302052711[/C][C]139.349103090079[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]108.081481481481[/C][C]0.751011417491994[/C][C]143.914565030742[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]108.088[/C][C]0.729207789316598[/C][C]148.226611925386[/C][/ROW]
[ROW][C]Median[/C][C]107.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]109.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]107.902777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]108.148648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]108.148648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]108.148648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]108.148648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]107.926315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]108.148648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]108.148648648649[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3959&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3959&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean108.6356164383561.2551027807898186.5551555626334
Geometric Mean108.112481811640
Harmonic Mean107.588923139812
Quadratic Mean109.156390258411
Winsorized Mean ( 1 / 24 )108.5972602739731.2356281449090687.888302578253
Winsorized Mean ( 2 / 24 )108.5890410958901.2290768857294488.3500799312845
Winsorized Mean ( 3 / 24 )108.7328767123291.1952930497852890.9675470227668
Winsorized Mean ( 4 / 24 )108.8863013698631.1656132149762693.415465757293
Winsorized Mean ( 5 / 24 )108.8315068493151.1416810429923995.3256669341408
Winsorized Mean ( 6 / 24 )108.6178082191781.1012538558591998.63103556122
Winsorized Mean ( 7 / 24 )108.6465753424661.0900286295371999.6731392170819
Winsorized Mean ( 8 / 24 )108.6356164383561.07709014153632100.860282950323
Winsorized Mean ( 9 / 24 )108.6479452054791.06698074283933101.827465898174
Winsorized Mean ( 10 / 24 )108.5931506849321.05313970094545103.113718519435
Winsorized Mean ( 11 / 24 )108.6835616438361.03917009259766104.586883723871
Winsorized Mean ( 12 / 24 )108.6506849315070.971572975126267111.829669734676
Winsorized Mean ( 13 / 24 )108.5438356164380.94905822561444114.37004884096
Winsorized Mean ( 14 / 24 )108.5821917808220.937728850740169115.792738695323
Winsorized Mean ( 15 / 24 )108.5205479452050.92809390209802116.928413924375
Winsorized Mean ( 16 / 24 )108.6082191780820.915592466122766118.620699925593
Winsorized Mean ( 17 / 24 )108.4452054794520.863164775015517125.636736598180
Winsorized Mean ( 18 / 24 )108.3712328767120.81658857014542132.712159879256
Winsorized Mean ( 19 / 24 )108.3191780821920.764879437416958141.616015261166
Winsorized Mean ( 20 / 24 )108.2095890410960.74932786824136144.408867769804
Winsorized Mean ( 21 / 24 )108.1808219178080.713518244965719151.616055624486
Winsorized Mean ( 22 / 24 )108.0301369863010.692849664815285155.921468209272
Winsorized Mean ( 23 / 24 )108.0301369863010.641697606238332168.350537599135
Winsorized Mean ( 24 / 24 )107.9643835616440.624162665468132172.974754074194
Trimmed Mean ( 1 / 24 )108.6197183098591.2069010480198989.9988598800762
Trimmed Mean ( 2 / 24 )108.6434782608701.1728210797045992.6343157885894
Trimmed Mean ( 3 / 24 )108.6731343283581.1364138212319895.6281350138333
Trimmed Mean ( 4 / 24 )108.6507692307691.1084316776525698.022071564095
Trimmed Mean ( 5 / 24 )108.5825396825401.08547298965830100.032465770264
Trimmed Mean ( 6 / 24 )108.5229508196721.06501851863789101.897712500312
Trimmed Mean ( 7 / 24 )108.5033898305081.05111881641825103.226569761391
Trimmed Mean ( 8 / 24 )108.4771929824561.03638692305762104.668623820937
Trimmed Mean ( 9 / 24 )108.4509090909091.02076380172114106.244861845656
Trimmed Mean ( 10 / 24 )108.4207547169811.00312414196778108.083087806358
Trimmed Mean ( 11 / 24 )108.3960784313730.983666453848046110.195969383050
Trimmed Mean ( 12 / 24 )108.3571428571430.961654257810272112.677858988403
Trimmed Mean ( 13 / 24 )108.3191489361700.94782792878719114.281448822438
Trimmed Mean ( 14 / 24 )108.2911111111110.93398690440402115.944999443233
Trimmed Mean ( 15 / 24 )108.2558139534880.917398594283154118.00303012027
Trimmed Mean ( 16 / 24 )108.2243902439020.896842567742351120.672673372696
Trimmed Mean ( 17 / 24 )108.1794871794870.871425062471293124.140894998703
Trimmed Mean ( 18 / 24 )108.1486486486490.849356067885771127.330165448578
Trimmed Mean ( 19 / 24 )108.1228571428570.829782655701046130.302623705130
Trimmed Mean ( 20 / 24 )108.10.814452781524708132.72715429571
Trimmed Mean ( 21 / 24 )108.0870967741940.7950754604815135.945708484998
Trimmed Mean ( 22 / 24 )108.0758620689660.775576302052711139.349103090079
Trimmed Mean ( 23 / 24 )108.0814814814810.751011417491994143.914565030742
Trimmed Mean ( 24 / 24 )108.0880.729207789316598148.226611925386
Median107.6
Midrange109.2
Midmean - Weighted Average at Xnp107.902777777778
Midmean - Weighted Average at X(n+1)p108.148648648649
Midmean - Empirical Distribution Function108.148648648649
Midmean - Empirical Distribution Function - Averaging108.148648648649
Midmean - Empirical Distribution Function - Interpolation108.148648648649
Midmean - Closest Observation107.926315789474
Midmean - True Basic - Statistics Graphics Toolkit108.148648648649
Midmean - MS Excel (old versions)108.148648648649
Number of observations73



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')