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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, 17 Aug 2010 09:15:12 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/17/t12820364825g56otrf5co22cm.htm/, Retrieved Sat, 27 Apr 2024 13:03:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79066, Retrieved Sat, 27 Apr 2024 13:03:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsMagali De Reu
Estimated Impact152
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Tijdreeks 2 stap 9] [2010-08-17 09:15:12] [07915b1f88a41fb8d82e27c5eaa7bbed] [Current]
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Dataseries X:
120
119
118
116
114
113
114
116
117
117
118
120
123
125
120
116
111
108
113
112
126
124
124
118
119
122
114
108
104
101
107
104
123
125
134
131
127
124
123
117
112
118
123
124
144
148
152
154
146
132
136
128
120
124
126
121
140
142
142
139
131
117
122
112
98
103
108
102
126
129
126
126
112
99
106
104
90
98
99
91
118
115
119
123




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational 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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79066&T=0

[TABLE]
[ROW][C]Summary of computational 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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79066&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79066&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 computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean119.6428571428571.4238807097910684.025899304734
Geometric Mean118.943826519284
Harmonic Mean118.246085796343
Quadratic Mean120.344050439523
Winsorized Mean ( 1 / 28 )119.6309523809521.4141912254424584.5931937836232
Winsorized Mean ( 2 / 28 )119.7023809523811.3524992019201888.5045852762328
Winsorized Mean ( 3 / 28 )119.6309523809521.3349939202262189.6116083889588
Winsorized Mean ( 4 / 28 )119.5833333333331.3037313867441491.723904593548
Winsorized Mean ( 5 / 28 )119.4642857142861.2776428773420293.5036603990757
Winsorized Mean ( 6 / 28 )119.6071428571431.2510486544660595.6055085708805
Winsorized Mean ( 7 / 28 )119.5238095238101.2011512204115399.5077118456905
Winsorized Mean ( 8 / 28 )119.5238095238101.16526957457629102.571810104344
Winsorized Mean ( 9 / 28 )119.3095238095241.08475803627721109.987222790239
Winsorized Mean ( 10 / 28 )119.0714285714291.04211182193764114.259742634946
Winsorized Mean ( 11 / 28 )118.8095238095240.998633057483388118.972151902252
Winsorized Mean ( 12 / 28 )118.9523809523810.92642483985935128.399386366238
Winsorized Mean ( 13 / 28 )119.1071428571430.900853464323285132.215890346401
Winsorized Mean ( 14 / 28 )118.9404761904760.822857479853207144.545658394810
Winsorized Mean ( 15 / 28 )118.7619047619050.797230405140801148.968107583566
Winsorized Mean ( 16 / 28 )118.5714285714290.771383947201711153.712595396314
Winsorized Mean ( 17 / 28 )118.9761904761900.649368860468916183.218194956679
Winsorized Mean ( 18 / 28 )119.1904761904760.618484672761318192.713710524680
Winsorized Mean ( 19 / 28 )119.1904761904760.618484672761318192.713710524680
Winsorized Mean ( 20 / 28 )119.1904761904760.618484672761318192.713710524680
Winsorized Mean ( 21 / 28 )119.1904761904760.618484672761318192.713710524680
Winsorized Mean ( 22 / 28 )119.1904761904760.548161321970315217.436859211550
Winsorized Mean ( 23 / 28 )119.1904761904760.548161321970315217.436859211550
Winsorized Mean ( 24 / 28 )119.1904761904760.474077353905455251.415671321533
Winsorized Mean ( 25 / 28 )119.1904761904760.474077353905455251.415671321533
Winsorized Mean ( 26 / 28 )119.1904761904760.474077353905455251.415671321533
Winsorized Mean ( 27 / 28 )119.5119047619050.432637923719663276.240010894988
Winsorized Mean ( 28 / 28 )119.8452380952380.391934625060114305.778643764522
Trimmed Mean ( 1 / 28 )119.5853658536591.3483739769314188.6885744604828
Trimmed Mean ( 2 / 28 )119.53751.2708942020423394.057790025246
Trimmed Mean ( 3 / 28 )119.4487179487181.2195880794550897.9418542710654
Trimmed Mean ( 4 / 28 )119.3815789473681.16738831394311102.263811896601
Trimmed Mean ( 5 / 28 )119.3243243243241.11751365412836106.776614212732
Trimmed Mean ( 6 / 28 )119.2916666666671.06690092424724111.811381877688
Trimmed Mean ( 7 / 28 )119.2285714285711.01422010110584117.556900418926
Trimmed Mean ( 8 / 28 )119.1764705882350.964683933025103123.539396177685
Trimmed Mean ( 9 / 28 )119.1212121212120.914150643662062130.308076625113
Trimmed Mean ( 10 / 28 )119.093750.87279164350731136.451524124844
Trimmed Mean ( 11 / 28 )119.0967741935480.832544562250527143.051530925392
Trimmed Mean ( 12 / 28 )119.1333333333330.793143879006846150.203937124887
Trimmed Mean ( 13 / 28 )119.1551724137930.760807084168643156.616801937376
Trimmed Mean ( 14 / 28 )119.1607142857140.726482713889811164.02415640104
Trimmed Mean ( 15 / 28 )119.1851851851850.700441147841237170.157315218437
Trimmed Mean ( 16 / 28 )119.2307692307690.673017665997434177.158454011850
Trimmed Mean ( 17 / 28 )119.30.643491750260297185.394762173318
Trimmed Mean ( 18 / 28 )119.3333333333330.63184782858454188.864039622741
Trimmed Mean ( 19 / 28 )119.3478260869570.622615172826805191.687949950034
Trimmed Mean ( 20 / 28 )119.3636363636360.6100730461679195.654663180753
Trimmed Mean ( 21 / 28 )119.3809523809520.593178783867987201.256274883089
Trimmed Mean ( 22 / 28 )119.40.570424942814228209.317635044030
Trimmed Mean ( 23 / 28 )119.4210526315790.556395096564771214.633546141751
Trimmed Mean ( 24 / 28 )119.4444444444440.536662887363866222.568855154426
Trimmed Mean ( 25 / 28 )119.4705882352940.527725577752965226.387716024672
Trimmed Mean ( 26 / 28 )119.50.513919160204994232.526843234125
Trimmed Mean ( 27 / 28 )119.5333333333330.493016362912649242.453075243086
Trimmed Mean ( 28 / 28 )119.5357142857140.475545197717111251.365621731760
Median119
Midrange122
Midmean - Weighted Average at Xnp119.469387755102
Midmean - Weighted Average at X(n+1)p119.469387755102
Midmean - Empirical Distribution Function119.469387755102
Midmean - Empirical Distribution Function - Averaging119.469387755102
Midmean - Empirical Distribution Function - Interpolation119.469387755102
Midmean - Closest Observation119.469387755102
Midmean - True Basic - Statistics Graphics Toolkit119.469387755102
Midmean - MS Excel (old versions)119.469387755102
Number of observations84

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 119.642857142857 & 1.42388070979106 & 84.025899304734 \tabularnewline
Geometric Mean & 118.943826519284 &  &  \tabularnewline
Harmonic Mean & 118.246085796343 &  &  \tabularnewline
Quadratic Mean & 120.344050439523 &  &  \tabularnewline
Winsorized Mean ( 1 / 28 ) & 119.630952380952 & 1.41419122544245 & 84.5931937836232 \tabularnewline
Winsorized Mean ( 2 / 28 ) & 119.702380952381 & 1.35249920192018 & 88.5045852762328 \tabularnewline
Winsorized Mean ( 3 / 28 ) & 119.630952380952 & 1.33499392022621 & 89.6116083889588 \tabularnewline
Winsorized Mean ( 4 / 28 ) & 119.583333333333 & 1.30373138674414 & 91.723904593548 \tabularnewline
Winsorized Mean ( 5 / 28 ) & 119.464285714286 & 1.27764287734202 & 93.5036603990757 \tabularnewline
Winsorized Mean ( 6 / 28 ) & 119.607142857143 & 1.25104865446605 & 95.6055085708805 \tabularnewline
Winsorized Mean ( 7 / 28 ) & 119.523809523810 & 1.20115122041153 & 99.5077118456905 \tabularnewline
Winsorized Mean ( 8 / 28 ) & 119.523809523810 & 1.16526957457629 & 102.571810104344 \tabularnewline
Winsorized Mean ( 9 / 28 ) & 119.309523809524 & 1.08475803627721 & 109.987222790239 \tabularnewline
Winsorized Mean ( 10 / 28 ) & 119.071428571429 & 1.04211182193764 & 114.259742634946 \tabularnewline
Winsorized Mean ( 11 / 28 ) & 118.809523809524 & 0.998633057483388 & 118.972151902252 \tabularnewline
Winsorized Mean ( 12 / 28 ) & 118.952380952381 & 0.92642483985935 & 128.399386366238 \tabularnewline
Winsorized Mean ( 13 / 28 ) & 119.107142857143 & 0.900853464323285 & 132.215890346401 \tabularnewline
Winsorized Mean ( 14 / 28 ) & 118.940476190476 & 0.822857479853207 & 144.545658394810 \tabularnewline
Winsorized Mean ( 15 / 28 ) & 118.761904761905 & 0.797230405140801 & 148.968107583566 \tabularnewline
Winsorized Mean ( 16 / 28 ) & 118.571428571429 & 0.771383947201711 & 153.712595396314 \tabularnewline
Winsorized Mean ( 17 / 28 ) & 118.976190476190 & 0.649368860468916 & 183.218194956679 \tabularnewline
Winsorized Mean ( 18 / 28 ) & 119.190476190476 & 0.618484672761318 & 192.713710524680 \tabularnewline
Winsorized Mean ( 19 / 28 ) & 119.190476190476 & 0.618484672761318 & 192.713710524680 \tabularnewline
Winsorized Mean ( 20 / 28 ) & 119.190476190476 & 0.618484672761318 & 192.713710524680 \tabularnewline
Winsorized Mean ( 21 / 28 ) & 119.190476190476 & 0.618484672761318 & 192.713710524680 \tabularnewline
Winsorized Mean ( 22 / 28 ) & 119.190476190476 & 0.548161321970315 & 217.436859211550 \tabularnewline
Winsorized Mean ( 23 / 28 ) & 119.190476190476 & 0.548161321970315 & 217.436859211550 \tabularnewline
Winsorized Mean ( 24 / 28 ) & 119.190476190476 & 0.474077353905455 & 251.415671321533 \tabularnewline
Winsorized Mean ( 25 / 28 ) & 119.190476190476 & 0.474077353905455 & 251.415671321533 \tabularnewline
Winsorized Mean ( 26 / 28 ) & 119.190476190476 & 0.474077353905455 & 251.415671321533 \tabularnewline
Winsorized Mean ( 27 / 28 ) & 119.511904761905 & 0.432637923719663 & 276.240010894988 \tabularnewline
Winsorized Mean ( 28 / 28 ) & 119.845238095238 & 0.391934625060114 & 305.778643764522 \tabularnewline
Trimmed Mean ( 1 / 28 ) & 119.585365853659 & 1.34837397693141 & 88.6885744604828 \tabularnewline
Trimmed Mean ( 2 / 28 ) & 119.5375 & 1.27089420204233 & 94.057790025246 \tabularnewline
Trimmed Mean ( 3 / 28 ) & 119.448717948718 & 1.21958807945508 & 97.9418542710654 \tabularnewline
Trimmed Mean ( 4 / 28 ) & 119.381578947368 & 1.16738831394311 & 102.263811896601 \tabularnewline
Trimmed Mean ( 5 / 28 ) & 119.324324324324 & 1.11751365412836 & 106.776614212732 \tabularnewline
Trimmed Mean ( 6 / 28 ) & 119.291666666667 & 1.06690092424724 & 111.811381877688 \tabularnewline
Trimmed Mean ( 7 / 28 ) & 119.228571428571 & 1.01422010110584 & 117.556900418926 \tabularnewline
Trimmed Mean ( 8 / 28 ) & 119.176470588235 & 0.964683933025103 & 123.539396177685 \tabularnewline
Trimmed Mean ( 9 / 28 ) & 119.121212121212 & 0.914150643662062 & 130.308076625113 \tabularnewline
Trimmed Mean ( 10 / 28 ) & 119.09375 & 0.87279164350731 & 136.451524124844 \tabularnewline
Trimmed Mean ( 11 / 28 ) & 119.096774193548 & 0.832544562250527 & 143.051530925392 \tabularnewline
Trimmed Mean ( 12 / 28 ) & 119.133333333333 & 0.793143879006846 & 150.203937124887 \tabularnewline
Trimmed Mean ( 13 / 28 ) & 119.155172413793 & 0.760807084168643 & 156.616801937376 \tabularnewline
Trimmed Mean ( 14 / 28 ) & 119.160714285714 & 0.726482713889811 & 164.02415640104 \tabularnewline
Trimmed Mean ( 15 / 28 ) & 119.185185185185 & 0.700441147841237 & 170.157315218437 \tabularnewline
Trimmed Mean ( 16 / 28 ) & 119.230769230769 & 0.673017665997434 & 177.158454011850 \tabularnewline
Trimmed Mean ( 17 / 28 ) & 119.3 & 0.643491750260297 & 185.394762173318 \tabularnewline
Trimmed Mean ( 18 / 28 ) & 119.333333333333 & 0.63184782858454 & 188.864039622741 \tabularnewline
Trimmed Mean ( 19 / 28 ) & 119.347826086957 & 0.622615172826805 & 191.687949950034 \tabularnewline
Trimmed Mean ( 20 / 28 ) & 119.363636363636 & 0.6100730461679 & 195.654663180753 \tabularnewline
Trimmed Mean ( 21 / 28 ) & 119.380952380952 & 0.593178783867987 & 201.256274883089 \tabularnewline
Trimmed Mean ( 22 / 28 ) & 119.4 & 0.570424942814228 & 209.317635044030 \tabularnewline
Trimmed Mean ( 23 / 28 ) & 119.421052631579 & 0.556395096564771 & 214.633546141751 \tabularnewline
Trimmed Mean ( 24 / 28 ) & 119.444444444444 & 0.536662887363866 & 222.568855154426 \tabularnewline
Trimmed Mean ( 25 / 28 ) & 119.470588235294 & 0.527725577752965 & 226.387716024672 \tabularnewline
Trimmed Mean ( 26 / 28 ) & 119.5 & 0.513919160204994 & 232.526843234125 \tabularnewline
Trimmed Mean ( 27 / 28 ) & 119.533333333333 & 0.493016362912649 & 242.453075243086 \tabularnewline
Trimmed Mean ( 28 / 28 ) & 119.535714285714 & 0.475545197717111 & 251.365621731760 \tabularnewline
Median & 119 &  &  \tabularnewline
Midrange & 122 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 119.469387755102 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 119.469387755102 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 119.469387755102 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 119.469387755102 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 119.469387755102 &  &  \tabularnewline
Midmean - Closest Observation & 119.469387755102 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 119.469387755102 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 119.469387755102 &  &  \tabularnewline
Number of observations & 84 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79066&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]119.642857142857[/C][C]1.42388070979106[/C][C]84.025899304734[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]118.943826519284[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]118.246085796343[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]120.344050439523[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 28 )[/C][C]119.630952380952[/C][C]1.41419122544245[/C][C]84.5931937836232[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 28 )[/C][C]119.702380952381[/C][C]1.35249920192018[/C][C]88.5045852762328[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 28 )[/C][C]119.630952380952[/C][C]1.33499392022621[/C][C]89.6116083889588[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 28 )[/C][C]119.583333333333[/C][C]1.30373138674414[/C][C]91.723904593548[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 28 )[/C][C]119.464285714286[/C][C]1.27764287734202[/C][C]93.5036603990757[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 28 )[/C][C]119.607142857143[/C][C]1.25104865446605[/C][C]95.6055085708805[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 28 )[/C][C]119.523809523810[/C][C]1.20115122041153[/C][C]99.5077118456905[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 28 )[/C][C]119.523809523810[/C][C]1.16526957457629[/C][C]102.571810104344[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 28 )[/C][C]119.309523809524[/C][C]1.08475803627721[/C][C]109.987222790239[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 28 )[/C][C]119.071428571429[/C][C]1.04211182193764[/C][C]114.259742634946[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 28 )[/C][C]118.809523809524[/C][C]0.998633057483388[/C][C]118.972151902252[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 28 )[/C][C]118.952380952381[/C][C]0.92642483985935[/C][C]128.399386366238[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 28 )[/C][C]119.107142857143[/C][C]0.900853464323285[/C][C]132.215890346401[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 28 )[/C][C]118.940476190476[/C][C]0.822857479853207[/C][C]144.545658394810[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 28 )[/C][C]118.761904761905[/C][C]0.797230405140801[/C][C]148.968107583566[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 28 )[/C][C]118.571428571429[/C][C]0.771383947201711[/C][C]153.712595396314[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 28 )[/C][C]118.976190476190[/C][C]0.649368860468916[/C][C]183.218194956679[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 28 )[/C][C]119.190476190476[/C][C]0.618484672761318[/C][C]192.713710524680[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 28 )[/C][C]119.190476190476[/C][C]0.618484672761318[/C][C]192.713710524680[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 28 )[/C][C]119.190476190476[/C][C]0.618484672761318[/C][C]192.713710524680[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 28 )[/C][C]119.190476190476[/C][C]0.618484672761318[/C][C]192.713710524680[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 28 )[/C][C]119.190476190476[/C][C]0.548161321970315[/C][C]217.436859211550[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 28 )[/C][C]119.190476190476[/C][C]0.548161321970315[/C][C]217.436859211550[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 28 )[/C][C]119.190476190476[/C][C]0.474077353905455[/C][C]251.415671321533[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 28 )[/C][C]119.190476190476[/C][C]0.474077353905455[/C][C]251.415671321533[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 28 )[/C][C]119.190476190476[/C][C]0.474077353905455[/C][C]251.415671321533[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 28 )[/C][C]119.511904761905[/C][C]0.432637923719663[/C][C]276.240010894988[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 28 )[/C][C]119.845238095238[/C][C]0.391934625060114[/C][C]305.778643764522[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 28 )[/C][C]119.585365853659[/C][C]1.34837397693141[/C][C]88.6885744604828[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 28 )[/C][C]119.5375[/C][C]1.27089420204233[/C][C]94.057790025246[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 28 )[/C][C]119.448717948718[/C][C]1.21958807945508[/C][C]97.9418542710654[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 28 )[/C][C]119.381578947368[/C][C]1.16738831394311[/C][C]102.263811896601[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 28 )[/C][C]119.324324324324[/C][C]1.11751365412836[/C][C]106.776614212732[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 28 )[/C][C]119.291666666667[/C][C]1.06690092424724[/C][C]111.811381877688[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 28 )[/C][C]119.228571428571[/C][C]1.01422010110584[/C][C]117.556900418926[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 28 )[/C][C]119.176470588235[/C][C]0.964683933025103[/C][C]123.539396177685[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 28 )[/C][C]119.121212121212[/C][C]0.914150643662062[/C][C]130.308076625113[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 28 )[/C][C]119.09375[/C][C]0.87279164350731[/C][C]136.451524124844[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 28 )[/C][C]119.096774193548[/C][C]0.832544562250527[/C][C]143.051530925392[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 28 )[/C][C]119.133333333333[/C][C]0.793143879006846[/C][C]150.203937124887[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 28 )[/C][C]119.155172413793[/C][C]0.760807084168643[/C][C]156.616801937376[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 28 )[/C][C]119.160714285714[/C][C]0.726482713889811[/C][C]164.02415640104[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 28 )[/C][C]119.185185185185[/C][C]0.700441147841237[/C][C]170.157315218437[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 28 )[/C][C]119.230769230769[/C][C]0.673017665997434[/C][C]177.158454011850[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 28 )[/C][C]119.3[/C][C]0.643491750260297[/C][C]185.394762173318[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 28 )[/C][C]119.333333333333[/C][C]0.63184782858454[/C][C]188.864039622741[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 28 )[/C][C]119.347826086957[/C][C]0.622615172826805[/C][C]191.687949950034[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 28 )[/C][C]119.363636363636[/C][C]0.6100730461679[/C][C]195.654663180753[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 28 )[/C][C]119.380952380952[/C][C]0.593178783867987[/C][C]201.256274883089[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 28 )[/C][C]119.4[/C][C]0.570424942814228[/C][C]209.317635044030[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 28 )[/C][C]119.421052631579[/C][C]0.556395096564771[/C][C]214.633546141751[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 28 )[/C][C]119.444444444444[/C][C]0.536662887363866[/C][C]222.568855154426[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 28 )[/C][C]119.470588235294[/C][C]0.527725577752965[/C][C]226.387716024672[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 28 )[/C][C]119.5[/C][C]0.513919160204994[/C][C]232.526843234125[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 28 )[/C][C]119.533333333333[/C][C]0.493016362912649[/C][C]242.453075243086[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 28 )[/C][C]119.535714285714[/C][C]0.475545197717111[/C][C]251.365621731760[/C][/ROW]
[ROW][C]Median[/C][C]119[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]122[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]119.469387755102[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]119.469387755102[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]119.469387755102[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]119.469387755102[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]119.469387755102[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]119.469387755102[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]119.469387755102[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]119.469387755102[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]84[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79066&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79066&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 Mean119.6428571428571.4238807097910684.025899304734
Geometric Mean118.943826519284
Harmonic Mean118.246085796343
Quadratic Mean120.344050439523
Winsorized Mean ( 1 / 28 )119.6309523809521.4141912254424584.5931937836232
Winsorized Mean ( 2 / 28 )119.7023809523811.3524992019201888.5045852762328
Winsorized Mean ( 3 / 28 )119.6309523809521.3349939202262189.6116083889588
Winsorized Mean ( 4 / 28 )119.5833333333331.3037313867441491.723904593548
Winsorized Mean ( 5 / 28 )119.4642857142861.2776428773420293.5036603990757
Winsorized Mean ( 6 / 28 )119.6071428571431.2510486544660595.6055085708805
Winsorized Mean ( 7 / 28 )119.5238095238101.2011512204115399.5077118456905
Winsorized Mean ( 8 / 28 )119.5238095238101.16526957457629102.571810104344
Winsorized Mean ( 9 / 28 )119.3095238095241.08475803627721109.987222790239
Winsorized Mean ( 10 / 28 )119.0714285714291.04211182193764114.259742634946
Winsorized Mean ( 11 / 28 )118.8095238095240.998633057483388118.972151902252
Winsorized Mean ( 12 / 28 )118.9523809523810.92642483985935128.399386366238
Winsorized Mean ( 13 / 28 )119.1071428571430.900853464323285132.215890346401
Winsorized Mean ( 14 / 28 )118.9404761904760.822857479853207144.545658394810
Winsorized Mean ( 15 / 28 )118.7619047619050.797230405140801148.968107583566
Winsorized Mean ( 16 / 28 )118.5714285714290.771383947201711153.712595396314
Winsorized Mean ( 17 / 28 )118.9761904761900.649368860468916183.218194956679
Winsorized Mean ( 18 / 28 )119.1904761904760.618484672761318192.713710524680
Winsorized Mean ( 19 / 28 )119.1904761904760.618484672761318192.713710524680
Winsorized Mean ( 20 / 28 )119.1904761904760.618484672761318192.713710524680
Winsorized Mean ( 21 / 28 )119.1904761904760.618484672761318192.713710524680
Winsorized Mean ( 22 / 28 )119.1904761904760.548161321970315217.436859211550
Winsorized Mean ( 23 / 28 )119.1904761904760.548161321970315217.436859211550
Winsorized Mean ( 24 / 28 )119.1904761904760.474077353905455251.415671321533
Winsorized Mean ( 25 / 28 )119.1904761904760.474077353905455251.415671321533
Winsorized Mean ( 26 / 28 )119.1904761904760.474077353905455251.415671321533
Winsorized Mean ( 27 / 28 )119.5119047619050.432637923719663276.240010894988
Winsorized Mean ( 28 / 28 )119.8452380952380.391934625060114305.778643764522
Trimmed Mean ( 1 / 28 )119.5853658536591.3483739769314188.6885744604828
Trimmed Mean ( 2 / 28 )119.53751.2708942020423394.057790025246
Trimmed Mean ( 3 / 28 )119.4487179487181.2195880794550897.9418542710654
Trimmed Mean ( 4 / 28 )119.3815789473681.16738831394311102.263811896601
Trimmed Mean ( 5 / 28 )119.3243243243241.11751365412836106.776614212732
Trimmed Mean ( 6 / 28 )119.2916666666671.06690092424724111.811381877688
Trimmed Mean ( 7 / 28 )119.2285714285711.01422010110584117.556900418926
Trimmed Mean ( 8 / 28 )119.1764705882350.964683933025103123.539396177685
Trimmed Mean ( 9 / 28 )119.1212121212120.914150643662062130.308076625113
Trimmed Mean ( 10 / 28 )119.093750.87279164350731136.451524124844
Trimmed Mean ( 11 / 28 )119.0967741935480.832544562250527143.051530925392
Trimmed Mean ( 12 / 28 )119.1333333333330.793143879006846150.203937124887
Trimmed Mean ( 13 / 28 )119.1551724137930.760807084168643156.616801937376
Trimmed Mean ( 14 / 28 )119.1607142857140.726482713889811164.02415640104
Trimmed Mean ( 15 / 28 )119.1851851851850.700441147841237170.157315218437
Trimmed Mean ( 16 / 28 )119.2307692307690.673017665997434177.158454011850
Trimmed Mean ( 17 / 28 )119.30.643491750260297185.394762173318
Trimmed Mean ( 18 / 28 )119.3333333333330.63184782858454188.864039622741
Trimmed Mean ( 19 / 28 )119.3478260869570.622615172826805191.687949950034
Trimmed Mean ( 20 / 28 )119.3636363636360.6100730461679195.654663180753
Trimmed Mean ( 21 / 28 )119.3809523809520.593178783867987201.256274883089
Trimmed Mean ( 22 / 28 )119.40.570424942814228209.317635044030
Trimmed Mean ( 23 / 28 )119.4210526315790.556395096564771214.633546141751
Trimmed Mean ( 24 / 28 )119.4444444444440.536662887363866222.568855154426
Trimmed Mean ( 25 / 28 )119.4705882352940.527725577752965226.387716024672
Trimmed Mean ( 26 / 28 )119.50.513919160204994232.526843234125
Trimmed Mean ( 27 / 28 )119.5333333333330.493016362912649242.453075243086
Trimmed Mean ( 28 / 28 )119.5357142857140.475545197717111251.365621731760
Median119
Midrange122
Midmean - Weighted Average at Xnp119.469387755102
Midmean - Weighted Average at X(n+1)p119.469387755102
Midmean - Empirical Distribution Function119.469387755102
Midmean - Empirical Distribution Function - Averaging119.469387755102
Midmean - Empirical Distribution Function - Interpolation119.469387755102
Midmean - Closest Observation119.469387755102
Midmean - True Basic - Statistics Graphics Toolkit119.469387755102
Midmean - MS Excel (old versions)119.469387755102
Number of observations84



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')