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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 18 Oct 2011 13:52:48 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/18/t13189604065bmg5drtplf2ntx.htm/, Retrieved Thu, 16 May 2024 23:22:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=132418, Retrieved Thu, 16 May 2024 23:22:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact51
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2011-10-18 17:52:48] [860f1af8dde2fbc4c0f468abef92388b] [Current]
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Dataseries X:
99,1
99,7
100,1
100,2
100,1
100,4
99,8
99,7
99,4
100,2
100,5
100,6
100,9
101,9
102,1
102,6
103,5
103,9
103,7
103
103,1
103,2
103,2
103,1
103,7
104,2
104,4
104,9
105,4
105,9
105,5
106,1
105,4
105,7
106,2
106,7
106,8
106,8
106,8
107,3
107,3
107,5
107,4
106,9
108,1
108,6
108,2
108,3
108,3
109,3
109,2
109,4
109,7
109,6
109,3
108,4
108,7
109,4
109
110,3
109,5
109,7
109,5
110,9
110,9
110,4
111,1
110,8
111,3
111,7
112,2
111,7
111,3
111,9
111,7
111,8
111,5
112,9
112
112,4
111,1
111,7
111,4
112,2
112,5
113,2
114,7
115,2
114,1
113,7
115,5
115
115,4
115
114,6
114,6
114,5
115,2
116,3
116,5
118,4
118,5
118,7
119,2
119,5
118,5
118,6
118,2
118,6
120,6
124,5
124,6
126,5
126
126,3
126,3
125,1
126,7
123,9
123,6
124,9
126,2
126,3
126,4
126,2
125,8
124,9
126,2
125,9
124,6
122,9
119,9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net

\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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132418&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=132418&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132418&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean111.7333333333330.6858637272488162.908940791385
Geometric Mean111.461872122165
Harmonic Mean111.194892544593
Quadratic Mean112.008755745416
Winsorized Mean ( 1 / 44 )111.7340909090910.685297017878206163.044764524203
Winsorized Mean ( 2 / 44 )111.7371212121210.684431145343999163.255459621086
Winsorized Mean ( 3 / 44 )111.7348484848480.684060606798406163.340568619787
Winsorized Mean ( 4 / 44 )111.7378787878790.683655157683761163.441872019878
Winsorized Mean ( 5 / 44 )111.7492424242420.682157095067082163.817459691236
Winsorized Mean ( 6 / 44 )111.7446969696970.681418994742553163.988233130947
Winsorized Mean ( 7 / 44 )111.750.680729680894076164.162079510367
Winsorized Mean ( 8 / 44 )111.750.680729680894076164.162079510367
Winsorized Mean ( 9 / 44 )111.750.676772951955623165.121847256283
Winsorized Mean ( 10 / 44 )111.750.674590459288543165.656063558707
Winsorized Mean ( 11 / 44 )111.750.672200459867879166.245051397264
Winsorized Mean ( 12 / 44 )111.7136363636360.658751098917733169.583984827003
Winsorized Mean ( 13 / 44 )111.7924242424240.643741216732286173.660504153978
Winsorized Mean ( 14 / 44 )111.8136363636360.641270653317668174.362627987355
Winsorized Mean ( 15 / 44 )111.8363636363640.629509200013975177.656440340953
Winsorized Mean ( 16 / 44 )111.8848484848480.624159379027908179.25685689303
Winsorized Mean ( 17 / 44 )111.8848484848480.620763676483097180.237428063971
Winsorized Mean ( 18 / 44 )111.803030303030.608204887013433183.824616819564
Winsorized Mean ( 19 / 44 )111.7742424242420.600107574992908186.257009712906
Winsorized Mean ( 20 / 44 )111.6681818181820.584346779855687191.099165200773
Winsorized Mean ( 21 / 44 )111.350.527547299428589211.071121244689
Winsorized Mean ( 22 / 44 )111.2666666666670.508386373193726218.86240964265
Winsorized Mean ( 23 / 44 )111.196969696970.499445609136937222.640799443853
Winsorized Mean ( 24 / 44 )111.1787878787880.488413083527461227.632697870873
Winsorized Mean ( 25 / 44 )111.1409090909090.470231035868518236.353835908835
Winsorized Mean ( 26 / 44 )111.1606060606060.463402413537372239.879212566167
Winsorized Mean ( 27 / 44 )111.2628787878790.452212548852433246.041112901947
Winsorized Mean ( 28 / 44 )111.3477272727270.438386873682094253.994209127424
Winsorized Mean ( 29 / 44 )111.3477272727270.438386873682094253.994209127424
Winsorized Mean ( 30 / 44 )111.3477272727270.433211604874116257.028496051215
Winsorized Mean ( 31 / 44 )111.3477272727270.422569749328744263.501415919157
Winsorized Mean ( 32 / 44 )110.9840909090910.368352217231943301.298826821523
Winsorized Mean ( 33 / 44 )110.9840909090910.357413520508078310.520124564181
Winsorized Mean ( 34 / 44 )110.8037878787880.331858416266208333.888738231982
Winsorized Mean ( 35 / 44 )110.9098484848480.315199909483387351.871447763515
Winsorized Mean ( 36 / 44 )110.8825757575760.306524578008963361.741223094787
Winsorized Mean ( 37 / 44 )110.8825757575760.306524578008963361.741223094787
Winsorized Mean ( 38 / 44 )110.8250.300374457874378368.956138229133
Winsorized Mean ( 39 / 44 )110.8545454545450.297363625296161372.791209227892
Winsorized Mean ( 40 / 44 )110.8848484848480.27554434768585402.421060043914
Winsorized Mean ( 41 / 44 )110.8537878787880.27227166399288407.144049634511
Winsorized Mean ( 42 / 44 )110.8856060606060.269113512394866412.040276513152
Winsorized Mean ( 43 / 44 )110.8856060606060.262470893434399422.468200605719
Winsorized Mean ( 44 / 44 )110.9522727272730.229095885418269484.304956087287
Trimmed Mean ( 1 / 44 )111.7153846153850.679834296639009164.327373843431
Trimmed Mean ( 2 / 44 )111.696093750.673801796637013165.769955359992
Trimmed Mean ( 3 / 44 )111.6746031746030.66762781810088167.270745985796
Trimmed Mean ( 4 / 44 )111.6532258064520.660946911785772168.929189039983
Trimmed Mean ( 5 / 44 )111.6303278688520.653679557805242170.772248475471
Trimmed Mean ( 6 / 44 )111.6041666666670.64601384483752172.758165414762
Trimmed Mean ( 7 / 44 )111.5779661016950.637682788562123174.974090728223
Trimmed Mean ( 8 / 44 )111.550.628574337013073177.46508794819
Trimmed Mean ( 9 / 44 )111.5210526315790.618453572826847180.322432485651
Trimmed Mean ( 10 / 44 )111.4910714285710.607873524113575183.411625948263
Trimmed Mean ( 11 / 44 )111.460.596432541433145186.877798002398
Trimmed Mean ( 12 / 44 )111.4277777777780.584021746782906190.793884631145
Trimmed Mean ( 13 / 44 )111.3981132075470.572166609623587194.695236201974
Trimmed Mean ( 14 / 44 )111.3596153846150.560976622313149198.510260419466
Trimmed Mean ( 15 / 44 )111.3176470588240.548709524991464202.871723541805
Trimmed Mean ( 16 / 44 )111.2720.536460679459418207.418743368343
Trimmed Mean ( 17 / 44 )111.2204081632650.523264685773261212.550954014617
Trimmed Mean ( 18 / 44 )111.1666666666670.50872145091384218.52168110264
Trimmed Mean ( 19 / 44 )111.1170212765960.493934007435586224.963293889187
Trimmed Mean ( 20 / 44 )111.0673913043480.478149174725937232.28606714214
Trimmed Mean ( 21 / 44 )111.0233333333330.462309919775249240.149147972657
Trimmed Mean ( 22 / 44 )1110.451923209463542245.616949241804
Trimmed Mean ( 23 / 44 )110.9813953488370.442460820459091250.8276218303
Trimmed Mean ( 24 / 44 )110.9666666666670.432720560607403256.439551915224
Trimmed Mean ( 25 / 44 )110.952439024390.422875067986787262.376402450515
Trimmed Mean ( 26 / 44 )110.940.413787690929246268.108506927457
Trimmed Mean ( 27 / 44 )110.9256410256410.404076941703726274.516136847455
Trimmed Mean ( 28 / 44 )110.9039473684210.39412546221104281.392495542539
Trimmed Mean ( 29 / 44 )110.8756756756760.384192517432321288.594052837605
Trimmed Mean ( 30 / 44 )110.8458333333330.372462397404675297.60274891025
Trimmed Mean ( 31 / 44 )110.8142857142860.359279735614943308.434555944593
Trimmed Mean ( 32 / 44 )110.7808823529410.345129522027831320.983501214388
Trimmed Mean ( 33 / 44 )110.7681818181820.336630493274016329.049756428385
Trimmed Mean ( 34 / 44 )110.75468750.327984841097242337.682336566168
Trimmed Mean ( 35 / 44 )110.7516129032260.321318525115105344.678579809712
Trimmed Mean ( 36 / 44 )110.7416666666670.315532834849518350.967171830091
Trimmed Mean ( 37 / 44 )110.732758620690.309668635527736357.58467573566
Trimmed Mean ( 38 / 44 )110.7232142857140.302371482535696366.182727806161
Trimmed Mean ( 39 / 44 )110.7166666666670.294317839954434376.180617130813
Trimmed Mean ( 40 / 44 )110.7076923076920.284727465600027388.81985647008
Trimmed Mean ( 41 / 44 )110.6960.27659681111388400.207072360008
Trimmed Mean ( 42 / 44 )110.6854166666670.266860350484587414.76905979354
Trimmed Mean ( 43 / 44 )110.6717391304350.254935116183624434.117279671743
Trimmed Mean ( 44 / 44 )110.6568181818180.240910836086064459.326861255368
Median110.9
Midrange112.9
Midmean - Weighted Average at Xnp110.69552238806
Midmean - Weighted Average at X(n+1)p110.768181818182
Midmean - Empirical Distribution Function110.69552238806
Midmean - Empirical Distribution Function - Averaging110.768181818182
Midmean - Empirical Distribution Function - Interpolation110.768181818182
Midmean - Closest Observation110.69552238806
Midmean - True Basic - Statistics Graphics Toolkit110.768181818182
Midmean - MS Excel (old versions)110.780882352941
Number of observations132

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 111.733333333333 & 0.6858637272488 & 162.908940791385 \tabularnewline
Geometric Mean & 111.461872122165 &  &  \tabularnewline
Harmonic Mean & 111.194892544593 &  &  \tabularnewline
Quadratic Mean & 112.008755745416 &  &  \tabularnewline
Winsorized Mean ( 1 / 44 ) & 111.734090909091 & 0.685297017878206 & 163.044764524203 \tabularnewline
Winsorized Mean ( 2 / 44 ) & 111.737121212121 & 0.684431145343999 & 163.255459621086 \tabularnewline
Winsorized Mean ( 3 / 44 ) & 111.734848484848 & 0.684060606798406 & 163.340568619787 \tabularnewline
Winsorized Mean ( 4 / 44 ) & 111.737878787879 & 0.683655157683761 & 163.441872019878 \tabularnewline
Winsorized Mean ( 5 / 44 ) & 111.749242424242 & 0.682157095067082 & 163.817459691236 \tabularnewline
Winsorized Mean ( 6 / 44 ) & 111.744696969697 & 0.681418994742553 & 163.988233130947 \tabularnewline
Winsorized Mean ( 7 / 44 ) & 111.75 & 0.680729680894076 & 164.162079510367 \tabularnewline
Winsorized Mean ( 8 / 44 ) & 111.75 & 0.680729680894076 & 164.162079510367 \tabularnewline
Winsorized Mean ( 9 / 44 ) & 111.75 & 0.676772951955623 & 165.121847256283 \tabularnewline
Winsorized Mean ( 10 / 44 ) & 111.75 & 0.674590459288543 & 165.656063558707 \tabularnewline
Winsorized Mean ( 11 / 44 ) & 111.75 & 0.672200459867879 & 166.245051397264 \tabularnewline
Winsorized Mean ( 12 / 44 ) & 111.713636363636 & 0.658751098917733 & 169.583984827003 \tabularnewline
Winsorized Mean ( 13 / 44 ) & 111.792424242424 & 0.643741216732286 & 173.660504153978 \tabularnewline
Winsorized Mean ( 14 / 44 ) & 111.813636363636 & 0.641270653317668 & 174.362627987355 \tabularnewline
Winsorized Mean ( 15 / 44 ) & 111.836363636364 & 0.629509200013975 & 177.656440340953 \tabularnewline
Winsorized Mean ( 16 / 44 ) & 111.884848484848 & 0.624159379027908 & 179.25685689303 \tabularnewline
Winsorized Mean ( 17 / 44 ) & 111.884848484848 & 0.620763676483097 & 180.237428063971 \tabularnewline
Winsorized Mean ( 18 / 44 ) & 111.80303030303 & 0.608204887013433 & 183.824616819564 \tabularnewline
Winsorized Mean ( 19 / 44 ) & 111.774242424242 & 0.600107574992908 & 186.257009712906 \tabularnewline
Winsorized Mean ( 20 / 44 ) & 111.668181818182 & 0.584346779855687 & 191.099165200773 \tabularnewline
Winsorized Mean ( 21 / 44 ) & 111.35 & 0.527547299428589 & 211.071121244689 \tabularnewline
Winsorized Mean ( 22 / 44 ) & 111.266666666667 & 0.508386373193726 & 218.86240964265 \tabularnewline
Winsorized Mean ( 23 / 44 ) & 111.19696969697 & 0.499445609136937 & 222.640799443853 \tabularnewline
Winsorized Mean ( 24 / 44 ) & 111.178787878788 & 0.488413083527461 & 227.632697870873 \tabularnewline
Winsorized Mean ( 25 / 44 ) & 111.140909090909 & 0.470231035868518 & 236.353835908835 \tabularnewline
Winsorized Mean ( 26 / 44 ) & 111.160606060606 & 0.463402413537372 & 239.879212566167 \tabularnewline
Winsorized Mean ( 27 / 44 ) & 111.262878787879 & 0.452212548852433 & 246.041112901947 \tabularnewline
Winsorized Mean ( 28 / 44 ) & 111.347727272727 & 0.438386873682094 & 253.994209127424 \tabularnewline
Winsorized Mean ( 29 / 44 ) & 111.347727272727 & 0.438386873682094 & 253.994209127424 \tabularnewline
Winsorized Mean ( 30 / 44 ) & 111.347727272727 & 0.433211604874116 & 257.028496051215 \tabularnewline
Winsorized Mean ( 31 / 44 ) & 111.347727272727 & 0.422569749328744 & 263.501415919157 \tabularnewline
Winsorized Mean ( 32 / 44 ) & 110.984090909091 & 0.368352217231943 & 301.298826821523 \tabularnewline
Winsorized Mean ( 33 / 44 ) & 110.984090909091 & 0.357413520508078 & 310.520124564181 \tabularnewline
Winsorized Mean ( 34 / 44 ) & 110.803787878788 & 0.331858416266208 & 333.888738231982 \tabularnewline
Winsorized Mean ( 35 / 44 ) & 110.909848484848 & 0.315199909483387 & 351.871447763515 \tabularnewline
Winsorized Mean ( 36 / 44 ) & 110.882575757576 & 0.306524578008963 & 361.741223094787 \tabularnewline
Winsorized Mean ( 37 / 44 ) & 110.882575757576 & 0.306524578008963 & 361.741223094787 \tabularnewline
Winsorized Mean ( 38 / 44 ) & 110.825 & 0.300374457874378 & 368.956138229133 \tabularnewline
Winsorized Mean ( 39 / 44 ) & 110.854545454545 & 0.297363625296161 & 372.791209227892 \tabularnewline
Winsorized Mean ( 40 / 44 ) & 110.884848484848 & 0.27554434768585 & 402.421060043914 \tabularnewline
Winsorized Mean ( 41 / 44 ) & 110.853787878788 & 0.27227166399288 & 407.144049634511 \tabularnewline
Winsorized Mean ( 42 / 44 ) & 110.885606060606 & 0.269113512394866 & 412.040276513152 \tabularnewline
Winsorized Mean ( 43 / 44 ) & 110.885606060606 & 0.262470893434399 & 422.468200605719 \tabularnewline
Winsorized Mean ( 44 / 44 ) & 110.952272727273 & 0.229095885418269 & 484.304956087287 \tabularnewline
Trimmed Mean ( 1 / 44 ) & 111.715384615385 & 0.679834296639009 & 164.327373843431 \tabularnewline
Trimmed Mean ( 2 / 44 ) & 111.69609375 & 0.673801796637013 & 165.769955359992 \tabularnewline
Trimmed Mean ( 3 / 44 ) & 111.674603174603 & 0.66762781810088 & 167.270745985796 \tabularnewline
Trimmed Mean ( 4 / 44 ) & 111.653225806452 & 0.660946911785772 & 168.929189039983 \tabularnewline
Trimmed Mean ( 5 / 44 ) & 111.630327868852 & 0.653679557805242 & 170.772248475471 \tabularnewline
Trimmed Mean ( 6 / 44 ) & 111.604166666667 & 0.64601384483752 & 172.758165414762 \tabularnewline
Trimmed Mean ( 7 / 44 ) & 111.577966101695 & 0.637682788562123 & 174.974090728223 \tabularnewline
Trimmed Mean ( 8 / 44 ) & 111.55 & 0.628574337013073 & 177.46508794819 \tabularnewline
Trimmed Mean ( 9 / 44 ) & 111.521052631579 & 0.618453572826847 & 180.322432485651 \tabularnewline
Trimmed Mean ( 10 / 44 ) & 111.491071428571 & 0.607873524113575 & 183.411625948263 \tabularnewline
Trimmed Mean ( 11 / 44 ) & 111.46 & 0.596432541433145 & 186.877798002398 \tabularnewline
Trimmed Mean ( 12 / 44 ) & 111.427777777778 & 0.584021746782906 & 190.793884631145 \tabularnewline
Trimmed Mean ( 13 / 44 ) & 111.398113207547 & 0.572166609623587 & 194.695236201974 \tabularnewline
Trimmed Mean ( 14 / 44 ) & 111.359615384615 & 0.560976622313149 & 198.510260419466 \tabularnewline
Trimmed Mean ( 15 / 44 ) & 111.317647058824 & 0.548709524991464 & 202.871723541805 \tabularnewline
Trimmed Mean ( 16 / 44 ) & 111.272 & 0.536460679459418 & 207.418743368343 \tabularnewline
Trimmed Mean ( 17 / 44 ) & 111.220408163265 & 0.523264685773261 & 212.550954014617 \tabularnewline
Trimmed Mean ( 18 / 44 ) & 111.166666666667 & 0.50872145091384 & 218.52168110264 \tabularnewline
Trimmed Mean ( 19 / 44 ) & 111.117021276596 & 0.493934007435586 & 224.963293889187 \tabularnewline
Trimmed Mean ( 20 / 44 ) & 111.067391304348 & 0.478149174725937 & 232.28606714214 \tabularnewline
Trimmed Mean ( 21 / 44 ) & 111.023333333333 & 0.462309919775249 & 240.149147972657 \tabularnewline
Trimmed Mean ( 22 / 44 ) & 111 & 0.451923209463542 & 245.616949241804 \tabularnewline
Trimmed Mean ( 23 / 44 ) & 110.981395348837 & 0.442460820459091 & 250.8276218303 \tabularnewline
Trimmed Mean ( 24 / 44 ) & 110.966666666667 & 0.432720560607403 & 256.439551915224 \tabularnewline
Trimmed Mean ( 25 / 44 ) & 110.95243902439 & 0.422875067986787 & 262.376402450515 \tabularnewline
Trimmed Mean ( 26 / 44 ) & 110.94 & 0.413787690929246 & 268.108506927457 \tabularnewline
Trimmed Mean ( 27 / 44 ) & 110.925641025641 & 0.404076941703726 & 274.516136847455 \tabularnewline
Trimmed Mean ( 28 / 44 ) & 110.903947368421 & 0.39412546221104 & 281.392495542539 \tabularnewline
Trimmed Mean ( 29 / 44 ) & 110.875675675676 & 0.384192517432321 & 288.594052837605 \tabularnewline
Trimmed Mean ( 30 / 44 ) & 110.845833333333 & 0.372462397404675 & 297.60274891025 \tabularnewline
Trimmed Mean ( 31 / 44 ) & 110.814285714286 & 0.359279735614943 & 308.434555944593 \tabularnewline
Trimmed Mean ( 32 / 44 ) & 110.780882352941 & 0.345129522027831 & 320.983501214388 \tabularnewline
Trimmed Mean ( 33 / 44 ) & 110.768181818182 & 0.336630493274016 & 329.049756428385 \tabularnewline
Trimmed Mean ( 34 / 44 ) & 110.7546875 & 0.327984841097242 & 337.682336566168 \tabularnewline
Trimmed Mean ( 35 / 44 ) & 110.751612903226 & 0.321318525115105 & 344.678579809712 \tabularnewline
Trimmed Mean ( 36 / 44 ) & 110.741666666667 & 0.315532834849518 & 350.967171830091 \tabularnewline
Trimmed Mean ( 37 / 44 ) & 110.73275862069 & 0.309668635527736 & 357.58467573566 \tabularnewline
Trimmed Mean ( 38 / 44 ) & 110.723214285714 & 0.302371482535696 & 366.182727806161 \tabularnewline
Trimmed Mean ( 39 / 44 ) & 110.716666666667 & 0.294317839954434 & 376.180617130813 \tabularnewline
Trimmed Mean ( 40 / 44 ) & 110.707692307692 & 0.284727465600027 & 388.81985647008 \tabularnewline
Trimmed Mean ( 41 / 44 ) & 110.696 & 0.27659681111388 & 400.207072360008 \tabularnewline
Trimmed Mean ( 42 / 44 ) & 110.685416666667 & 0.266860350484587 & 414.76905979354 \tabularnewline
Trimmed Mean ( 43 / 44 ) & 110.671739130435 & 0.254935116183624 & 434.117279671743 \tabularnewline
Trimmed Mean ( 44 / 44 ) & 110.656818181818 & 0.240910836086064 & 459.326861255368 \tabularnewline
Median & 110.9 &  &  \tabularnewline
Midrange & 112.9 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 110.69552238806 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 110.768181818182 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 110.69552238806 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 110.768181818182 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 110.768181818182 &  &  \tabularnewline
Midmean - Closest Observation & 110.69552238806 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 110.768181818182 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 110.780882352941 &  &  \tabularnewline
Number of observations & 132 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132418&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]111.733333333333[/C][C]0.6858637272488[/C][C]162.908940791385[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]111.461872122165[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]111.194892544593[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]112.008755745416[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 44 )[/C][C]111.734090909091[/C][C]0.685297017878206[/C][C]163.044764524203[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 44 )[/C][C]111.737121212121[/C][C]0.684431145343999[/C][C]163.255459621086[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 44 )[/C][C]111.734848484848[/C][C]0.684060606798406[/C][C]163.340568619787[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 44 )[/C][C]111.737878787879[/C][C]0.683655157683761[/C][C]163.441872019878[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 44 )[/C][C]111.749242424242[/C][C]0.682157095067082[/C][C]163.817459691236[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 44 )[/C][C]111.744696969697[/C][C]0.681418994742553[/C][C]163.988233130947[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 44 )[/C][C]111.75[/C][C]0.680729680894076[/C][C]164.162079510367[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 44 )[/C][C]111.75[/C][C]0.680729680894076[/C][C]164.162079510367[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 44 )[/C][C]111.75[/C][C]0.676772951955623[/C][C]165.121847256283[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 44 )[/C][C]111.75[/C][C]0.674590459288543[/C][C]165.656063558707[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 44 )[/C][C]111.75[/C][C]0.672200459867879[/C][C]166.245051397264[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 44 )[/C][C]111.713636363636[/C][C]0.658751098917733[/C][C]169.583984827003[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 44 )[/C][C]111.792424242424[/C][C]0.643741216732286[/C][C]173.660504153978[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 44 )[/C][C]111.813636363636[/C][C]0.641270653317668[/C][C]174.362627987355[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 44 )[/C][C]111.836363636364[/C][C]0.629509200013975[/C][C]177.656440340953[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 44 )[/C][C]111.884848484848[/C][C]0.624159379027908[/C][C]179.25685689303[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 44 )[/C][C]111.884848484848[/C][C]0.620763676483097[/C][C]180.237428063971[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 44 )[/C][C]111.80303030303[/C][C]0.608204887013433[/C][C]183.824616819564[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 44 )[/C][C]111.774242424242[/C][C]0.600107574992908[/C][C]186.257009712906[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 44 )[/C][C]111.668181818182[/C][C]0.584346779855687[/C][C]191.099165200773[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 44 )[/C][C]111.35[/C][C]0.527547299428589[/C][C]211.071121244689[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 44 )[/C][C]111.266666666667[/C][C]0.508386373193726[/C][C]218.86240964265[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 44 )[/C][C]111.19696969697[/C][C]0.499445609136937[/C][C]222.640799443853[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 44 )[/C][C]111.178787878788[/C][C]0.488413083527461[/C][C]227.632697870873[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 44 )[/C][C]111.140909090909[/C][C]0.470231035868518[/C][C]236.353835908835[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 44 )[/C][C]111.160606060606[/C][C]0.463402413537372[/C][C]239.879212566167[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 44 )[/C][C]111.262878787879[/C][C]0.452212548852433[/C][C]246.041112901947[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 44 )[/C][C]111.347727272727[/C][C]0.438386873682094[/C][C]253.994209127424[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 44 )[/C][C]111.347727272727[/C][C]0.438386873682094[/C][C]253.994209127424[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 44 )[/C][C]111.347727272727[/C][C]0.433211604874116[/C][C]257.028496051215[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 44 )[/C][C]111.347727272727[/C][C]0.422569749328744[/C][C]263.501415919157[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 44 )[/C][C]110.984090909091[/C][C]0.368352217231943[/C][C]301.298826821523[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 44 )[/C][C]110.984090909091[/C][C]0.357413520508078[/C][C]310.520124564181[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 44 )[/C][C]110.803787878788[/C][C]0.331858416266208[/C][C]333.888738231982[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 44 )[/C][C]110.909848484848[/C][C]0.315199909483387[/C][C]351.871447763515[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 44 )[/C][C]110.882575757576[/C][C]0.306524578008963[/C][C]361.741223094787[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 44 )[/C][C]110.882575757576[/C][C]0.306524578008963[/C][C]361.741223094787[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 44 )[/C][C]110.825[/C][C]0.300374457874378[/C][C]368.956138229133[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 44 )[/C][C]110.854545454545[/C][C]0.297363625296161[/C][C]372.791209227892[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 44 )[/C][C]110.884848484848[/C][C]0.27554434768585[/C][C]402.421060043914[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 44 )[/C][C]110.853787878788[/C][C]0.27227166399288[/C][C]407.144049634511[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 44 )[/C][C]110.885606060606[/C][C]0.269113512394866[/C][C]412.040276513152[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 44 )[/C][C]110.885606060606[/C][C]0.262470893434399[/C][C]422.468200605719[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 44 )[/C][C]110.952272727273[/C][C]0.229095885418269[/C][C]484.304956087287[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 44 )[/C][C]111.715384615385[/C][C]0.679834296639009[/C][C]164.327373843431[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 44 )[/C][C]111.69609375[/C][C]0.673801796637013[/C][C]165.769955359992[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 44 )[/C][C]111.674603174603[/C][C]0.66762781810088[/C][C]167.270745985796[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 44 )[/C][C]111.653225806452[/C][C]0.660946911785772[/C][C]168.929189039983[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 44 )[/C][C]111.630327868852[/C][C]0.653679557805242[/C][C]170.772248475471[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 44 )[/C][C]111.604166666667[/C][C]0.64601384483752[/C][C]172.758165414762[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 44 )[/C][C]111.577966101695[/C][C]0.637682788562123[/C][C]174.974090728223[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 44 )[/C][C]111.55[/C][C]0.628574337013073[/C][C]177.46508794819[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 44 )[/C][C]111.521052631579[/C][C]0.618453572826847[/C][C]180.322432485651[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 44 )[/C][C]111.491071428571[/C][C]0.607873524113575[/C][C]183.411625948263[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 44 )[/C][C]111.46[/C][C]0.596432541433145[/C][C]186.877798002398[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 44 )[/C][C]111.427777777778[/C][C]0.584021746782906[/C][C]190.793884631145[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 44 )[/C][C]111.398113207547[/C][C]0.572166609623587[/C][C]194.695236201974[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 44 )[/C][C]111.359615384615[/C][C]0.560976622313149[/C][C]198.510260419466[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 44 )[/C][C]111.317647058824[/C][C]0.548709524991464[/C][C]202.871723541805[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 44 )[/C][C]111.272[/C][C]0.536460679459418[/C][C]207.418743368343[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 44 )[/C][C]111.220408163265[/C][C]0.523264685773261[/C][C]212.550954014617[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 44 )[/C][C]111.166666666667[/C][C]0.50872145091384[/C][C]218.52168110264[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 44 )[/C][C]111.117021276596[/C][C]0.493934007435586[/C][C]224.963293889187[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 44 )[/C][C]111.067391304348[/C][C]0.478149174725937[/C][C]232.28606714214[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 44 )[/C][C]111.023333333333[/C][C]0.462309919775249[/C][C]240.149147972657[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 44 )[/C][C]111[/C][C]0.451923209463542[/C][C]245.616949241804[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 44 )[/C][C]110.981395348837[/C][C]0.442460820459091[/C][C]250.8276218303[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 44 )[/C][C]110.966666666667[/C][C]0.432720560607403[/C][C]256.439551915224[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 44 )[/C][C]110.95243902439[/C][C]0.422875067986787[/C][C]262.376402450515[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 44 )[/C][C]110.94[/C][C]0.413787690929246[/C][C]268.108506927457[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 44 )[/C][C]110.925641025641[/C][C]0.404076941703726[/C][C]274.516136847455[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 44 )[/C][C]110.903947368421[/C][C]0.39412546221104[/C][C]281.392495542539[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 44 )[/C][C]110.875675675676[/C][C]0.384192517432321[/C][C]288.594052837605[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 44 )[/C][C]110.845833333333[/C][C]0.372462397404675[/C][C]297.60274891025[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 44 )[/C][C]110.814285714286[/C][C]0.359279735614943[/C][C]308.434555944593[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 44 )[/C][C]110.780882352941[/C][C]0.345129522027831[/C][C]320.983501214388[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 44 )[/C][C]110.768181818182[/C][C]0.336630493274016[/C][C]329.049756428385[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 44 )[/C][C]110.7546875[/C][C]0.327984841097242[/C][C]337.682336566168[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 44 )[/C][C]110.751612903226[/C][C]0.321318525115105[/C][C]344.678579809712[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 44 )[/C][C]110.741666666667[/C][C]0.315532834849518[/C][C]350.967171830091[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 44 )[/C][C]110.73275862069[/C][C]0.309668635527736[/C][C]357.58467573566[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 44 )[/C][C]110.723214285714[/C][C]0.302371482535696[/C][C]366.182727806161[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 44 )[/C][C]110.716666666667[/C][C]0.294317839954434[/C][C]376.180617130813[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 44 )[/C][C]110.707692307692[/C][C]0.284727465600027[/C][C]388.81985647008[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 44 )[/C][C]110.696[/C][C]0.27659681111388[/C][C]400.207072360008[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 44 )[/C][C]110.685416666667[/C][C]0.266860350484587[/C][C]414.76905979354[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 44 )[/C][C]110.671739130435[/C][C]0.254935116183624[/C][C]434.117279671743[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 44 )[/C][C]110.656818181818[/C][C]0.240910836086064[/C][C]459.326861255368[/C][/ROW]
[ROW][C]Median[/C][C]110.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]112.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]110.69552238806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]110.768181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]110.69552238806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]110.768181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]110.768181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]110.69552238806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]110.768181818182[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]110.780882352941[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]132[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=132418&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132418&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 Mean111.7333333333330.6858637272488162.908940791385
Geometric Mean111.461872122165
Harmonic Mean111.194892544593
Quadratic Mean112.008755745416
Winsorized Mean ( 1 / 44 )111.7340909090910.685297017878206163.044764524203
Winsorized Mean ( 2 / 44 )111.7371212121210.684431145343999163.255459621086
Winsorized Mean ( 3 / 44 )111.7348484848480.684060606798406163.340568619787
Winsorized Mean ( 4 / 44 )111.7378787878790.683655157683761163.441872019878
Winsorized Mean ( 5 / 44 )111.7492424242420.682157095067082163.817459691236
Winsorized Mean ( 6 / 44 )111.7446969696970.681418994742553163.988233130947
Winsorized Mean ( 7 / 44 )111.750.680729680894076164.162079510367
Winsorized Mean ( 8 / 44 )111.750.680729680894076164.162079510367
Winsorized Mean ( 9 / 44 )111.750.676772951955623165.121847256283
Winsorized Mean ( 10 / 44 )111.750.674590459288543165.656063558707
Winsorized Mean ( 11 / 44 )111.750.672200459867879166.245051397264
Winsorized Mean ( 12 / 44 )111.7136363636360.658751098917733169.583984827003
Winsorized Mean ( 13 / 44 )111.7924242424240.643741216732286173.660504153978
Winsorized Mean ( 14 / 44 )111.8136363636360.641270653317668174.362627987355
Winsorized Mean ( 15 / 44 )111.8363636363640.629509200013975177.656440340953
Winsorized Mean ( 16 / 44 )111.8848484848480.624159379027908179.25685689303
Winsorized Mean ( 17 / 44 )111.8848484848480.620763676483097180.237428063971
Winsorized Mean ( 18 / 44 )111.803030303030.608204887013433183.824616819564
Winsorized Mean ( 19 / 44 )111.7742424242420.600107574992908186.257009712906
Winsorized Mean ( 20 / 44 )111.6681818181820.584346779855687191.099165200773
Winsorized Mean ( 21 / 44 )111.350.527547299428589211.071121244689
Winsorized Mean ( 22 / 44 )111.2666666666670.508386373193726218.86240964265
Winsorized Mean ( 23 / 44 )111.196969696970.499445609136937222.640799443853
Winsorized Mean ( 24 / 44 )111.1787878787880.488413083527461227.632697870873
Winsorized Mean ( 25 / 44 )111.1409090909090.470231035868518236.353835908835
Winsorized Mean ( 26 / 44 )111.1606060606060.463402413537372239.879212566167
Winsorized Mean ( 27 / 44 )111.2628787878790.452212548852433246.041112901947
Winsorized Mean ( 28 / 44 )111.3477272727270.438386873682094253.994209127424
Winsorized Mean ( 29 / 44 )111.3477272727270.438386873682094253.994209127424
Winsorized Mean ( 30 / 44 )111.3477272727270.433211604874116257.028496051215
Winsorized Mean ( 31 / 44 )111.3477272727270.422569749328744263.501415919157
Winsorized Mean ( 32 / 44 )110.9840909090910.368352217231943301.298826821523
Winsorized Mean ( 33 / 44 )110.9840909090910.357413520508078310.520124564181
Winsorized Mean ( 34 / 44 )110.8037878787880.331858416266208333.888738231982
Winsorized Mean ( 35 / 44 )110.9098484848480.315199909483387351.871447763515
Winsorized Mean ( 36 / 44 )110.8825757575760.306524578008963361.741223094787
Winsorized Mean ( 37 / 44 )110.8825757575760.306524578008963361.741223094787
Winsorized Mean ( 38 / 44 )110.8250.300374457874378368.956138229133
Winsorized Mean ( 39 / 44 )110.8545454545450.297363625296161372.791209227892
Winsorized Mean ( 40 / 44 )110.8848484848480.27554434768585402.421060043914
Winsorized Mean ( 41 / 44 )110.8537878787880.27227166399288407.144049634511
Winsorized Mean ( 42 / 44 )110.8856060606060.269113512394866412.040276513152
Winsorized Mean ( 43 / 44 )110.8856060606060.262470893434399422.468200605719
Winsorized Mean ( 44 / 44 )110.9522727272730.229095885418269484.304956087287
Trimmed Mean ( 1 / 44 )111.7153846153850.679834296639009164.327373843431
Trimmed Mean ( 2 / 44 )111.696093750.673801796637013165.769955359992
Trimmed Mean ( 3 / 44 )111.6746031746030.66762781810088167.270745985796
Trimmed Mean ( 4 / 44 )111.6532258064520.660946911785772168.929189039983
Trimmed Mean ( 5 / 44 )111.6303278688520.653679557805242170.772248475471
Trimmed Mean ( 6 / 44 )111.6041666666670.64601384483752172.758165414762
Trimmed Mean ( 7 / 44 )111.5779661016950.637682788562123174.974090728223
Trimmed Mean ( 8 / 44 )111.550.628574337013073177.46508794819
Trimmed Mean ( 9 / 44 )111.5210526315790.618453572826847180.322432485651
Trimmed Mean ( 10 / 44 )111.4910714285710.607873524113575183.411625948263
Trimmed Mean ( 11 / 44 )111.460.596432541433145186.877798002398
Trimmed Mean ( 12 / 44 )111.4277777777780.584021746782906190.793884631145
Trimmed Mean ( 13 / 44 )111.3981132075470.572166609623587194.695236201974
Trimmed Mean ( 14 / 44 )111.3596153846150.560976622313149198.510260419466
Trimmed Mean ( 15 / 44 )111.3176470588240.548709524991464202.871723541805
Trimmed Mean ( 16 / 44 )111.2720.536460679459418207.418743368343
Trimmed Mean ( 17 / 44 )111.2204081632650.523264685773261212.550954014617
Trimmed Mean ( 18 / 44 )111.1666666666670.50872145091384218.52168110264
Trimmed Mean ( 19 / 44 )111.1170212765960.493934007435586224.963293889187
Trimmed Mean ( 20 / 44 )111.0673913043480.478149174725937232.28606714214
Trimmed Mean ( 21 / 44 )111.0233333333330.462309919775249240.149147972657
Trimmed Mean ( 22 / 44 )1110.451923209463542245.616949241804
Trimmed Mean ( 23 / 44 )110.9813953488370.442460820459091250.8276218303
Trimmed Mean ( 24 / 44 )110.9666666666670.432720560607403256.439551915224
Trimmed Mean ( 25 / 44 )110.952439024390.422875067986787262.376402450515
Trimmed Mean ( 26 / 44 )110.940.413787690929246268.108506927457
Trimmed Mean ( 27 / 44 )110.9256410256410.404076941703726274.516136847455
Trimmed Mean ( 28 / 44 )110.9039473684210.39412546221104281.392495542539
Trimmed Mean ( 29 / 44 )110.8756756756760.384192517432321288.594052837605
Trimmed Mean ( 30 / 44 )110.8458333333330.372462397404675297.60274891025
Trimmed Mean ( 31 / 44 )110.8142857142860.359279735614943308.434555944593
Trimmed Mean ( 32 / 44 )110.7808823529410.345129522027831320.983501214388
Trimmed Mean ( 33 / 44 )110.7681818181820.336630493274016329.049756428385
Trimmed Mean ( 34 / 44 )110.75468750.327984841097242337.682336566168
Trimmed Mean ( 35 / 44 )110.7516129032260.321318525115105344.678579809712
Trimmed Mean ( 36 / 44 )110.7416666666670.315532834849518350.967171830091
Trimmed Mean ( 37 / 44 )110.732758620690.309668635527736357.58467573566
Trimmed Mean ( 38 / 44 )110.7232142857140.302371482535696366.182727806161
Trimmed Mean ( 39 / 44 )110.7166666666670.294317839954434376.180617130813
Trimmed Mean ( 40 / 44 )110.7076923076920.284727465600027388.81985647008
Trimmed Mean ( 41 / 44 )110.6960.27659681111388400.207072360008
Trimmed Mean ( 42 / 44 )110.6854166666670.266860350484587414.76905979354
Trimmed Mean ( 43 / 44 )110.6717391304350.254935116183624434.117279671743
Trimmed Mean ( 44 / 44 )110.6568181818180.240910836086064459.326861255368
Median110.9
Midrange112.9
Midmean - Weighted Average at Xnp110.69552238806
Midmean - Weighted Average at X(n+1)p110.768181818182
Midmean - Empirical Distribution Function110.69552238806
Midmean - Empirical Distribution Function - Averaging110.768181818182
Midmean - Empirical Distribution Function - Interpolation110.768181818182
Midmean - Closest Observation110.69552238806
Midmean - True Basic - Statistics Graphics Toolkit110.768181818182
Midmean - MS Excel (old versions)110.780882352941
Number of observations132



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')