Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 29 Nov 2011 15:58:05 -0500
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/Nov/29/t13226003095eqxtlxi5eysy5a.htm/, Retrieved Fri, 29 Mar 2024 00:57:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148726, Retrieved Fri, 29 Mar 2024 00:57:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMPD        [Classical Decomposition] [ws8 autocorrelati...] [2011-11-29 19:02:03] [43a0606d8103c0ba382f0586f4417c48]
- RMP             [Central Tendency] [means of Monthly ...] [2011-11-29 20:58:05] [635499bc27d9f41bf7bccae25a54e146] [Current]
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Dataseries X:
9.492
8.641
9.793
9.603
9.238
9.535
10.295
9.941
9.984
9.563
8.872
9.302
9.215
8.834
9.998
9.604
9.507
9.718
10.095
9.583
9.883
9.365
8.919
9.449
9.769
9.321
9.939
9.336
10.195
9.464
10.010
10.213
9.563
9.890
9.305
9.391
9.928
8.686
9.843
9.627
10.074
9.503
10.119
10.000
9.313
9.866
9.172
9.241
9.659
8.904
9.755
9.080
9.435
8.971
10.063
9.793
9.454
9.759
8.820
9.403
9.676
8.642
9.402
9.610
9.294
9.448
10.319
9.548
9.801
9.596
8.923
9.746
9.829
9.125
9.782
9.441
9.162
9.915
10.444
10.209
9.985
9.842
9.429
10.132
9.849
9.172
10.313
9.819
9.955
10.048
10.082
10.541
10.208
10.233
9.439
9.963
10.158
9.225
10.474
9.757
10.490
10.281
10.444
10.640
10.695
10.786
9.832
9.747
10.411
9.511
10.402
9.701
10.540
10.112
10.915
11.183
10.384
10.834
9.886
10.216
10.943
9.867
10.203
10.837
10.573
10.647
11.502
10.656
10.866
10.835
9.945
10.331




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148726&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148726&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148726&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean9.833666666666670.0486167910718397202.268937333518
Geometric Mean9.81800475589859
Harmonic Mean9.80241573402062
Quadratic Mean9.84939747964926
Winsorized Mean ( 1 / 44 )9.831257575757580.0480389504588283204.65179779861
Winsorized Mean ( 2 / 44 )9.828287878787880.047195447967451208.246521689255
Winsorized Mean ( 3 / 44 )9.830696969696970.0465475673709276211.196793408305
Winsorized Mean ( 4 / 44 )9.829636363636360.0462184094120321212.677945621326
Winsorized Mean ( 5 / 44 )9.829977272727270.0457989191758526214.633389818293
Winsorized Mean ( 6 / 44 )9.831340909090910.0455544972220932215.814936144721
Winsorized Mean ( 7 / 44 )9.832083333333330.0454227362048791216.457310915524
Winsorized Mean ( 8 / 44 )9.829416666666670.0449039623945462218.898648192804
Winsorized Mean ( 9 / 44 )9.826484848484850.0434270288389437226.275780572693
Winsorized Mean ( 10 / 44 )9.831787878787880.0417901317149856235.265778673348
Winsorized Mean ( 11 / 44 )9.834787878787880.0411728948093196238.865591655259
Winsorized Mean ( 12 / 44 )9.837515151515150.04064226374387242.051358494984
Winsorized Mean ( 13 / 44 )9.831901515151520.0395474849928926248.610032140311
Winsorized Mean ( 14 / 44 )9.828507575757580.0390684531493655251.57145429284
Winsorized Mean ( 15 / 44 )9.83328030303030.0384390780887253255.814675896573
Winsorized Mean ( 16 / 44 )9.828431818181820.0374560505713329262.399042831922
Winsorized Mean ( 17 / 44 )9.828045454545450.0369747944224322265.803924215543
Winsorized Mean ( 18 / 44 )9.824363636363640.0363861071561283270.003152417721
Winsorized Mean ( 19 / 44 )9.831992424242430.0354774097017456277.133886236307
Winsorized Mean ( 20 / 44 )9.828204545454550.034687124304074283.338695341206
Winsorized Mean ( 21 / 44 )9.827250.0344488735263011285.270576191615
Winsorized Mean ( 22 / 44 )9.825583333333330.0339152156230725289.710183256184
Winsorized Mean ( 23 / 44 )9.817742424242430.0326183101135316300.988689790204
Winsorized Mean ( 24 / 44 )9.818287878787880.0320419112579897306.420169500334
Winsorized Mean ( 25 / 44 )9.822643939393940.0312838391989186313.984606458835
Winsorized Mean ( 26 / 44 )9.82421969696970.0302958603231088324.27597672399
Winsorized Mean ( 27 / 44 )9.823606060606060.0297130831361914330.615507504862
Winsorized Mean ( 28 / 44 )9.813636363636360.0285197260033788344.09995251966
Winsorized Mean ( 29 / 44 )9.815613636363640.0274816336113851357.169947578998
Winsorized Mean ( 30 / 44 )9.816295454545460.0272598248308308360.101193439924
Winsorized Mean ( 31 / 44 )9.816295454545450.0270554509339857362.821358198643
Winsorized Mean ( 32 / 44 )9.816537878787880.026977026074857363.88510177321
Winsorized Mean ( 33 / 44 )9.817037878787880.0266532388815256368.32438723207
Winsorized Mean ( 34 / 44 )9.815234848484850.0263989522444189371.803954854304
Winsorized Mean ( 35 / 44 )9.806750.0251968754488511389.205003608777
Winsorized Mean ( 36 / 44 )9.802386363636360.0241586284805925405.750946147914
Winsorized Mean ( 37 / 44 )9.806590909090910.0229490604339884427.319930473799
Winsorized Mean ( 38 / 44 )9.807742424242430.0224098668136415437.652865400887
Winsorized Mean ( 39 / 44 )9.803901515151520.021770337379547450.333007901024
Winsorized Mean ( 40 / 44 )9.801174242424240.0212442165217928461.357293754278
Winsorized Mean ( 41 / 44 )9.806143939393940.0202229423945934484.901937020579
Winsorized Mean ( 42 / 44 )9.80678030303030.0194482097065621504.251057089401
Winsorized Mean ( 43 / 44 )9.80678030303030.0184643541727472531.119594613539
Winsorized Mean ( 44 / 44 )9.794113636363640.0172259636777527568.566950423371
Trimmed Mean ( 1 / 44 )9.830007692307690.0467575414229934210.233630621855
Trimmed Mean ( 2 / 44 )9.828718750.0453426002217516216.765661914665
Trimmed Mean ( 3 / 44 )9.828944444444440.0442748347391795221.99844454183
Trimmed Mean ( 4 / 44 )9.828322580645160.0433610966585708226.662223468061
Trimmed Mean ( 5 / 44 )9.827967213114750.0424579375113689231.475379850543
Trimmed Mean ( 6 / 44 )9.8275250.0415719365090447236.398056603927
Trimmed Mean ( 7 / 44 )9.826813559322030.0406480014822895241.753916575791
Trimmed Mean ( 8 / 44 )9.825956896551720.0396503333449925247.815240569539
Trimmed Mean ( 9 / 44 )9.825456140350880.0386419680987977254.269040211143
Trimmed Mean ( 10 / 44 )9.825321428571430.0377849751346691260.032496873508
Trimmed Mean ( 11 / 44 )9.824545454545450.0371005253360486264.80879625172
Trimmed Mean ( 12 / 44 )9.823407407407410.0364314271124983269.641026607968
Trimmed Mean ( 13 / 44 )9.821943396226410.0357604811072031274.659151446596
Trimmed Mean ( 14 / 44 )9.820971153846150.0351654668019858279.278850730102
Trimmed Mean ( 15 / 44 )9.820274509803920.0345631869456364284.125260938755
Trimmed Mean ( 16 / 44 )9.819130.0339673332524475289.075681244199
Trimmed Mean ( 17 / 44 )9.818346938775510.0334232813747897293.757720215383
Trimmed Mean ( 18 / 44 )9.81756250.0328682904983677298.694040704294
Trimmed Mean ( 19 / 44 )9.817031914893620.0323128242620253303.812252228005
Trimmed Mean ( 20 / 44 )9.815902173913040.0317902603718638308.770738556161
Trimmed Mean ( 21 / 44 )9.8150.0312906035841301313.672440789156
Trimmed Mean ( 22 / 44 )9.8141250.0307471180718306319.188451323226
Trimmed Mean ( 23 / 44 )9.813325581395350.0301884887686381325.068460915808
Trimmed Mean ( 24 / 44 )9.813023809523810.0297039126338173330.361320762568
Trimmed Mean ( 25 / 44 )9.812670731707320.0292122256381181335.909726744787
Trimmed Mean ( 26 / 44 )9.81201250.028731639672586341.505483564937
Trimmed Mean ( 27 / 44 )9.811217948717950.0282896490770104346.812995877387
Trimmed Mean ( 28 / 44 )9.810421052631580.0278417348166249352.363856535749
Trimmed Mean ( 29 / 44 )9.810216216216220.0274615834812451357.234178535848
Trimmed Mean ( 30 / 44 )9.8098750.0271344745574157361.528098848666
Trimmed Mean ( 31 / 44 )9.809471428571430.0267679602168959366.463165257535
Trimmed Mean ( 32 / 44 )9.809044117647060.0263524636694596372.22493656314
Trimmed Mean ( 33 / 44 )9.808575757575760.0258617812589596379.269148530813
Trimmed Mean ( 34 / 44 )9.8080468750.0253139261276433387.456565431366
Trimmed Mean ( 35 / 44 )9.807596774193550.0246874964303518397.269800194712
Trimmed Mean ( 36 / 44 )9.807650.0241067051764292406.843238353022
Trimmed Mean ( 37 / 44 )9.807982758620690.0235525116586773416.430438534873
Trimmed Mean ( 38 / 44 )9.808071428571430.0230564645292003425.393555727064
Trimmed Mean ( 39 / 44 )9.808092592592590.0225232897325485435.464477394654
Trimmed Mean ( 40 / 44 )9.808365384615390.0219600629699841446.645594688042
Trimmed Mean ( 41 / 44 )9.808840.0213388475866559459.67055906683
Trimmed Mean ( 42 / 44 )9.809020833333330.020738781671869472.979608374908
Trimmed Mean ( 43 / 44 )9.809173913043480.02011633566837487.622302329492
Trimmed Mean ( 44 / 44 )9.809340909090910.0195079520616154502.838067169139
Median9.824
Midrange10.0715
Midmean - Weighted Average at Xnp9.80308955223881
Midmean - Weighted Average at X(n+1)p9.80857575757576
Midmean - Empirical Distribution Function9.80308955223881
Midmean - Empirical Distribution Function - Averaging9.80857575757576
Midmean - Empirical Distribution Function - Interpolation9.80857575757576
Midmean - Closest Observation9.80308955223881
Midmean - True Basic - Statistics Graphics Toolkit9.80857575757576
Midmean - MS Excel (old versions)9.80904411764706
Number of observations132

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 9.83366666666667 & 0.0486167910718397 & 202.268937333518 \tabularnewline
Geometric Mean & 9.81800475589859 &  &  \tabularnewline
Harmonic Mean & 9.80241573402062 &  &  \tabularnewline
Quadratic Mean & 9.84939747964926 &  &  \tabularnewline
Winsorized Mean ( 1 / 44 ) & 9.83125757575758 & 0.0480389504588283 & 204.65179779861 \tabularnewline
Winsorized Mean ( 2 / 44 ) & 9.82828787878788 & 0.047195447967451 & 208.246521689255 \tabularnewline
Winsorized Mean ( 3 / 44 ) & 9.83069696969697 & 0.0465475673709276 & 211.196793408305 \tabularnewline
Winsorized Mean ( 4 / 44 ) & 9.82963636363636 & 0.0462184094120321 & 212.677945621326 \tabularnewline
Winsorized Mean ( 5 / 44 ) & 9.82997727272727 & 0.0457989191758526 & 214.633389818293 \tabularnewline
Winsorized Mean ( 6 / 44 ) & 9.83134090909091 & 0.0455544972220932 & 215.814936144721 \tabularnewline
Winsorized Mean ( 7 / 44 ) & 9.83208333333333 & 0.0454227362048791 & 216.457310915524 \tabularnewline
Winsorized Mean ( 8 / 44 ) & 9.82941666666667 & 0.0449039623945462 & 218.898648192804 \tabularnewline
Winsorized Mean ( 9 / 44 ) & 9.82648484848485 & 0.0434270288389437 & 226.275780572693 \tabularnewline
Winsorized Mean ( 10 / 44 ) & 9.83178787878788 & 0.0417901317149856 & 235.265778673348 \tabularnewline
Winsorized Mean ( 11 / 44 ) & 9.83478787878788 & 0.0411728948093196 & 238.865591655259 \tabularnewline
Winsorized Mean ( 12 / 44 ) & 9.83751515151515 & 0.04064226374387 & 242.051358494984 \tabularnewline
Winsorized Mean ( 13 / 44 ) & 9.83190151515152 & 0.0395474849928926 & 248.610032140311 \tabularnewline
Winsorized Mean ( 14 / 44 ) & 9.82850757575758 & 0.0390684531493655 & 251.57145429284 \tabularnewline
Winsorized Mean ( 15 / 44 ) & 9.8332803030303 & 0.0384390780887253 & 255.814675896573 \tabularnewline
Winsorized Mean ( 16 / 44 ) & 9.82843181818182 & 0.0374560505713329 & 262.399042831922 \tabularnewline
Winsorized Mean ( 17 / 44 ) & 9.82804545454545 & 0.0369747944224322 & 265.803924215543 \tabularnewline
Winsorized Mean ( 18 / 44 ) & 9.82436363636364 & 0.0363861071561283 & 270.003152417721 \tabularnewline
Winsorized Mean ( 19 / 44 ) & 9.83199242424243 & 0.0354774097017456 & 277.133886236307 \tabularnewline
Winsorized Mean ( 20 / 44 ) & 9.82820454545455 & 0.034687124304074 & 283.338695341206 \tabularnewline
Winsorized Mean ( 21 / 44 ) & 9.82725 & 0.0344488735263011 & 285.270576191615 \tabularnewline
Winsorized Mean ( 22 / 44 ) & 9.82558333333333 & 0.0339152156230725 & 289.710183256184 \tabularnewline
Winsorized Mean ( 23 / 44 ) & 9.81774242424243 & 0.0326183101135316 & 300.988689790204 \tabularnewline
Winsorized Mean ( 24 / 44 ) & 9.81828787878788 & 0.0320419112579897 & 306.420169500334 \tabularnewline
Winsorized Mean ( 25 / 44 ) & 9.82264393939394 & 0.0312838391989186 & 313.984606458835 \tabularnewline
Winsorized Mean ( 26 / 44 ) & 9.8242196969697 & 0.0302958603231088 & 324.27597672399 \tabularnewline
Winsorized Mean ( 27 / 44 ) & 9.82360606060606 & 0.0297130831361914 & 330.615507504862 \tabularnewline
Winsorized Mean ( 28 / 44 ) & 9.81363636363636 & 0.0285197260033788 & 344.09995251966 \tabularnewline
Winsorized Mean ( 29 / 44 ) & 9.81561363636364 & 0.0274816336113851 & 357.169947578998 \tabularnewline
Winsorized Mean ( 30 / 44 ) & 9.81629545454546 & 0.0272598248308308 & 360.101193439924 \tabularnewline
Winsorized Mean ( 31 / 44 ) & 9.81629545454545 & 0.0270554509339857 & 362.821358198643 \tabularnewline
Winsorized Mean ( 32 / 44 ) & 9.81653787878788 & 0.026977026074857 & 363.88510177321 \tabularnewline
Winsorized Mean ( 33 / 44 ) & 9.81703787878788 & 0.0266532388815256 & 368.32438723207 \tabularnewline
Winsorized Mean ( 34 / 44 ) & 9.81523484848485 & 0.0263989522444189 & 371.803954854304 \tabularnewline
Winsorized Mean ( 35 / 44 ) & 9.80675 & 0.0251968754488511 & 389.205003608777 \tabularnewline
Winsorized Mean ( 36 / 44 ) & 9.80238636363636 & 0.0241586284805925 & 405.750946147914 \tabularnewline
Winsorized Mean ( 37 / 44 ) & 9.80659090909091 & 0.0229490604339884 & 427.319930473799 \tabularnewline
Winsorized Mean ( 38 / 44 ) & 9.80774242424243 & 0.0224098668136415 & 437.652865400887 \tabularnewline
Winsorized Mean ( 39 / 44 ) & 9.80390151515152 & 0.021770337379547 & 450.333007901024 \tabularnewline
Winsorized Mean ( 40 / 44 ) & 9.80117424242424 & 0.0212442165217928 & 461.357293754278 \tabularnewline
Winsorized Mean ( 41 / 44 ) & 9.80614393939394 & 0.0202229423945934 & 484.901937020579 \tabularnewline
Winsorized Mean ( 42 / 44 ) & 9.8067803030303 & 0.0194482097065621 & 504.251057089401 \tabularnewline
Winsorized Mean ( 43 / 44 ) & 9.8067803030303 & 0.0184643541727472 & 531.119594613539 \tabularnewline
Winsorized Mean ( 44 / 44 ) & 9.79411363636364 & 0.0172259636777527 & 568.566950423371 \tabularnewline
Trimmed Mean ( 1 / 44 ) & 9.83000769230769 & 0.0467575414229934 & 210.233630621855 \tabularnewline
Trimmed Mean ( 2 / 44 ) & 9.82871875 & 0.0453426002217516 & 216.765661914665 \tabularnewline
Trimmed Mean ( 3 / 44 ) & 9.82894444444444 & 0.0442748347391795 & 221.99844454183 \tabularnewline
Trimmed Mean ( 4 / 44 ) & 9.82832258064516 & 0.0433610966585708 & 226.662223468061 \tabularnewline
Trimmed Mean ( 5 / 44 ) & 9.82796721311475 & 0.0424579375113689 & 231.475379850543 \tabularnewline
Trimmed Mean ( 6 / 44 ) & 9.827525 & 0.0415719365090447 & 236.398056603927 \tabularnewline
Trimmed Mean ( 7 / 44 ) & 9.82681355932203 & 0.0406480014822895 & 241.753916575791 \tabularnewline
Trimmed Mean ( 8 / 44 ) & 9.82595689655172 & 0.0396503333449925 & 247.815240569539 \tabularnewline
Trimmed Mean ( 9 / 44 ) & 9.82545614035088 & 0.0386419680987977 & 254.269040211143 \tabularnewline
Trimmed Mean ( 10 / 44 ) & 9.82532142857143 & 0.0377849751346691 & 260.032496873508 \tabularnewline
Trimmed Mean ( 11 / 44 ) & 9.82454545454545 & 0.0371005253360486 & 264.80879625172 \tabularnewline
Trimmed Mean ( 12 / 44 ) & 9.82340740740741 & 0.0364314271124983 & 269.641026607968 \tabularnewline
Trimmed Mean ( 13 / 44 ) & 9.82194339622641 & 0.0357604811072031 & 274.659151446596 \tabularnewline
Trimmed Mean ( 14 / 44 ) & 9.82097115384615 & 0.0351654668019858 & 279.278850730102 \tabularnewline
Trimmed Mean ( 15 / 44 ) & 9.82027450980392 & 0.0345631869456364 & 284.125260938755 \tabularnewline
Trimmed Mean ( 16 / 44 ) & 9.81913 & 0.0339673332524475 & 289.075681244199 \tabularnewline
Trimmed Mean ( 17 / 44 ) & 9.81834693877551 & 0.0334232813747897 & 293.757720215383 \tabularnewline
Trimmed Mean ( 18 / 44 ) & 9.8175625 & 0.0328682904983677 & 298.694040704294 \tabularnewline
Trimmed Mean ( 19 / 44 ) & 9.81703191489362 & 0.0323128242620253 & 303.812252228005 \tabularnewline
Trimmed Mean ( 20 / 44 ) & 9.81590217391304 & 0.0317902603718638 & 308.770738556161 \tabularnewline
Trimmed Mean ( 21 / 44 ) & 9.815 & 0.0312906035841301 & 313.672440789156 \tabularnewline
Trimmed Mean ( 22 / 44 ) & 9.814125 & 0.0307471180718306 & 319.188451323226 \tabularnewline
Trimmed Mean ( 23 / 44 ) & 9.81332558139535 & 0.0301884887686381 & 325.068460915808 \tabularnewline
Trimmed Mean ( 24 / 44 ) & 9.81302380952381 & 0.0297039126338173 & 330.361320762568 \tabularnewline
Trimmed Mean ( 25 / 44 ) & 9.81267073170732 & 0.0292122256381181 & 335.909726744787 \tabularnewline
Trimmed Mean ( 26 / 44 ) & 9.8120125 & 0.028731639672586 & 341.505483564937 \tabularnewline
Trimmed Mean ( 27 / 44 ) & 9.81121794871795 & 0.0282896490770104 & 346.812995877387 \tabularnewline
Trimmed Mean ( 28 / 44 ) & 9.81042105263158 & 0.0278417348166249 & 352.363856535749 \tabularnewline
Trimmed Mean ( 29 / 44 ) & 9.81021621621622 & 0.0274615834812451 & 357.234178535848 \tabularnewline
Trimmed Mean ( 30 / 44 ) & 9.809875 & 0.0271344745574157 & 361.528098848666 \tabularnewline
Trimmed Mean ( 31 / 44 ) & 9.80947142857143 & 0.0267679602168959 & 366.463165257535 \tabularnewline
Trimmed Mean ( 32 / 44 ) & 9.80904411764706 & 0.0263524636694596 & 372.22493656314 \tabularnewline
Trimmed Mean ( 33 / 44 ) & 9.80857575757576 & 0.0258617812589596 & 379.269148530813 \tabularnewline
Trimmed Mean ( 34 / 44 ) & 9.808046875 & 0.0253139261276433 & 387.456565431366 \tabularnewline
Trimmed Mean ( 35 / 44 ) & 9.80759677419355 & 0.0246874964303518 & 397.269800194712 \tabularnewline
Trimmed Mean ( 36 / 44 ) & 9.80765 & 0.0241067051764292 & 406.843238353022 \tabularnewline
Trimmed Mean ( 37 / 44 ) & 9.80798275862069 & 0.0235525116586773 & 416.430438534873 \tabularnewline
Trimmed Mean ( 38 / 44 ) & 9.80807142857143 & 0.0230564645292003 & 425.393555727064 \tabularnewline
Trimmed Mean ( 39 / 44 ) & 9.80809259259259 & 0.0225232897325485 & 435.464477394654 \tabularnewline
Trimmed Mean ( 40 / 44 ) & 9.80836538461539 & 0.0219600629699841 & 446.645594688042 \tabularnewline
Trimmed Mean ( 41 / 44 ) & 9.80884 & 0.0213388475866559 & 459.67055906683 \tabularnewline
Trimmed Mean ( 42 / 44 ) & 9.80902083333333 & 0.020738781671869 & 472.979608374908 \tabularnewline
Trimmed Mean ( 43 / 44 ) & 9.80917391304348 & 0.02011633566837 & 487.622302329492 \tabularnewline
Trimmed Mean ( 44 / 44 ) & 9.80934090909091 & 0.0195079520616154 & 502.838067169139 \tabularnewline
Median & 9.824 &  &  \tabularnewline
Midrange & 10.0715 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 9.80308955223881 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 9.80857575757576 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 9.80308955223881 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 9.80857575757576 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 9.80857575757576 &  &  \tabularnewline
Midmean - Closest Observation & 9.80308955223881 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 9.80857575757576 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 9.80904411764706 &  &  \tabularnewline
Number of observations & 132 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148726&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]9.83366666666667[/C][C]0.0486167910718397[/C][C]202.268937333518[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]9.81800475589859[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]9.80241573402062[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]9.84939747964926[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 44 )[/C][C]9.83125757575758[/C][C]0.0480389504588283[/C][C]204.65179779861[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 44 )[/C][C]9.82828787878788[/C][C]0.047195447967451[/C][C]208.246521689255[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 44 )[/C][C]9.83069696969697[/C][C]0.0465475673709276[/C][C]211.196793408305[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 44 )[/C][C]9.82963636363636[/C][C]0.0462184094120321[/C][C]212.677945621326[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 44 )[/C][C]9.82997727272727[/C][C]0.0457989191758526[/C][C]214.633389818293[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 44 )[/C][C]9.83134090909091[/C][C]0.0455544972220932[/C][C]215.814936144721[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 44 )[/C][C]9.83208333333333[/C][C]0.0454227362048791[/C][C]216.457310915524[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 44 )[/C][C]9.82941666666667[/C][C]0.0449039623945462[/C][C]218.898648192804[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 44 )[/C][C]9.82648484848485[/C][C]0.0434270288389437[/C][C]226.275780572693[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 44 )[/C][C]9.83178787878788[/C][C]0.0417901317149856[/C][C]235.265778673348[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 44 )[/C][C]9.83478787878788[/C][C]0.0411728948093196[/C][C]238.865591655259[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 44 )[/C][C]9.83751515151515[/C][C]0.04064226374387[/C][C]242.051358494984[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 44 )[/C][C]9.83190151515152[/C][C]0.0395474849928926[/C][C]248.610032140311[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 44 )[/C][C]9.82850757575758[/C][C]0.0390684531493655[/C][C]251.57145429284[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 44 )[/C][C]9.8332803030303[/C][C]0.0384390780887253[/C][C]255.814675896573[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 44 )[/C][C]9.82843181818182[/C][C]0.0374560505713329[/C][C]262.399042831922[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 44 )[/C][C]9.82804545454545[/C][C]0.0369747944224322[/C][C]265.803924215543[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 44 )[/C][C]9.82436363636364[/C][C]0.0363861071561283[/C][C]270.003152417721[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 44 )[/C][C]9.83199242424243[/C][C]0.0354774097017456[/C][C]277.133886236307[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 44 )[/C][C]9.82820454545455[/C][C]0.034687124304074[/C][C]283.338695341206[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 44 )[/C][C]9.82725[/C][C]0.0344488735263011[/C][C]285.270576191615[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 44 )[/C][C]9.82558333333333[/C][C]0.0339152156230725[/C][C]289.710183256184[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 44 )[/C][C]9.81774242424243[/C][C]0.0326183101135316[/C][C]300.988689790204[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 44 )[/C][C]9.81828787878788[/C][C]0.0320419112579897[/C][C]306.420169500334[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 44 )[/C][C]9.82264393939394[/C][C]0.0312838391989186[/C][C]313.984606458835[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 44 )[/C][C]9.8242196969697[/C][C]0.0302958603231088[/C][C]324.27597672399[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 44 )[/C][C]9.82360606060606[/C][C]0.0297130831361914[/C][C]330.615507504862[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 44 )[/C][C]9.81363636363636[/C][C]0.0285197260033788[/C][C]344.09995251966[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 44 )[/C][C]9.81561363636364[/C][C]0.0274816336113851[/C][C]357.169947578998[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 44 )[/C][C]9.81629545454546[/C][C]0.0272598248308308[/C][C]360.101193439924[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 44 )[/C][C]9.81629545454545[/C][C]0.0270554509339857[/C][C]362.821358198643[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 44 )[/C][C]9.81653787878788[/C][C]0.026977026074857[/C][C]363.88510177321[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 44 )[/C][C]9.81703787878788[/C][C]0.0266532388815256[/C][C]368.32438723207[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 44 )[/C][C]9.81523484848485[/C][C]0.0263989522444189[/C][C]371.803954854304[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 44 )[/C][C]9.80675[/C][C]0.0251968754488511[/C][C]389.205003608777[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 44 )[/C][C]9.80238636363636[/C][C]0.0241586284805925[/C][C]405.750946147914[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 44 )[/C][C]9.80659090909091[/C][C]0.0229490604339884[/C][C]427.319930473799[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 44 )[/C][C]9.80774242424243[/C][C]0.0224098668136415[/C][C]437.652865400887[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 44 )[/C][C]9.80390151515152[/C][C]0.021770337379547[/C][C]450.333007901024[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 44 )[/C][C]9.80117424242424[/C][C]0.0212442165217928[/C][C]461.357293754278[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 44 )[/C][C]9.80614393939394[/C][C]0.0202229423945934[/C][C]484.901937020579[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 44 )[/C][C]9.8067803030303[/C][C]0.0194482097065621[/C][C]504.251057089401[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 44 )[/C][C]9.8067803030303[/C][C]0.0184643541727472[/C][C]531.119594613539[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 44 )[/C][C]9.79411363636364[/C][C]0.0172259636777527[/C][C]568.566950423371[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 44 )[/C][C]9.83000769230769[/C][C]0.0467575414229934[/C][C]210.233630621855[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 44 )[/C][C]9.82871875[/C][C]0.0453426002217516[/C][C]216.765661914665[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 44 )[/C][C]9.82894444444444[/C][C]0.0442748347391795[/C][C]221.99844454183[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 44 )[/C][C]9.82832258064516[/C][C]0.0433610966585708[/C][C]226.662223468061[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 44 )[/C][C]9.82796721311475[/C][C]0.0424579375113689[/C][C]231.475379850543[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 44 )[/C][C]9.827525[/C][C]0.0415719365090447[/C][C]236.398056603927[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 44 )[/C][C]9.82681355932203[/C][C]0.0406480014822895[/C][C]241.753916575791[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 44 )[/C][C]9.82595689655172[/C][C]0.0396503333449925[/C][C]247.815240569539[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 44 )[/C][C]9.82545614035088[/C][C]0.0386419680987977[/C][C]254.269040211143[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 44 )[/C][C]9.82532142857143[/C][C]0.0377849751346691[/C][C]260.032496873508[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 44 )[/C][C]9.82454545454545[/C][C]0.0371005253360486[/C][C]264.80879625172[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 44 )[/C][C]9.82340740740741[/C][C]0.0364314271124983[/C][C]269.641026607968[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 44 )[/C][C]9.82194339622641[/C][C]0.0357604811072031[/C][C]274.659151446596[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 44 )[/C][C]9.82097115384615[/C][C]0.0351654668019858[/C][C]279.278850730102[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 44 )[/C][C]9.82027450980392[/C][C]0.0345631869456364[/C][C]284.125260938755[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 44 )[/C][C]9.81913[/C][C]0.0339673332524475[/C][C]289.075681244199[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 44 )[/C][C]9.81834693877551[/C][C]0.0334232813747897[/C][C]293.757720215383[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 44 )[/C][C]9.8175625[/C][C]0.0328682904983677[/C][C]298.694040704294[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 44 )[/C][C]9.81703191489362[/C][C]0.0323128242620253[/C][C]303.812252228005[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 44 )[/C][C]9.81590217391304[/C][C]0.0317902603718638[/C][C]308.770738556161[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 44 )[/C][C]9.815[/C][C]0.0312906035841301[/C][C]313.672440789156[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 44 )[/C][C]9.814125[/C][C]0.0307471180718306[/C][C]319.188451323226[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 44 )[/C][C]9.81332558139535[/C][C]0.0301884887686381[/C][C]325.068460915808[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 44 )[/C][C]9.81302380952381[/C][C]0.0297039126338173[/C][C]330.361320762568[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 44 )[/C][C]9.81267073170732[/C][C]0.0292122256381181[/C][C]335.909726744787[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 44 )[/C][C]9.8120125[/C][C]0.028731639672586[/C][C]341.505483564937[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 44 )[/C][C]9.81121794871795[/C][C]0.0282896490770104[/C][C]346.812995877387[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 44 )[/C][C]9.81042105263158[/C][C]0.0278417348166249[/C][C]352.363856535749[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 44 )[/C][C]9.81021621621622[/C][C]0.0274615834812451[/C][C]357.234178535848[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 44 )[/C][C]9.809875[/C][C]0.0271344745574157[/C][C]361.528098848666[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 44 )[/C][C]9.80947142857143[/C][C]0.0267679602168959[/C][C]366.463165257535[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 44 )[/C][C]9.80904411764706[/C][C]0.0263524636694596[/C][C]372.22493656314[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 44 )[/C][C]9.80857575757576[/C][C]0.0258617812589596[/C][C]379.269148530813[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 44 )[/C][C]9.808046875[/C][C]0.0253139261276433[/C][C]387.456565431366[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 44 )[/C][C]9.80759677419355[/C][C]0.0246874964303518[/C][C]397.269800194712[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 44 )[/C][C]9.80765[/C][C]0.0241067051764292[/C][C]406.843238353022[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 44 )[/C][C]9.80798275862069[/C][C]0.0235525116586773[/C][C]416.430438534873[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 44 )[/C][C]9.80807142857143[/C][C]0.0230564645292003[/C][C]425.393555727064[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 44 )[/C][C]9.80809259259259[/C][C]0.0225232897325485[/C][C]435.464477394654[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 44 )[/C][C]9.80836538461539[/C][C]0.0219600629699841[/C][C]446.645594688042[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 44 )[/C][C]9.80884[/C][C]0.0213388475866559[/C][C]459.67055906683[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 44 )[/C][C]9.80902083333333[/C][C]0.020738781671869[/C][C]472.979608374908[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 44 )[/C][C]9.80917391304348[/C][C]0.02011633566837[/C][C]487.622302329492[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 44 )[/C][C]9.80934090909091[/C][C]0.0195079520616154[/C][C]502.838067169139[/C][/ROW]
[ROW][C]Median[/C][C]9.824[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]10.0715[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]9.80308955223881[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]9.80857575757576[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]9.80308955223881[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]9.80857575757576[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]9.80857575757576[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]9.80308955223881[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]9.80857575757576[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]9.80904411764706[/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=148726&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148726&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 Mean9.833666666666670.0486167910718397202.268937333518
Geometric Mean9.81800475589859
Harmonic Mean9.80241573402062
Quadratic Mean9.84939747964926
Winsorized Mean ( 1 / 44 )9.831257575757580.0480389504588283204.65179779861
Winsorized Mean ( 2 / 44 )9.828287878787880.047195447967451208.246521689255
Winsorized Mean ( 3 / 44 )9.830696969696970.0465475673709276211.196793408305
Winsorized Mean ( 4 / 44 )9.829636363636360.0462184094120321212.677945621326
Winsorized Mean ( 5 / 44 )9.829977272727270.0457989191758526214.633389818293
Winsorized Mean ( 6 / 44 )9.831340909090910.0455544972220932215.814936144721
Winsorized Mean ( 7 / 44 )9.832083333333330.0454227362048791216.457310915524
Winsorized Mean ( 8 / 44 )9.829416666666670.0449039623945462218.898648192804
Winsorized Mean ( 9 / 44 )9.826484848484850.0434270288389437226.275780572693
Winsorized Mean ( 10 / 44 )9.831787878787880.0417901317149856235.265778673348
Winsorized Mean ( 11 / 44 )9.834787878787880.0411728948093196238.865591655259
Winsorized Mean ( 12 / 44 )9.837515151515150.04064226374387242.051358494984
Winsorized Mean ( 13 / 44 )9.831901515151520.0395474849928926248.610032140311
Winsorized Mean ( 14 / 44 )9.828507575757580.0390684531493655251.57145429284
Winsorized Mean ( 15 / 44 )9.83328030303030.0384390780887253255.814675896573
Winsorized Mean ( 16 / 44 )9.828431818181820.0374560505713329262.399042831922
Winsorized Mean ( 17 / 44 )9.828045454545450.0369747944224322265.803924215543
Winsorized Mean ( 18 / 44 )9.824363636363640.0363861071561283270.003152417721
Winsorized Mean ( 19 / 44 )9.831992424242430.0354774097017456277.133886236307
Winsorized Mean ( 20 / 44 )9.828204545454550.034687124304074283.338695341206
Winsorized Mean ( 21 / 44 )9.827250.0344488735263011285.270576191615
Winsorized Mean ( 22 / 44 )9.825583333333330.0339152156230725289.710183256184
Winsorized Mean ( 23 / 44 )9.817742424242430.0326183101135316300.988689790204
Winsorized Mean ( 24 / 44 )9.818287878787880.0320419112579897306.420169500334
Winsorized Mean ( 25 / 44 )9.822643939393940.0312838391989186313.984606458835
Winsorized Mean ( 26 / 44 )9.82421969696970.0302958603231088324.27597672399
Winsorized Mean ( 27 / 44 )9.823606060606060.0297130831361914330.615507504862
Winsorized Mean ( 28 / 44 )9.813636363636360.0285197260033788344.09995251966
Winsorized Mean ( 29 / 44 )9.815613636363640.0274816336113851357.169947578998
Winsorized Mean ( 30 / 44 )9.816295454545460.0272598248308308360.101193439924
Winsorized Mean ( 31 / 44 )9.816295454545450.0270554509339857362.821358198643
Winsorized Mean ( 32 / 44 )9.816537878787880.026977026074857363.88510177321
Winsorized Mean ( 33 / 44 )9.817037878787880.0266532388815256368.32438723207
Winsorized Mean ( 34 / 44 )9.815234848484850.0263989522444189371.803954854304
Winsorized Mean ( 35 / 44 )9.806750.0251968754488511389.205003608777
Winsorized Mean ( 36 / 44 )9.802386363636360.0241586284805925405.750946147914
Winsorized Mean ( 37 / 44 )9.806590909090910.0229490604339884427.319930473799
Winsorized Mean ( 38 / 44 )9.807742424242430.0224098668136415437.652865400887
Winsorized Mean ( 39 / 44 )9.803901515151520.021770337379547450.333007901024
Winsorized Mean ( 40 / 44 )9.801174242424240.0212442165217928461.357293754278
Winsorized Mean ( 41 / 44 )9.806143939393940.0202229423945934484.901937020579
Winsorized Mean ( 42 / 44 )9.80678030303030.0194482097065621504.251057089401
Winsorized Mean ( 43 / 44 )9.80678030303030.0184643541727472531.119594613539
Winsorized Mean ( 44 / 44 )9.794113636363640.0172259636777527568.566950423371
Trimmed Mean ( 1 / 44 )9.830007692307690.0467575414229934210.233630621855
Trimmed Mean ( 2 / 44 )9.828718750.0453426002217516216.765661914665
Trimmed Mean ( 3 / 44 )9.828944444444440.0442748347391795221.99844454183
Trimmed Mean ( 4 / 44 )9.828322580645160.0433610966585708226.662223468061
Trimmed Mean ( 5 / 44 )9.827967213114750.0424579375113689231.475379850543
Trimmed Mean ( 6 / 44 )9.8275250.0415719365090447236.398056603927
Trimmed Mean ( 7 / 44 )9.826813559322030.0406480014822895241.753916575791
Trimmed Mean ( 8 / 44 )9.825956896551720.0396503333449925247.815240569539
Trimmed Mean ( 9 / 44 )9.825456140350880.0386419680987977254.269040211143
Trimmed Mean ( 10 / 44 )9.825321428571430.0377849751346691260.032496873508
Trimmed Mean ( 11 / 44 )9.824545454545450.0371005253360486264.80879625172
Trimmed Mean ( 12 / 44 )9.823407407407410.0364314271124983269.641026607968
Trimmed Mean ( 13 / 44 )9.821943396226410.0357604811072031274.659151446596
Trimmed Mean ( 14 / 44 )9.820971153846150.0351654668019858279.278850730102
Trimmed Mean ( 15 / 44 )9.820274509803920.0345631869456364284.125260938755
Trimmed Mean ( 16 / 44 )9.819130.0339673332524475289.075681244199
Trimmed Mean ( 17 / 44 )9.818346938775510.0334232813747897293.757720215383
Trimmed Mean ( 18 / 44 )9.81756250.0328682904983677298.694040704294
Trimmed Mean ( 19 / 44 )9.817031914893620.0323128242620253303.812252228005
Trimmed Mean ( 20 / 44 )9.815902173913040.0317902603718638308.770738556161
Trimmed Mean ( 21 / 44 )9.8150.0312906035841301313.672440789156
Trimmed Mean ( 22 / 44 )9.8141250.0307471180718306319.188451323226
Trimmed Mean ( 23 / 44 )9.813325581395350.0301884887686381325.068460915808
Trimmed Mean ( 24 / 44 )9.813023809523810.0297039126338173330.361320762568
Trimmed Mean ( 25 / 44 )9.812670731707320.0292122256381181335.909726744787
Trimmed Mean ( 26 / 44 )9.81201250.028731639672586341.505483564937
Trimmed Mean ( 27 / 44 )9.811217948717950.0282896490770104346.812995877387
Trimmed Mean ( 28 / 44 )9.810421052631580.0278417348166249352.363856535749
Trimmed Mean ( 29 / 44 )9.810216216216220.0274615834812451357.234178535848
Trimmed Mean ( 30 / 44 )9.8098750.0271344745574157361.528098848666
Trimmed Mean ( 31 / 44 )9.809471428571430.0267679602168959366.463165257535
Trimmed Mean ( 32 / 44 )9.809044117647060.0263524636694596372.22493656314
Trimmed Mean ( 33 / 44 )9.808575757575760.0258617812589596379.269148530813
Trimmed Mean ( 34 / 44 )9.8080468750.0253139261276433387.456565431366
Trimmed Mean ( 35 / 44 )9.807596774193550.0246874964303518397.269800194712
Trimmed Mean ( 36 / 44 )9.807650.0241067051764292406.843238353022
Trimmed Mean ( 37 / 44 )9.807982758620690.0235525116586773416.430438534873
Trimmed Mean ( 38 / 44 )9.808071428571430.0230564645292003425.393555727064
Trimmed Mean ( 39 / 44 )9.808092592592590.0225232897325485435.464477394654
Trimmed Mean ( 40 / 44 )9.808365384615390.0219600629699841446.645594688042
Trimmed Mean ( 41 / 44 )9.808840.0213388475866559459.67055906683
Trimmed Mean ( 42 / 44 )9.809020833333330.020738781671869472.979608374908
Trimmed Mean ( 43 / 44 )9.809173913043480.02011633566837487.622302329492
Trimmed Mean ( 44 / 44 )9.809340909090910.0195079520616154502.838067169139
Median9.824
Midrange10.0715
Midmean - Weighted Average at Xnp9.80308955223881
Midmean - Weighted Average at X(n+1)p9.80857575757576
Midmean - Empirical Distribution Function9.80308955223881
Midmean - Empirical Distribution Function - Averaging9.80857575757576
Midmean - Empirical Distribution Function - Interpolation9.80857575757576
Midmean - Closest Observation9.80308955223881
Midmean - True Basic - Statistics Graphics Toolkit9.80857575757576
Midmean - MS Excel (old versions)9.80904411764706
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')