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 computationWed, 17 Dec 2014 16:14:22 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/17/t1418832877qh8pgu7xll663ho.htm/, Retrieved Sun, 19 May 2024 21:18:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270491, Retrieved Sun, 19 May 2024 21:18:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact60
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [] [2014-11-04 10:08:09] [32b17a345b130fdf5cc88718ed94a974]
- R  D  [Central Tendency] [] [2014-12-15 18:08:27] [6656361aa4da5489a6a45e803df0211c]
-    D    [Central Tendency] [] [2014-12-15 18:16:29] [6656361aa4da5489a6a45e803df0211c]
-   PD        [Central Tendency] [] [2014-12-17 16:14:22] [457d039f1491608548baeb848eb0333c] [Current]
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Dataseries X:
468,088
0,171424
129,737
-17,985
-186,775
-0,00291279
-724,803
-638,511
-332,531
0,886784
540,237
-0,854078
0,629996
129,495
328,387
-191,964
0,254265
182,544
133,117
492,768
196,708
0,832232
-143,274
-173,664
213,479
-311,883
159,726
0,517419
129,492
325,246
-222,581
385,626
-0,601865
280,522
0,363567
-0,0759941
167,576
-258,301
197,181
128,358
-473,549
-395,707
-0,877499
-256,221
269,252
-0,207211
287,527
-252,162
-209,929
217,166
-434,571
-629,709
-662,264
-0,262066
-0,0155961
-235,755
-4,951
-132,381
-606,649
-102,386
143,855
-166,305
-187,111
-310,378
-343,195
-235,383
0,233283
134,636
-204,059
-0,229175
-334,509
173,544
-532,583
257,923
-502,687
-828,448
-0,0256706
340,201
481,909
322,237
233,759
193,428
-347,631
-0,618713
31,483
165,483
18,704
288,749
118,952
0,883819
0,429261
0,600361
493,893
-554,906
114,545
288,783
188,765
190,776
-191,674
528,506
220,924
391,256
58,398
291,302
189,842
236,254
0,507146
361,777
525,397
-0,276251
-32,531
0,689749
-0,884549
517,259
-14,775
297,594
489,719
-0,186396
-465,557
-88,416
0,323765
-117,148
266,525
-0,549622
-169,771
0,376565




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270491&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270491&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270491&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean5.516420931825425.81146836036510.213719764207455
Geometric MeanNaN
Harmonic Mean-0.277950087558358
Quadratic Mean288.633709508545
Winsorized Mean ( 1 / 42 )6.2458971223015925.59581707174460.244020228180036
Winsorized Mean ( 2 / 42 )7.1892304556349225.3695299402580.283380514836681
Winsorized Mean ( 3 / 42 )7.5610161699206425.22038382356470.299797823174126
Winsorized Mean ( 4 / 42 )7.0986669635714325.04568959840230.283428688824134
Winsorized Mean ( 5 / 42 )7.9691034715079424.8551471265390.320621858761759
Winsorized Mean ( 6 / 42 )10.287865376269824.3598513637730.422328741774244
Winsorized Mean ( 7 / 42 )11.094143154047624.06454799381310.461016062171618
Winsorized Mean ( 8 / 42 )12.114778074682523.59073871802960.513539580912895
Winsorized Mean ( 9 / 42 )8.7080637889682522.43005139861560.388232003316127
Winsorized Mean ( 10 / 42 )8.8955241064285722.26069336134090.39960678501942
Winsorized Mean ( 11 / 42 )9.51859553521.52946635544270.442119436582954
Winsorized Mean ( 12 / 42 )11.165071725476220.66689814816530.540239355002937
Winsorized Mean ( 13 / 42 )14.906389185793719.756614387740.754501196067474
Winsorized Mean ( 14 / 42 )15.050278074682519.6402744787560.7662967282337
Winsorized Mean ( 15 / 42 )15.726111408015919.4451088188760.808743810821468
Winsorized Mean ( 16 / 42 )12.848016169920619.02400782600130.675358015378885
Winsorized Mean ( 17 / 42 )14.784936804841318.52359042979810.798167982652939
Winsorized Mean ( 18 / 42 )14.640079661984118.45039921074080.793483083740619
Winsorized Mean ( 19 / 42 )22.487833630238117.38782416890061.2933092382231
Winsorized Mean ( 20 / 42 )22.624024106428617.32149108616371.30612451283138
Winsorized Mean ( 21 / 42 )22.133024106428617.09248117382111.29489825855872
Winsorized Mean ( 22 / 42 )23.029960614365116.49218721570481.39641639481479
Winsorized Mean ( 23 / 42 )22.600079661984116.42436013476231.37600974872384
Winsorized Mean ( 24 / 42 )23.400079661984115.92661187593871.46924404539148
Winsorized Mean ( 25 / 42 )21.610992360396815.12011775521591.42928730518265
Winsorized Mean ( 26 / 42 )22.307420931825414.91394671032751.49574229847409
Winsorized Mean ( 27 / 42 )22.14884950325414.29218749202761.54971725046351
Winsorized Mean ( 28 / 42 )21.378182836587314.19191194501641.50636383028675
Winsorized Mean ( 29 / 42 )21.579801884206413.97265492865171.54443103292817
Winsorized Mean ( 30 / 42 )17.779325693730213.54415059403981.31269403498467
Winsorized Mean ( 31 / 42 )20.888674900079413.14587553703181.58899077062126
Winsorized Mean ( 32 / 42 )21.044357439761912.94007236252411.62629364428507
Winsorized Mean ( 33 / 42 )21.257547915952412.75922618939751.66605306626014
Winsorized Mean ( 34 / 42 )27.220230455634912.0135926894162.26578602749
Winsorized Mean ( 35 / 42 )29.946897122301611.64047173632972.57265322236365
Winsorized Mean ( 36 / 42 )32.521754265158710.96566576177772.96578018805913
Winsorized Mean ( 37 / 42 )34.213770138174610.20786712544453.35170606334523
Winsorized Mean ( 38 / 42 )36.62707172547629.565042087274423.82926404204806
Winsorized Mean ( 39 / 42 )53.2769764873817.813569568073826.81851950292606
Winsorized Mean ( 40 / 42 )56.06713521753977.210418252194187.77585061733112
Winsorized Mean ( 41 / 42 )51.94728601119056.537121950515277.94650710273132
Winsorized Mean ( 42 / 42 )52.14895267785715.933197293434938.78935085060458
Trimmed Mean ( 1 / 42 )7.9296777210483924.97180091063620.317545288360476
Trimmed Mean ( 2 / 42 )9.6686642410655824.28037812813060.398208964870432
Trimmed Mean ( 3 / 42 )10.970366978416723.64695562589570.463923016221295
Trimmed Mean ( 4 / 42 )12.183864723813623.00530133414420.529611177304181
Trimmed Mean ( 5 / 42 )13.564758943189722.34802044990340.6069780978408
Trimmed Mean ( 6 / 42 )14.80169331061421.66772570961010.683121685634461
Trimmed Mean ( 7 / 42 )15.648036048303621.02922255386650.744109108561719
Trimmed Mean ( 8 / 42 )16.393218521909120.37955802466360.804395193559635
Trimmed Mean ( 9 / 42 )17.017157753796319.7471224779640.861753795915626
Trimmed Mean ( 10 / 42 )18.114585258584919.25245189049360.940897573027019
Trimmed Mean ( 11 / 42 )19.231509975096218.72593988964811.02699838237372
Trimmed Mean ( 12 / 42 )20.322265072647118.25444970332591.11327733253686
Trimmed Mean ( 13 / 42 )21.283770374117.85855782200791.1917967053236
Trimmed Mean ( 14 / 42 )21.914500381734717.54720296271721.2488885224783
Trimmed Mean ( 15 / 42 )22.558021223020817.21122605419081.31065742510123
Trimmed Mean ( 16 / 42 )23.168532312872316.85744559753111.37437977651048
Trimmed Mean ( 17 / 42 )24.051946058804316.51108735639061.45671484497931
Trimmed Mean ( 18 / 42 )24.815111526777816.18407650695171.5333041410252
Trimmed Mean ( 19 / 42 )25.624489061477315.81932829211811.61982156184499
Trimmed Mean ( 20 / 42 )25.866360900116315.54337104676041.66414099118527
Trimmed Mean ( 21 / 42 )26.109536159642915.23399919041641.71389901189361
Trimmed Mean ( 22 / 42 )26.400500456219514.9063993981791.77108500523907
Trimmed Mean ( 23 / 42 )26.64180046762514.60530465352071.82411809268237
Trimmed Mean ( 24 / 42 )26.925667146282114.2637206852011.88770291710901
Trimmed Mean ( 25 / 42 )27.169211018552613.93169576023881.95017257670053
Trimmed Mean ( 26 / 42 )27.547770775810813.64910812984462.01828357675443
Trimmed Mean ( 27 / 42 )27.900486630694413.34366454475622.09091636987073
Trimmed Mean ( 28 / 42 )28.283929105857113.06616491833322.16466953253987
Trimmed Mean ( 29 / 42 )28.740927020735312.74908117260072.25435281426421
Trimmed Mean ( 30 / 42 )29.212349051666712.4015294243832.35554406654324
Trimmed Mean ( 31 / 42 )29.962641209531212.04420077398642.48772349214286
Trimmed Mean ( 32 / 42 )30.557500603387111.67608093238672.61710250043128
Trimmed Mean ( 33 / 42 )31.181800623511.26117326158492.76896553309148
Trimmed Mean ( 34 / 42 )31.835121334655210.78337460955482.9522410643554
Trimmed Mean ( 35 / 42 )32.140518525178610.3320039332433.11077296648786
Trimmed Mean ( 36 / 42 )32.2867599520379.841355628972263.28072281596928
Trimmed Mean ( 37 / 42 )32.27094302711549.358843110171583.44817651575353
Trimmed Mean ( 38 / 42 )32.13862074828.902918211181323.60989733768828
Trimmed Mean ( 39 / 42 )31.8285632793758.455936824515943.76404932296748
Trimmed Mean ( 40 / 42 )30.32215298717398.20040121882153.69764261260519
Trimmed Mean ( 41 / 42 )28.47904630477277.963049390927553.57639955583089
Trimmed Mean ( 42 / 42 )26.76185803357147.796245421936943.43265977213459
Median0.370066
Midrange-144.1055
Midmean - Weighted Average at Xnp27.3158894826984
Midmean - Weighted Average at X(n+1)p29.9626412095312
Midmean - Empirical Distribution Function29.9626412095312
Midmean - Empirical Distribution Function - Averaging29.9626412095312
Midmean - Empirical Distribution Function - Interpolation30.5575006033871
Midmean - Closest Observation29.9626412095312
Midmean - True Basic - Statistics Graphics Toolkit29.9626412095312
Midmean - MS Excel (old versions)29.9626412095312
Number of observations126

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 5.5164209318254 & 25.8114683603651 & 0.213719764207455 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -0.277950087558358 &  &  \tabularnewline
Quadratic Mean & 288.633709508545 &  &  \tabularnewline
Winsorized Mean ( 1 / 42 ) & 6.24589712230159 & 25.5958170717446 & 0.244020228180036 \tabularnewline
Winsorized Mean ( 2 / 42 ) & 7.18923045563492 & 25.369529940258 & 0.283380514836681 \tabularnewline
Winsorized Mean ( 3 / 42 ) & 7.56101616992064 & 25.2203838235647 & 0.299797823174126 \tabularnewline
Winsorized Mean ( 4 / 42 ) & 7.09866696357143 & 25.0456895984023 & 0.283428688824134 \tabularnewline
Winsorized Mean ( 5 / 42 ) & 7.96910347150794 & 24.855147126539 & 0.320621858761759 \tabularnewline
Winsorized Mean ( 6 / 42 ) & 10.2878653762698 & 24.359851363773 & 0.422328741774244 \tabularnewline
Winsorized Mean ( 7 / 42 ) & 11.0941431540476 & 24.0645479938131 & 0.461016062171618 \tabularnewline
Winsorized Mean ( 8 / 42 ) & 12.1147780746825 & 23.5907387180296 & 0.513539580912895 \tabularnewline
Winsorized Mean ( 9 / 42 ) & 8.70806378896825 & 22.4300513986156 & 0.388232003316127 \tabularnewline
Winsorized Mean ( 10 / 42 ) & 8.89552410642857 & 22.2606933613409 & 0.39960678501942 \tabularnewline
Winsorized Mean ( 11 / 42 ) & 9.518595535 & 21.5294663554427 & 0.442119436582954 \tabularnewline
Winsorized Mean ( 12 / 42 ) & 11.1650717254762 & 20.6668981481653 & 0.540239355002937 \tabularnewline
Winsorized Mean ( 13 / 42 ) & 14.9063891857937 & 19.75661438774 & 0.754501196067474 \tabularnewline
Winsorized Mean ( 14 / 42 ) & 15.0502780746825 & 19.640274478756 & 0.7662967282337 \tabularnewline
Winsorized Mean ( 15 / 42 ) & 15.7261114080159 & 19.445108818876 & 0.808743810821468 \tabularnewline
Winsorized Mean ( 16 / 42 ) & 12.8480161699206 & 19.0240078260013 & 0.675358015378885 \tabularnewline
Winsorized Mean ( 17 / 42 ) & 14.7849368048413 & 18.5235904297981 & 0.798167982652939 \tabularnewline
Winsorized Mean ( 18 / 42 ) & 14.6400796619841 & 18.4503992107408 & 0.793483083740619 \tabularnewline
Winsorized Mean ( 19 / 42 ) & 22.4878336302381 & 17.3878241689006 & 1.2933092382231 \tabularnewline
Winsorized Mean ( 20 / 42 ) & 22.6240241064286 & 17.3214910861637 & 1.30612451283138 \tabularnewline
Winsorized Mean ( 21 / 42 ) & 22.1330241064286 & 17.0924811738211 & 1.29489825855872 \tabularnewline
Winsorized Mean ( 22 / 42 ) & 23.0299606143651 & 16.4921872157048 & 1.39641639481479 \tabularnewline
Winsorized Mean ( 23 / 42 ) & 22.6000796619841 & 16.4243601347623 & 1.37600974872384 \tabularnewline
Winsorized Mean ( 24 / 42 ) & 23.4000796619841 & 15.9266118759387 & 1.46924404539148 \tabularnewline
Winsorized Mean ( 25 / 42 ) & 21.6109923603968 & 15.1201177552159 & 1.42928730518265 \tabularnewline
Winsorized Mean ( 26 / 42 ) & 22.3074209318254 & 14.9139467103275 & 1.49574229847409 \tabularnewline
Winsorized Mean ( 27 / 42 ) & 22.148849503254 & 14.2921874920276 & 1.54971725046351 \tabularnewline
Winsorized Mean ( 28 / 42 ) & 21.3781828365873 & 14.1919119450164 & 1.50636383028675 \tabularnewline
Winsorized Mean ( 29 / 42 ) & 21.5798018842064 & 13.9726549286517 & 1.54443103292817 \tabularnewline
Winsorized Mean ( 30 / 42 ) & 17.7793256937302 & 13.5441505940398 & 1.31269403498467 \tabularnewline
Winsorized Mean ( 31 / 42 ) & 20.8886749000794 & 13.1458755370318 & 1.58899077062126 \tabularnewline
Winsorized Mean ( 32 / 42 ) & 21.0443574397619 & 12.9400723625241 & 1.62629364428507 \tabularnewline
Winsorized Mean ( 33 / 42 ) & 21.2575479159524 & 12.7592261893975 & 1.66605306626014 \tabularnewline
Winsorized Mean ( 34 / 42 ) & 27.2202304556349 & 12.013592689416 & 2.26578602749 \tabularnewline
Winsorized Mean ( 35 / 42 ) & 29.9468971223016 & 11.6404717363297 & 2.57265322236365 \tabularnewline
Winsorized Mean ( 36 / 42 ) & 32.5217542651587 & 10.9656657617777 & 2.96578018805913 \tabularnewline
Winsorized Mean ( 37 / 42 ) & 34.2137701381746 & 10.2078671254445 & 3.35170606334523 \tabularnewline
Winsorized Mean ( 38 / 42 ) & 36.6270717254762 & 9.56504208727442 & 3.82926404204806 \tabularnewline
Winsorized Mean ( 39 / 42 ) & 53.276976487381 & 7.81356956807382 & 6.81851950292606 \tabularnewline
Winsorized Mean ( 40 / 42 ) & 56.0671352175397 & 7.21041825219418 & 7.77585061733112 \tabularnewline
Winsorized Mean ( 41 / 42 ) & 51.9472860111905 & 6.53712195051527 & 7.94650710273132 \tabularnewline
Winsorized Mean ( 42 / 42 ) & 52.1489526778571 & 5.93319729343493 & 8.78935085060458 \tabularnewline
Trimmed Mean ( 1 / 42 ) & 7.92967772104839 & 24.9718009106362 & 0.317545288360476 \tabularnewline
Trimmed Mean ( 2 / 42 ) & 9.66866424106558 & 24.2803781281306 & 0.398208964870432 \tabularnewline
Trimmed Mean ( 3 / 42 ) & 10.9703669784167 & 23.6469556258957 & 0.463923016221295 \tabularnewline
Trimmed Mean ( 4 / 42 ) & 12.1838647238136 & 23.0053013341442 & 0.529611177304181 \tabularnewline
Trimmed Mean ( 5 / 42 ) & 13.5647589431897 & 22.3480204499034 & 0.6069780978408 \tabularnewline
Trimmed Mean ( 6 / 42 ) & 14.801693310614 & 21.6677257096101 & 0.683121685634461 \tabularnewline
Trimmed Mean ( 7 / 42 ) & 15.6480360483036 & 21.0292225538665 & 0.744109108561719 \tabularnewline
Trimmed Mean ( 8 / 42 ) & 16.3932185219091 & 20.3795580246636 & 0.804395193559635 \tabularnewline
Trimmed Mean ( 9 / 42 ) & 17.0171577537963 & 19.747122477964 & 0.861753795915626 \tabularnewline
Trimmed Mean ( 10 / 42 ) & 18.1145852585849 & 19.2524518904936 & 0.940897573027019 \tabularnewline
Trimmed Mean ( 11 / 42 ) & 19.2315099750962 & 18.7259398896481 & 1.02699838237372 \tabularnewline
Trimmed Mean ( 12 / 42 ) & 20.3222650726471 & 18.2544497033259 & 1.11327733253686 \tabularnewline
Trimmed Mean ( 13 / 42 ) & 21.2837703741 & 17.8585578220079 & 1.1917967053236 \tabularnewline
Trimmed Mean ( 14 / 42 ) & 21.9145003817347 & 17.5472029627172 & 1.2488885224783 \tabularnewline
Trimmed Mean ( 15 / 42 ) & 22.5580212230208 & 17.2112260541908 & 1.31065742510123 \tabularnewline
Trimmed Mean ( 16 / 42 ) & 23.1685323128723 & 16.8574455975311 & 1.37437977651048 \tabularnewline
Trimmed Mean ( 17 / 42 ) & 24.0519460588043 & 16.5110873563906 & 1.45671484497931 \tabularnewline
Trimmed Mean ( 18 / 42 ) & 24.8151115267778 & 16.1840765069517 & 1.5333041410252 \tabularnewline
Trimmed Mean ( 19 / 42 ) & 25.6244890614773 & 15.8193282921181 & 1.61982156184499 \tabularnewline
Trimmed Mean ( 20 / 42 ) & 25.8663609001163 & 15.5433710467604 & 1.66414099118527 \tabularnewline
Trimmed Mean ( 21 / 42 ) & 26.1095361596429 & 15.2339991904164 & 1.71389901189361 \tabularnewline
Trimmed Mean ( 22 / 42 ) & 26.4005004562195 & 14.906399398179 & 1.77108500523907 \tabularnewline
Trimmed Mean ( 23 / 42 ) & 26.641800467625 & 14.6053046535207 & 1.82411809268237 \tabularnewline
Trimmed Mean ( 24 / 42 ) & 26.9256671462821 & 14.263720685201 & 1.88770291710901 \tabularnewline
Trimmed Mean ( 25 / 42 ) & 27.1692110185526 & 13.9316957602388 & 1.95017257670053 \tabularnewline
Trimmed Mean ( 26 / 42 ) & 27.5477707758108 & 13.6491081298446 & 2.01828357675443 \tabularnewline
Trimmed Mean ( 27 / 42 ) & 27.9004866306944 & 13.3436645447562 & 2.09091636987073 \tabularnewline
Trimmed Mean ( 28 / 42 ) & 28.2839291058571 & 13.0661649183332 & 2.16466953253987 \tabularnewline
Trimmed Mean ( 29 / 42 ) & 28.7409270207353 & 12.7490811726007 & 2.25435281426421 \tabularnewline
Trimmed Mean ( 30 / 42 ) & 29.2123490516667 & 12.401529424383 & 2.35554406654324 \tabularnewline
Trimmed Mean ( 31 / 42 ) & 29.9626412095312 & 12.0442007739864 & 2.48772349214286 \tabularnewline
Trimmed Mean ( 32 / 42 ) & 30.5575006033871 & 11.6760809323867 & 2.61710250043128 \tabularnewline
Trimmed Mean ( 33 / 42 ) & 31.1818006235 & 11.2611732615849 & 2.76896553309148 \tabularnewline
Trimmed Mean ( 34 / 42 ) & 31.8351213346552 & 10.7833746095548 & 2.9522410643554 \tabularnewline
Trimmed Mean ( 35 / 42 ) & 32.1405185251786 & 10.332003933243 & 3.11077296648786 \tabularnewline
Trimmed Mean ( 36 / 42 ) & 32.286759952037 & 9.84135562897226 & 3.28072281596928 \tabularnewline
Trimmed Mean ( 37 / 42 ) & 32.2709430271154 & 9.35884311017158 & 3.44817651575353 \tabularnewline
Trimmed Mean ( 38 / 42 ) & 32.1386207482 & 8.90291821118132 & 3.60989733768828 \tabularnewline
Trimmed Mean ( 39 / 42 ) & 31.828563279375 & 8.45593682451594 & 3.76404932296748 \tabularnewline
Trimmed Mean ( 40 / 42 ) & 30.3221529871739 & 8.2004012188215 & 3.69764261260519 \tabularnewline
Trimmed Mean ( 41 / 42 ) & 28.4790463047727 & 7.96304939092755 & 3.57639955583089 \tabularnewline
Trimmed Mean ( 42 / 42 ) & 26.7618580335714 & 7.79624542193694 & 3.43265977213459 \tabularnewline
Median & 0.370066 &  &  \tabularnewline
Midrange & -144.1055 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 27.3158894826984 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 29.9626412095312 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 29.9626412095312 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 29.9626412095312 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 30.5575006033871 &  &  \tabularnewline
Midmean - Closest Observation & 29.9626412095312 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 29.9626412095312 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 29.9626412095312 &  &  \tabularnewline
Number of observations & 126 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270491&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]5.5164209318254[/C][C]25.8114683603651[/C][C]0.213719764207455[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-0.277950087558358[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]288.633709508545[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 42 )[/C][C]6.24589712230159[/C][C]25.5958170717446[/C][C]0.244020228180036[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 42 )[/C][C]7.18923045563492[/C][C]25.369529940258[/C][C]0.283380514836681[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 42 )[/C][C]7.56101616992064[/C][C]25.2203838235647[/C][C]0.299797823174126[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 42 )[/C][C]7.09866696357143[/C][C]25.0456895984023[/C][C]0.283428688824134[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 42 )[/C][C]7.96910347150794[/C][C]24.855147126539[/C][C]0.320621858761759[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 42 )[/C][C]10.2878653762698[/C][C]24.359851363773[/C][C]0.422328741774244[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 42 )[/C][C]11.0941431540476[/C][C]24.0645479938131[/C][C]0.461016062171618[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 42 )[/C][C]12.1147780746825[/C][C]23.5907387180296[/C][C]0.513539580912895[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 42 )[/C][C]8.70806378896825[/C][C]22.4300513986156[/C][C]0.388232003316127[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 42 )[/C][C]8.89552410642857[/C][C]22.2606933613409[/C][C]0.39960678501942[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 42 )[/C][C]9.518595535[/C][C]21.5294663554427[/C][C]0.442119436582954[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 42 )[/C][C]11.1650717254762[/C][C]20.6668981481653[/C][C]0.540239355002937[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 42 )[/C][C]14.9063891857937[/C][C]19.75661438774[/C][C]0.754501196067474[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 42 )[/C][C]15.0502780746825[/C][C]19.640274478756[/C][C]0.7662967282337[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 42 )[/C][C]15.7261114080159[/C][C]19.445108818876[/C][C]0.808743810821468[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 42 )[/C][C]12.8480161699206[/C][C]19.0240078260013[/C][C]0.675358015378885[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 42 )[/C][C]14.7849368048413[/C][C]18.5235904297981[/C][C]0.798167982652939[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 42 )[/C][C]14.6400796619841[/C][C]18.4503992107408[/C][C]0.793483083740619[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 42 )[/C][C]22.4878336302381[/C][C]17.3878241689006[/C][C]1.2933092382231[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 42 )[/C][C]22.6240241064286[/C][C]17.3214910861637[/C][C]1.30612451283138[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 42 )[/C][C]22.1330241064286[/C][C]17.0924811738211[/C][C]1.29489825855872[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 42 )[/C][C]23.0299606143651[/C][C]16.4921872157048[/C][C]1.39641639481479[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 42 )[/C][C]22.6000796619841[/C][C]16.4243601347623[/C][C]1.37600974872384[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 42 )[/C][C]23.4000796619841[/C][C]15.9266118759387[/C][C]1.46924404539148[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 42 )[/C][C]21.6109923603968[/C][C]15.1201177552159[/C][C]1.42928730518265[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 42 )[/C][C]22.3074209318254[/C][C]14.9139467103275[/C][C]1.49574229847409[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 42 )[/C][C]22.148849503254[/C][C]14.2921874920276[/C][C]1.54971725046351[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 42 )[/C][C]21.3781828365873[/C][C]14.1919119450164[/C][C]1.50636383028675[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 42 )[/C][C]21.5798018842064[/C][C]13.9726549286517[/C][C]1.54443103292817[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 42 )[/C][C]17.7793256937302[/C][C]13.5441505940398[/C][C]1.31269403498467[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 42 )[/C][C]20.8886749000794[/C][C]13.1458755370318[/C][C]1.58899077062126[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 42 )[/C][C]21.0443574397619[/C][C]12.9400723625241[/C][C]1.62629364428507[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 42 )[/C][C]21.2575479159524[/C][C]12.7592261893975[/C][C]1.66605306626014[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 42 )[/C][C]27.2202304556349[/C][C]12.013592689416[/C][C]2.26578602749[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 42 )[/C][C]29.9468971223016[/C][C]11.6404717363297[/C][C]2.57265322236365[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 42 )[/C][C]32.5217542651587[/C][C]10.9656657617777[/C][C]2.96578018805913[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 42 )[/C][C]34.2137701381746[/C][C]10.2078671254445[/C][C]3.35170606334523[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 42 )[/C][C]36.6270717254762[/C][C]9.56504208727442[/C][C]3.82926404204806[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 42 )[/C][C]53.276976487381[/C][C]7.81356956807382[/C][C]6.81851950292606[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 42 )[/C][C]56.0671352175397[/C][C]7.21041825219418[/C][C]7.77585061733112[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 42 )[/C][C]51.9472860111905[/C][C]6.53712195051527[/C][C]7.94650710273132[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 42 )[/C][C]52.1489526778571[/C][C]5.93319729343493[/C][C]8.78935085060458[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 42 )[/C][C]7.92967772104839[/C][C]24.9718009106362[/C][C]0.317545288360476[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 42 )[/C][C]9.66866424106558[/C][C]24.2803781281306[/C][C]0.398208964870432[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 42 )[/C][C]10.9703669784167[/C][C]23.6469556258957[/C][C]0.463923016221295[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 42 )[/C][C]12.1838647238136[/C][C]23.0053013341442[/C][C]0.529611177304181[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 42 )[/C][C]13.5647589431897[/C][C]22.3480204499034[/C][C]0.6069780978408[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 42 )[/C][C]14.801693310614[/C][C]21.6677257096101[/C][C]0.683121685634461[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 42 )[/C][C]15.6480360483036[/C][C]21.0292225538665[/C][C]0.744109108561719[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 42 )[/C][C]16.3932185219091[/C][C]20.3795580246636[/C][C]0.804395193559635[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 42 )[/C][C]17.0171577537963[/C][C]19.747122477964[/C][C]0.861753795915626[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 42 )[/C][C]18.1145852585849[/C][C]19.2524518904936[/C][C]0.940897573027019[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 42 )[/C][C]19.2315099750962[/C][C]18.7259398896481[/C][C]1.02699838237372[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 42 )[/C][C]20.3222650726471[/C][C]18.2544497033259[/C][C]1.11327733253686[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 42 )[/C][C]21.2837703741[/C][C]17.8585578220079[/C][C]1.1917967053236[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 42 )[/C][C]21.9145003817347[/C][C]17.5472029627172[/C][C]1.2488885224783[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 42 )[/C][C]22.5580212230208[/C][C]17.2112260541908[/C][C]1.31065742510123[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 42 )[/C][C]23.1685323128723[/C][C]16.8574455975311[/C][C]1.37437977651048[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 42 )[/C][C]24.0519460588043[/C][C]16.5110873563906[/C][C]1.45671484497931[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 42 )[/C][C]24.8151115267778[/C][C]16.1840765069517[/C][C]1.5333041410252[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 42 )[/C][C]25.6244890614773[/C][C]15.8193282921181[/C][C]1.61982156184499[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 42 )[/C][C]25.8663609001163[/C][C]15.5433710467604[/C][C]1.66414099118527[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 42 )[/C][C]26.1095361596429[/C][C]15.2339991904164[/C][C]1.71389901189361[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 42 )[/C][C]26.4005004562195[/C][C]14.906399398179[/C][C]1.77108500523907[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 42 )[/C][C]26.641800467625[/C][C]14.6053046535207[/C][C]1.82411809268237[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 42 )[/C][C]26.9256671462821[/C][C]14.263720685201[/C][C]1.88770291710901[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 42 )[/C][C]27.1692110185526[/C][C]13.9316957602388[/C][C]1.95017257670053[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 42 )[/C][C]27.5477707758108[/C][C]13.6491081298446[/C][C]2.01828357675443[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 42 )[/C][C]27.9004866306944[/C][C]13.3436645447562[/C][C]2.09091636987073[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 42 )[/C][C]28.2839291058571[/C][C]13.0661649183332[/C][C]2.16466953253987[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 42 )[/C][C]28.7409270207353[/C][C]12.7490811726007[/C][C]2.25435281426421[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 42 )[/C][C]29.2123490516667[/C][C]12.401529424383[/C][C]2.35554406654324[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 42 )[/C][C]29.9626412095312[/C][C]12.0442007739864[/C][C]2.48772349214286[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 42 )[/C][C]30.5575006033871[/C][C]11.6760809323867[/C][C]2.61710250043128[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 42 )[/C][C]31.1818006235[/C][C]11.2611732615849[/C][C]2.76896553309148[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 42 )[/C][C]31.8351213346552[/C][C]10.7833746095548[/C][C]2.9522410643554[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 42 )[/C][C]32.1405185251786[/C][C]10.332003933243[/C][C]3.11077296648786[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 42 )[/C][C]32.286759952037[/C][C]9.84135562897226[/C][C]3.28072281596928[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 42 )[/C][C]32.2709430271154[/C][C]9.35884311017158[/C][C]3.44817651575353[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 42 )[/C][C]32.1386207482[/C][C]8.90291821118132[/C][C]3.60989733768828[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 42 )[/C][C]31.828563279375[/C][C]8.45593682451594[/C][C]3.76404932296748[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 42 )[/C][C]30.3221529871739[/C][C]8.2004012188215[/C][C]3.69764261260519[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 42 )[/C][C]28.4790463047727[/C][C]7.96304939092755[/C][C]3.57639955583089[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 42 )[/C][C]26.7618580335714[/C][C]7.79624542193694[/C][C]3.43265977213459[/C][/ROW]
[ROW][C]Median[/C][C]0.370066[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-144.1055[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]27.3158894826984[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]29.9626412095312[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]29.9626412095312[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]29.9626412095312[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]30.5575006033871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]29.9626412095312[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]29.9626412095312[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]29.9626412095312[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]126[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270491&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270491&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 Mean5.516420931825425.81146836036510.213719764207455
Geometric MeanNaN
Harmonic Mean-0.277950087558358
Quadratic Mean288.633709508545
Winsorized Mean ( 1 / 42 )6.2458971223015925.59581707174460.244020228180036
Winsorized Mean ( 2 / 42 )7.1892304556349225.3695299402580.283380514836681
Winsorized Mean ( 3 / 42 )7.5610161699206425.22038382356470.299797823174126
Winsorized Mean ( 4 / 42 )7.0986669635714325.04568959840230.283428688824134
Winsorized Mean ( 5 / 42 )7.9691034715079424.8551471265390.320621858761759
Winsorized Mean ( 6 / 42 )10.287865376269824.3598513637730.422328741774244
Winsorized Mean ( 7 / 42 )11.094143154047624.06454799381310.461016062171618
Winsorized Mean ( 8 / 42 )12.114778074682523.59073871802960.513539580912895
Winsorized Mean ( 9 / 42 )8.7080637889682522.43005139861560.388232003316127
Winsorized Mean ( 10 / 42 )8.8955241064285722.26069336134090.39960678501942
Winsorized Mean ( 11 / 42 )9.51859553521.52946635544270.442119436582954
Winsorized Mean ( 12 / 42 )11.165071725476220.66689814816530.540239355002937
Winsorized Mean ( 13 / 42 )14.906389185793719.756614387740.754501196067474
Winsorized Mean ( 14 / 42 )15.050278074682519.6402744787560.7662967282337
Winsorized Mean ( 15 / 42 )15.726111408015919.4451088188760.808743810821468
Winsorized Mean ( 16 / 42 )12.848016169920619.02400782600130.675358015378885
Winsorized Mean ( 17 / 42 )14.784936804841318.52359042979810.798167982652939
Winsorized Mean ( 18 / 42 )14.640079661984118.45039921074080.793483083740619
Winsorized Mean ( 19 / 42 )22.487833630238117.38782416890061.2933092382231
Winsorized Mean ( 20 / 42 )22.624024106428617.32149108616371.30612451283138
Winsorized Mean ( 21 / 42 )22.133024106428617.09248117382111.29489825855872
Winsorized Mean ( 22 / 42 )23.029960614365116.49218721570481.39641639481479
Winsorized Mean ( 23 / 42 )22.600079661984116.42436013476231.37600974872384
Winsorized Mean ( 24 / 42 )23.400079661984115.92661187593871.46924404539148
Winsorized Mean ( 25 / 42 )21.610992360396815.12011775521591.42928730518265
Winsorized Mean ( 26 / 42 )22.307420931825414.91394671032751.49574229847409
Winsorized Mean ( 27 / 42 )22.14884950325414.29218749202761.54971725046351
Winsorized Mean ( 28 / 42 )21.378182836587314.19191194501641.50636383028675
Winsorized Mean ( 29 / 42 )21.579801884206413.97265492865171.54443103292817
Winsorized Mean ( 30 / 42 )17.779325693730213.54415059403981.31269403498467
Winsorized Mean ( 31 / 42 )20.888674900079413.14587553703181.58899077062126
Winsorized Mean ( 32 / 42 )21.044357439761912.94007236252411.62629364428507
Winsorized Mean ( 33 / 42 )21.257547915952412.75922618939751.66605306626014
Winsorized Mean ( 34 / 42 )27.220230455634912.0135926894162.26578602749
Winsorized Mean ( 35 / 42 )29.946897122301611.64047173632972.57265322236365
Winsorized Mean ( 36 / 42 )32.521754265158710.96566576177772.96578018805913
Winsorized Mean ( 37 / 42 )34.213770138174610.20786712544453.35170606334523
Winsorized Mean ( 38 / 42 )36.62707172547629.565042087274423.82926404204806
Winsorized Mean ( 39 / 42 )53.2769764873817.813569568073826.81851950292606
Winsorized Mean ( 40 / 42 )56.06713521753977.210418252194187.77585061733112
Winsorized Mean ( 41 / 42 )51.94728601119056.537121950515277.94650710273132
Winsorized Mean ( 42 / 42 )52.14895267785715.933197293434938.78935085060458
Trimmed Mean ( 1 / 42 )7.9296777210483924.97180091063620.317545288360476
Trimmed Mean ( 2 / 42 )9.6686642410655824.28037812813060.398208964870432
Trimmed Mean ( 3 / 42 )10.970366978416723.64695562589570.463923016221295
Trimmed Mean ( 4 / 42 )12.183864723813623.00530133414420.529611177304181
Trimmed Mean ( 5 / 42 )13.564758943189722.34802044990340.6069780978408
Trimmed Mean ( 6 / 42 )14.80169331061421.66772570961010.683121685634461
Trimmed Mean ( 7 / 42 )15.648036048303621.02922255386650.744109108561719
Trimmed Mean ( 8 / 42 )16.393218521909120.37955802466360.804395193559635
Trimmed Mean ( 9 / 42 )17.017157753796319.7471224779640.861753795915626
Trimmed Mean ( 10 / 42 )18.114585258584919.25245189049360.940897573027019
Trimmed Mean ( 11 / 42 )19.231509975096218.72593988964811.02699838237372
Trimmed Mean ( 12 / 42 )20.322265072647118.25444970332591.11327733253686
Trimmed Mean ( 13 / 42 )21.283770374117.85855782200791.1917967053236
Trimmed Mean ( 14 / 42 )21.914500381734717.54720296271721.2488885224783
Trimmed Mean ( 15 / 42 )22.558021223020817.21122605419081.31065742510123
Trimmed Mean ( 16 / 42 )23.168532312872316.85744559753111.37437977651048
Trimmed Mean ( 17 / 42 )24.051946058804316.51108735639061.45671484497931
Trimmed Mean ( 18 / 42 )24.815111526777816.18407650695171.5333041410252
Trimmed Mean ( 19 / 42 )25.624489061477315.81932829211811.61982156184499
Trimmed Mean ( 20 / 42 )25.866360900116315.54337104676041.66414099118527
Trimmed Mean ( 21 / 42 )26.109536159642915.23399919041641.71389901189361
Trimmed Mean ( 22 / 42 )26.400500456219514.9063993981791.77108500523907
Trimmed Mean ( 23 / 42 )26.64180046762514.60530465352071.82411809268237
Trimmed Mean ( 24 / 42 )26.925667146282114.2637206852011.88770291710901
Trimmed Mean ( 25 / 42 )27.169211018552613.93169576023881.95017257670053
Trimmed Mean ( 26 / 42 )27.547770775810813.64910812984462.01828357675443
Trimmed Mean ( 27 / 42 )27.900486630694413.34366454475622.09091636987073
Trimmed Mean ( 28 / 42 )28.283929105857113.06616491833322.16466953253987
Trimmed Mean ( 29 / 42 )28.740927020735312.74908117260072.25435281426421
Trimmed Mean ( 30 / 42 )29.212349051666712.4015294243832.35554406654324
Trimmed Mean ( 31 / 42 )29.962641209531212.04420077398642.48772349214286
Trimmed Mean ( 32 / 42 )30.557500603387111.67608093238672.61710250043128
Trimmed Mean ( 33 / 42 )31.181800623511.26117326158492.76896553309148
Trimmed Mean ( 34 / 42 )31.835121334655210.78337460955482.9522410643554
Trimmed Mean ( 35 / 42 )32.140518525178610.3320039332433.11077296648786
Trimmed Mean ( 36 / 42 )32.2867599520379.841355628972263.28072281596928
Trimmed Mean ( 37 / 42 )32.27094302711549.358843110171583.44817651575353
Trimmed Mean ( 38 / 42 )32.13862074828.902918211181323.60989733768828
Trimmed Mean ( 39 / 42 )31.8285632793758.455936824515943.76404932296748
Trimmed Mean ( 40 / 42 )30.32215298717398.20040121882153.69764261260519
Trimmed Mean ( 41 / 42 )28.47904630477277.963049390927553.57639955583089
Trimmed Mean ( 42 / 42 )26.76185803357147.796245421936943.43265977213459
Median0.370066
Midrange-144.1055
Midmean - Weighted Average at Xnp27.3158894826984
Midmean - Weighted Average at X(n+1)p29.9626412095312
Midmean - Empirical Distribution Function29.9626412095312
Midmean - Empirical Distribution Function - Averaging29.9626412095312
Midmean - Empirical Distribution Function - Interpolation30.5575006033871
Midmean - Closest Observation29.9626412095312
Midmean - True Basic - Statistics Graphics Toolkit29.9626412095312
Midmean - MS Excel (old versions)29.9626412095312
Number of observations126



Parameters (Session):
par1 = 7 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
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')