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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 30 Nov 2007 07:03:39 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Nov/30/t1196430762vik8dejc3siouug.htm/, Retrieved Sat, 27 Apr 2024 22:58:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7689, Retrieved Sat, 27 Apr 2024 22:58:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsG29 paper
Estimated Impact193
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper G29 central...] [2007-11-30 14:03:39] [8e05505c645e933583b5ad9ab4281af9] [Current]
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Dataseries X:
145,9
158,5
152,2
153,7
157,9
154,4
150,7
151,2
147,3
146,6
145,2
139,3
145,7
163,3
181,8
188,1
222,9
206,3
184,9
183,6
186,6
176,5
173,9
184,9
182,5
183,6
172,4
168,9
163,3
152,4
145,8
148,6
143,4
141,2
144,6
144,5
140,8
133,3
127,3
119,6
120,2
121,9
112,4
111
107,8
110,5
118,3
123
112,1
104,2
102,4
100,3
102,6
101,5
103,4
99,4
97,9
98
90,2
87,1
91,8
94,8
91,8
89,3
91,7
86,2
82,8
82,3
79,8
79,4
85,3
87,5
88,3
88,6
94,9
94,7
92,6
91,8
96,4
96,4
107,1
111,9
107,8
109,2
115,3
119,2
107,8
106,8
104,2
94,8
97,5
98,3
100,6
94,9
93,6
98
104,3
103,9
105,3
102,6
103,3
107,9
107,8
109,8
110,6
110,8
119,3
128,1
127,6
137,9
151,4
143,6
143,4
141,9
135,2
133,1
129,6
134,1
136,8
143,5
162,5
163,1
157,2
158,8
155,4
148,5
154,2
153,3
149,4
147,9
156
163
159,1
159,5
157,3
156,4
156,6
162,4
166,8
162,6
168,1




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7689&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7689&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7689&T=0

As an alternative you can also use a QR Code:  

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

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean129.6531914893622.6429234054055449.0567343813989
Geometric Mean125.925004380601
Harmonic Mean122.302162165636
Quadratic Mean133.371122215923
Winsorized Mean ( 1 / 47 )129.5382978723402.6153493724537849.530016615258
Winsorized Mean ( 2 / 47 )129.3156028368792.5623430900511150.4677157945699
Winsorized Mean ( 3 / 47 )129.2943262411352.5557840659061350.5889084942294
Winsorized Mean ( 4 / 47 )129.3170212765962.5391519772102350.9292166980397
Winsorized Mean ( 5 / 47 )129.3489361702132.5352361042668651.0204694357719
Winsorized Mean ( 6 / 47 )129.3319148936172.5220372828083551.2807307708008
Winsorized Mean ( 7 / 47 )129.3517730496452.5196716634569851.3367574536182
Winsorized Mean ( 8 / 47 )129.3347517730502.5047929710006151.6349068647311
Winsorized Mean ( 9 / 47 )129.3092198581562.4958139017416551.8104413826369
Winsorized Mean ( 10 / 47 )128.9829787234042.4355836752939752.9577283801742
Winsorized Mean ( 11 / 47 )128.8503546099292.3997225489984753.6938550099074
Winsorized Mean ( 12 / 47 )128.8503546099292.3682819717217054.4066779836427
Winsorized Mean ( 13 / 47 )128.5368794326242.3260433401836955.2598815387823
Winsorized Mean ( 14 / 47 )128.4574468085112.3162651683986755.4588691144194
Winsorized Mean ( 15 / 47 )128.3191489361702.2995457713872155.8019546872343
Winsorized Mean ( 16 / 47 )128.0127659574472.2432112717237557.0667451483863
Winsorized Mean ( 17 / 47 )128.1333333333332.2297442769734257.4654836684937
Winsorized Mean ( 18 / 47 )128.2482269503552.2114930986248557.9916921423368
Winsorized Mean ( 19 / 47 )128.2482269503552.2085184631934558.06980067756
Winsorized Mean ( 20 / 47 )128.1914893617022.2021637810349758.2116055425518
Winsorized Mean ( 21 / 47 )128.1914893617022.1988908711400658.2982498332165
Winsorized Mean ( 22 / 47 )128.1758865248232.197153427067958.33724898123
Winsorized Mean ( 23 / 47 )127.9475177304962.1194187283926960.3691550029514
Winsorized Mean ( 24 / 47 )127.8794326241132.1122044927947860.5431117395781
Winsorized Mean ( 25 / 47 )128.0212765957452.0860196602158761.3710786323541
Winsorized Mean ( 26 / 47 )128.0397163120572.0725156339876561.7798554627549
Winsorized Mean ( 27 / 47 )127.9439716312062.0585240206667362.1532565793262
Winsorized Mean ( 28 / 47 )127.8248226950352.0462016992839162.4693170471754
Winsorized Mean ( 29 / 47 )127.8659574468082.0376767344082262.750855073164
Winsorized Mean ( 30 / 47 )127.9723404255322.0005204759395763.9695229139948
Winsorized Mean ( 31 / 47 )128.1262411347521.9759802936675764.8418618066983
Winsorized Mean ( 32 / 47 )128.1035460992911.959889688226865.3626307994873
Winsorized Mean ( 33 / 47 )128.1737588652481.9246725389948266.595099305666
Winsorized Mean ( 34 / 47 )128.1496453900711.8790935386414468.1975871636073
Winsorized Mean ( 35 / 47 )128.1496453900711.8692926304652068.5551546619957
Winsorized Mean ( 36 / 47 )128.0219858156031.8566330313142568.9538447589613
Winsorized Mean ( 37 / 47 )128.1007092198581.8283998730305170.0616484989882
Winsorized Mean ( 38 / 47 )127.8851063829791.8020620115819770.9659853884345
Winsorized Mean ( 39 / 47 )127.9680851063831.7833123555893771.7586488453901
Winsorized Mean ( 40 / 47 )127.8262411347521.7532007623950272.910213066603
Winsorized Mean ( 41 / 47 )127.7680851063831.7476231707259173.1096309814385
Winsorized Mean ( 42 / 47 )127.6489361702131.7305358778541173.7626638105297
Winsorized Mean ( 43 / 47 )127.5574468085111.6638145507274376.6656637019684
Winsorized Mean ( 44 / 47 )127.7758865248231.5961351182825480.053301917391
Winsorized Mean ( 45 / 47 )127.8397163120571.5841911117839180.6971553880897
Winsorized Mean ( 46 / 47 )127.8723404255321.5447328903456782.7795803563926
Winsorized Mean ( 47 / 47 )127.6723404255321.5262860959167083.6490227927099
Trimmed Mean ( 1 / 47 )129.3438848920862.5695529883238250.3371152413791
Trimmed Mean ( 2 / 47 )129.1437956204382.5194477280024751.2587715891326
Trimmed Mean ( 3 / 47 )129.0540740740742.4948541319715151.728104028307
Trimmed Mean ( 4 / 47 )128.9691729323312.4704404621583152.2049306218279
Trimmed Mean ( 5 / 47 )128.8755725190842.4486409982335652.6314688890917
Trimmed Mean ( 6 / 47 )128.7720930232562.4255868128270153.0890472945689
Trimmed Mean ( 7 / 47 )128.6685039370082.4030229006610853.5444351785455
Trimmed Mean ( 8 / 47 )128.55842.3785333469557854.0494419237547
Trimmed Mean ( 9 / 47 )128.4471544715452.3540718847341154.5638199515104
Trimmed Mean ( 10 / 47 )128.3355371900832.3284418995881755.1164867857692
Trimmed Mean ( 11 / 47 )128.2588235294122.3092049695027255.5424162096065
Trimmed Mean ( 12 / 47 )128.1940170940172.2927805075794355.9120319935711
Trimmed Mean ( 13 / 47 )128.1269565217392.278466277183256.2338612622078
Trimmed Mean ( 14 / 47 )128.0876106194692.2675969882340956.4860560690807
Trimmed Mean ( 15 / 47 )128.0540540540542.2562897014082856.7542607556682
Trimmed Mean ( 16 / 47 )128.0311926605502.2452338227613257.0235453263796
Trimmed Mean ( 17 / 47 )128.0327102803742.2387136454407857.1903023600706
Trimmed Mean ( 18 / 47 )128.0247619047622.2322740015198657.3517237658079
Trimmed Mean ( 19 / 47 )128.0077669902912.2263421674668057.4968973147297
Trimmed Mean ( 20 / 47 )127.9900990099012.2193298002501157.6706080346764
Trimmed Mean ( 21 / 47 )127.9757575757582.2114407506390757.8698559022099
Trimmed Mean ( 22 / 47 )127.9608247422682.2022274516789458.1051810269247
Trimmed Mean ( 23 / 47 )127.9463157894742.1913577635254658.3867764173904
Trimmed Mean ( 24 / 47 )127.9462365591402.1861556827753558.5256748031369
Trimmed Mean ( 25 / 47 )127.9505494505492.1801011355523358.6901898099938
Trimmed Mean ( 26 / 47 )127.9460674157302.1748997935070958.8284884653989
Trimmed Mean ( 27 / 47 )127.9402298850572.1693390012026258.9765960111035
Trimmed Mean ( 28 / 47 )127.942.1633736233424159.1391143071869
Trimmed Mean ( 29 / 47 )127.9469879518072.1567335646682959.3244293351023
Trimmed Mean ( 30 / 47 )127.9518518518522.1489095074782959.5426896323807
Trimmed Mean ( 31 / 47 )127.9506329113922.1425768938929259.7181054626771
Trimmed Mean ( 32 / 47 )127.9402597402602.1365534780722359.8816088870838
Trimmed Mean ( 33 / 47 )127.9306666666672.1299545089532360.0626286284106
Trimmed Mean ( 34 / 47 )127.9164383561642.1246165503251760.2068351282431
Trimmed Mean ( 35 / 47 )127.9028169014082.1217034762593460.2830783531104
Trimmed Mean ( 36 / 47 )127.8884057971012.1176646487347360.3912455513259
Trimmed Mean ( 37 / 47 )127.8805970149252.1125898574858160.5326190324116
Trimmed Mean ( 38 / 47 )127.8676923076922.1079737670015960.6590529300434
Trimmed Mean ( 39 / 47 )127.8666666666672.1036067337605160.7844919939411
Trimmed Mean ( 40 / 47 )127.8606557377052.0985400580754160.9283845908414
Trimmed Mean ( 41 / 47 )127.8627118644072.0939531911472861.0628319701601
Trimmed Mean ( 42 / 47 )127.8684210526322.0867528196141361.2762660966603
Trimmed Mean ( 43 / 47 )127.8818181818182.0778551666716161.5451068164025
Trimmed Mean ( 44 / 47 )127.9018867924532.0735680014524761.6820315045668
Trimmed Mean ( 45 / 47 )127.9098039215692.0747052800894661.6520356645805
Trimmed Mean ( 46 / 47 )127.9142857142862.0742202042652861.6686142827322
Trimmed Mean ( 47 / 47 )127.9170212765962.0757182124712861.6254270488391
Median128.1
Midrange151.15
Midmean - Weighted Average at Xnp127.527142857143
Midmean - Weighted Average at X(n+1)p127.902816901408
Midmean - Empirical Distribution Function127.902816901408
Midmean - Empirical Distribution Function - Averaging127.902816901408
Midmean - Empirical Distribution Function - Interpolation127.902816901408
Midmean - Closest Observation127.548611111111
Midmean - True Basic - Statistics Graphics Toolkit127.902816901408
Midmean - MS Excel (old versions)127.902816901408
Number of observations141

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 129.653191489362 & 2.64292340540554 & 49.0567343813989 \tabularnewline
Geometric Mean & 125.925004380601 &  &  \tabularnewline
Harmonic Mean & 122.302162165636 &  &  \tabularnewline
Quadratic Mean & 133.371122215923 &  &  \tabularnewline
Winsorized Mean ( 1 / 47 ) & 129.538297872340 & 2.61534937245378 & 49.530016615258 \tabularnewline
Winsorized Mean ( 2 / 47 ) & 129.315602836879 & 2.56234309005111 & 50.4677157945699 \tabularnewline
Winsorized Mean ( 3 / 47 ) & 129.294326241135 & 2.55578406590613 & 50.5889084942294 \tabularnewline
Winsorized Mean ( 4 / 47 ) & 129.317021276596 & 2.53915197721023 & 50.9292166980397 \tabularnewline
Winsorized Mean ( 5 / 47 ) & 129.348936170213 & 2.53523610426686 & 51.0204694357719 \tabularnewline
Winsorized Mean ( 6 / 47 ) & 129.331914893617 & 2.52203728280835 & 51.2807307708008 \tabularnewline
Winsorized Mean ( 7 / 47 ) & 129.351773049645 & 2.51967166345698 & 51.3367574536182 \tabularnewline
Winsorized Mean ( 8 / 47 ) & 129.334751773050 & 2.50479297100061 & 51.6349068647311 \tabularnewline
Winsorized Mean ( 9 / 47 ) & 129.309219858156 & 2.49581390174165 & 51.8104413826369 \tabularnewline
Winsorized Mean ( 10 / 47 ) & 128.982978723404 & 2.43558367529397 & 52.9577283801742 \tabularnewline
Winsorized Mean ( 11 / 47 ) & 128.850354609929 & 2.39972254899847 & 53.6938550099074 \tabularnewline
Winsorized Mean ( 12 / 47 ) & 128.850354609929 & 2.36828197172170 & 54.4066779836427 \tabularnewline
Winsorized Mean ( 13 / 47 ) & 128.536879432624 & 2.32604334018369 & 55.2598815387823 \tabularnewline
Winsorized Mean ( 14 / 47 ) & 128.457446808511 & 2.31626516839867 & 55.4588691144194 \tabularnewline
Winsorized Mean ( 15 / 47 ) & 128.319148936170 & 2.29954577138721 & 55.8019546872343 \tabularnewline
Winsorized Mean ( 16 / 47 ) & 128.012765957447 & 2.24321127172375 & 57.0667451483863 \tabularnewline
Winsorized Mean ( 17 / 47 ) & 128.133333333333 & 2.22974427697342 & 57.4654836684937 \tabularnewline
Winsorized Mean ( 18 / 47 ) & 128.248226950355 & 2.21149309862485 & 57.9916921423368 \tabularnewline
Winsorized Mean ( 19 / 47 ) & 128.248226950355 & 2.20851846319345 & 58.06980067756 \tabularnewline
Winsorized Mean ( 20 / 47 ) & 128.191489361702 & 2.20216378103497 & 58.2116055425518 \tabularnewline
Winsorized Mean ( 21 / 47 ) & 128.191489361702 & 2.19889087114006 & 58.2982498332165 \tabularnewline
Winsorized Mean ( 22 / 47 ) & 128.175886524823 & 2.1971534270679 & 58.33724898123 \tabularnewline
Winsorized Mean ( 23 / 47 ) & 127.947517730496 & 2.11941872839269 & 60.3691550029514 \tabularnewline
Winsorized Mean ( 24 / 47 ) & 127.879432624113 & 2.11220449279478 & 60.5431117395781 \tabularnewline
Winsorized Mean ( 25 / 47 ) & 128.021276595745 & 2.08601966021587 & 61.3710786323541 \tabularnewline
Winsorized Mean ( 26 / 47 ) & 128.039716312057 & 2.07251563398765 & 61.7798554627549 \tabularnewline
Winsorized Mean ( 27 / 47 ) & 127.943971631206 & 2.05852402066673 & 62.1532565793262 \tabularnewline
Winsorized Mean ( 28 / 47 ) & 127.824822695035 & 2.04620169928391 & 62.4693170471754 \tabularnewline
Winsorized Mean ( 29 / 47 ) & 127.865957446808 & 2.03767673440822 & 62.750855073164 \tabularnewline
Winsorized Mean ( 30 / 47 ) & 127.972340425532 & 2.00052047593957 & 63.9695229139948 \tabularnewline
Winsorized Mean ( 31 / 47 ) & 128.126241134752 & 1.97598029366757 & 64.8418618066983 \tabularnewline
Winsorized Mean ( 32 / 47 ) & 128.103546099291 & 1.9598896882268 & 65.3626307994873 \tabularnewline
Winsorized Mean ( 33 / 47 ) & 128.173758865248 & 1.92467253899482 & 66.595099305666 \tabularnewline
Winsorized Mean ( 34 / 47 ) & 128.149645390071 & 1.87909353864144 & 68.1975871636073 \tabularnewline
Winsorized Mean ( 35 / 47 ) & 128.149645390071 & 1.86929263046520 & 68.5551546619957 \tabularnewline
Winsorized Mean ( 36 / 47 ) & 128.021985815603 & 1.85663303131425 & 68.9538447589613 \tabularnewline
Winsorized Mean ( 37 / 47 ) & 128.100709219858 & 1.82839987303051 & 70.0616484989882 \tabularnewline
Winsorized Mean ( 38 / 47 ) & 127.885106382979 & 1.80206201158197 & 70.9659853884345 \tabularnewline
Winsorized Mean ( 39 / 47 ) & 127.968085106383 & 1.78331235558937 & 71.7586488453901 \tabularnewline
Winsorized Mean ( 40 / 47 ) & 127.826241134752 & 1.75320076239502 & 72.910213066603 \tabularnewline
Winsorized Mean ( 41 / 47 ) & 127.768085106383 & 1.74762317072591 & 73.1096309814385 \tabularnewline
Winsorized Mean ( 42 / 47 ) & 127.648936170213 & 1.73053587785411 & 73.7626638105297 \tabularnewline
Winsorized Mean ( 43 / 47 ) & 127.557446808511 & 1.66381455072743 & 76.6656637019684 \tabularnewline
Winsorized Mean ( 44 / 47 ) & 127.775886524823 & 1.59613511828254 & 80.053301917391 \tabularnewline
Winsorized Mean ( 45 / 47 ) & 127.839716312057 & 1.58419111178391 & 80.6971553880897 \tabularnewline
Winsorized Mean ( 46 / 47 ) & 127.872340425532 & 1.54473289034567 & 82.7795803563926 \tabularnewline
Winsorized Mean ( 47 / 47 ) & 127.672340425532 & 1.52628609591670 & 83.6490227927099 \tabularnewline
Trimmed Mean ( 1 / 47 ) & 129.343884892086 & 2.56955298832382 & 50.3371152413791 \tabularnewline
Trimmed Mean ( 2 / 47 ) & 129.143795620438 & 2.51944772800247 & 51.2587715891326 \tabularnewline
Trimmed Mean ( 3 / 47 ) & 129.054074074074 & 2.49485413197151 & 51.728104028307 \tabularnewline
Trimmed Mean ( 4 / 47 ) & 128.969172932331 & 2.47044046215831 & 52.2049306218279 \tabularnewline
Trimmed Mean ( 5 / 47 ) & 128.875572519084 & 2.44864099823356 & 52.6314688890917 \tabularnewline
Trimmed Mean ( 6 / 47 ) & 128.772093023256 & 2.42558681282701 & 53.0890472945689 \tabularnewline
Trimmed Mean ( 7 / 47 ) & 128.668503937008 & 2.40302290066108 & 53.5444351785455 \tabularnewline
Trimmed Mean ( 8 / 47 ) & 128.5584 & 2.37853334695578 & 54.0494419237547 \tabularnewline
Trimmed Mean ( 9 / 47 ) & 128.447154471545 & 2.35407188473411 & 54.5638199515104 \tabularnewline
Trimmed Mean ( 10 / 47 ) & 128.335537190083 & 2.32844189958817 & 55.1164867857692 \tabularnewline
Trimmed Mean ( 11 / 47 ) & 128.258823529412 & 2.30920496950272 & 55.5424162096065 \tabularnewline
Trimmed Mean ( 12 / 47 ) & 128.194017094017 & 2.29278050757943 & 55.9120319935711 \tabularnewline
Trimmed Mean ( 13 / 47 ) & 128.126956521739 & 2.2784662771832 & 56.2338612622078 \tabularnewline
Trimmed Mean ( 14 / 47 ) & 128.087610619469 & 2.26759698823409 & 56.4860560690807 \tabularnewline
Trimmed Mean ( 15 / 47 ) & 128.054054054054 & 2.25628970140828 & 56.7542607556682 \tabularnewline
Trimmed Mean ( 16 / 47 ) & 128.031192660550 & 2.24523382276132 & 57.0235453263796 \tabularnewline
Trimmed Mean ( 17 / 47 ) & 128.032710280374 & 2.23871364544078 & 57.1903023600706 \tabularnewline
Trimmed Mean ( 18 / 47 ) & 128.024761904762 & 2.23227400151986 & 57.3517237658079 \tabularnewline
Trimmed Mean ( 19 / 47 ) & 128.007766990291 & 2.22634216746680 & 57.4968973147297 \tabularnewline
Trimmed Mean ( 20 / 47 ) & 127.990099009901 & 2.21932980025011 & 57.6706080346764 \tabularnewline
Trimmed Mean ( 21 / 47 ) & 127.975757575758 & 2.21144075063907 & 57.8698559022099 \tabularnewline
Trimmed Mean ( 22 / 47 ) & 127.960824742268 & 2.20222745167894 & 58.1051810269247 \tabularnewline
Trimmed Mean ( 23 / 47 ) & 127.946315789474 & 2.19135776352546 & 58.3867764173904 \tabularnewline
Trimmed Mean ( 24 / 47 ) & 127.946236559140 & 2.18615568277535 & 58.5256748031369 \tabularnewline
Trimmed Mean ( 25 / 47 ) & 127.950549450549 & 2.18010113555233 & 58.6901898099938 \tabularnewline
Trimmed Mean ( 26 / 47 ) & 127.946067415730 & 2.17489979350709 & 58.8284884653989 \tabularnewline
Trimmed Mean ( 27 / 47 ) & 127.940229885057 & 2.16933900120262 & 58.9765960111035 \tabularnewline
Trimmed Mean ( 28 / 47 ) & 127.94 & 2.16337362334241 & 59.1391143071869 \tabularnewline
Trimmed Mean ( 29 / 47 ) & 127.946987951807 & 2.15673356466829 & 59.3244293351023 \tabularnewline
Trimmed Mean ( 30 / 47 ) & 127.951851851852 & 2.14890950747829 & 59.5426896323807 \tabularnewline
Trimmed Mean ( 31 / 47 ) & 127.950632911392 & 2.14257689389292 & 59.7181054626771 \tabularnewline
Trimmed Mean ( 32 / 47 ) & 127.940259740260 & 2.13655347807223 & 59.8816088870838 \tabularnewline
Trimmed Mean ( 33 / 47 ) & 127.930666666667 & 2.12995450895323 & 60.0626286284106 \tabularnewline
Trimmed Mean ( 34 / 47 ) & 127.916438356164 & 2.12461655032517 & 60.2068351282431 \tabularnewline
Trimmed Mean ( 35 / 47 ) & 127.902816901408 & 2.12170347625934 & 60.2830783531104 \tabularnewline
Trimmed Mean ( 36 / 47 ) & 127.888405797101 & 2.11766464873473 & 60.3912455513259 \tabularnewline
Trimmed Mean ( 37 / 47 ) & 127.880597014925 & 2.11258985748581 & 60.5326190324116 \tabularnewline
Trimmed Mean ( 38 / 47 ) & 127.867692307692 & 2.10797376700159 & 60.6590529300434 \tabularnewline
Trimmed Mean ( 39 / 47 ) & 127.866666666667 & 2.10360673376051 & 60.7844919939411 \tabularnewline
Trimmed Mean ( 40 / 47 ) & 127.860655737705 & 2.09854005807541 & 60.9283845908414 \tabularnewline
Trimmed Mean ( 41 / 47 ) & 127.862711864407 & 2.09395319114728 & 61.0628319701601 \tabularnewline
Trimmed Mean ( 42 / 47 ) & 127.868421052632 & 2.08675281961413 & 61.2762660966603 \tabularnewline
Trimmed Mean ( 43 / 47 ) & 127.881818181818 & 2.07785516667161 & 61.5451068164025 \tabularnewline
Trimmed Mean ( 44 / 47 ) & 127.901886792453 & 2.07356800145247 & 61.6820315045668 \tabularnewline
Trimmed Mean ( 45 / 47 ) & 127.909803921569 & 2.07470528008946 & 61.6520356645805 \tabularnewline
Trimmed Mean ( 46 / 47 ) & 127.914285714286 & 2.07422020426528 & 61.6686142827322 \tabularnewline
Trimmed Mean ( 47 / 47 ) & 127.917021276596 & 2.07571821247128 & 61.6254270488391 \tabularnewline
Median & 128.1 &  &  \tabularnewline
Midrange & 151.15 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 127.527142857143 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 127.902816901408 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 127.902816901408 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 127.902816901408 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 127.902816901408 &  &  \tabularnewline
Midmean - Closest Observation & 127.548611111111 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 127.902816901408 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 127.902816901408 &  &  \tabularnewline
Number of observations & 141 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7689&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]129.653191489362[/C][C]2.64292340540554[/C][C]49.0567343813989[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]125.925004380601[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]122.302162165636[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]133.371122215923[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 47 )[/C][C]129.538297872340[/C][C]2.61534937245378[/C][C]49.530016615258[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 47 )[/C][C]129.315602836879[/C][C]2.56234309005111[/C][C]50.4677157945699[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 47 )[/C][C]129.294326241135[/C][C]2.55578406590613[/C][C]50.5889084942294[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 47 )[/C][C]129.317021276596[/C][C]2.53915197721023[/C][C]50.9292166980397[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 47 )[/C][C]129.348936170213[/C][C]2.53523610426686[/C][C]51.0204694357719[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 47 )[/C][C]129.331914893617[/C][C]2.52203728280835[/C][C]51.2807307708008[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 47 )[/C][C]129.351773049645[/C][C]2.51967166345698[/C][C]51.3367574536182[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 47 )[/C][C]129.334751773050[/C][C]2.50479297100061[/C][C]51.6349068647311[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 47 )[/C][C]129.309219858156[/C][C]2.49581390174165[/C][C]51.8104413826369[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 47 )[/C][C]128.982978723404[/C][C]2.43558367529397[/C][C]52.9577283801742[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 47 )[/C][C]128.850354609929[/C][C]2.39972254899847[/C][C]53.6938550099074[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 47 )[/C][C]128.850354609929[/C][C]2.36828197172170[/C][C]54.4066779836427[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 47 )[/C][C]128.536879432624[/C][C]2.32604334018369[/C][C]55.2598815387823[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 47 )[/C][C]128.457446808511[/C][C]2.31626516839867[/C][C]55.4588691144194[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 47 )[/C][C]128.319148936170[/C][C]2.29954577138721[/C][C]55.8019546872343[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 47 )[/C][C]128.012765957447[/C][C]2.24321127172375[/C][C]57.0667451483863[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 47 )[/C][C]128.133333333333[/C][C]2.22974427697342[/C][C]57.4654836684937[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 47 )[/C][C]128.248226950355[/C][C]2.21149309862485[/C][C]57.9916921423368[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 47 )[/C][C]128.248226950355[/C][C]2.20851846319345[/C][C]58.06980067756[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 47 )[/C][C]128.191489361702[/C][C]2.20216378103497[/C][C]58.2116055425518[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 47 )[/C][C]128.191489361702[/C][C]2.19889087114006[/C][C]58.2982498332165[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 47 )[/C][C]128.175886524823[/C][C]2.1971534270679[/C][C]58.33724898123[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 47 )[/C][C]127.947517730496[/C][C]2.11941872839269[/C][C]60.3691550029514[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 47 )[/C][C]127.879432624113[/C][C]2.11220449279478[/C][C]60.5431117395781[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 47 )[/C][C]128.021276595745[/C][C]2.08601966021587[/C][C]61.3710786323541[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 47 )[/C][C]128.039716312057[/C][C]2.07251563398765[/C][C]61.7798554627549[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 47 )[/C][C]127.943971631206[/C][C]2.05852402066673[/C][C]62.1532565793262[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 47 )[/C][C]127.824822695035[/C][C]2.04620169928391[/C][C]62.4693170471754[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 47 )[/C][C]127.865957446808[/C][C]2.03767673440822[/C][C]62.750855073164[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 47 )[/C][C]127.972340425532[/C][C]2.00052047593957[/C][C]63.9695229139948[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 47 )[/C][C]128.126241134752[/C][C]1.97598029366757[/C][C]64.8418618066983[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 47 )[/C][C]128.103546099291[/C][C]1.9598896882268[/C][C]65.3626307994873[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 47 )[/C][C]128.173758865248[/C][C]1.92467253899482[/C][C]66.595099305666[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 47 )[/C][C]128.149645390071[/C][C]1.87909353864144[/C][C]68.1975871636073[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 47 )[/C][C]128.149645390071[/C][C]1.86929263046520[/C][C]68.5551546619957[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 47 )[/C][C]128.021985815603[/C][C]1.85663303131425[/C][C]68.9538447589613[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 47 )[/C][C]128.100709219858[/C][C]1.82839987303051[/C][C]70.0616484989882[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 47 )[/C][C]127.885106382979[/C][C]1.80206201158197[/C][C]70.9659853884345[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 47 )[/C][C]127.968085106383[/C][C]1.78331235558937[/C][C]71.7586488453901[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 47 )[/C][C]127.826241134752[/C][C]1.75320076239502[/C][C]72.910213066603[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 47 )[/C][C]127.768085106383[/C][C]1.74762317072591[/C][C]73.1096309814385[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 47 )[/C][C]127.648936170213[/C][C]1.73053587785411[/C][C]73.7626638105297[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 47 )[/C][C]127.557446808511[/C][C]1.66381455072743[/C][C]76.6656637019684[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 47 )[/C][C]127.775886524823[/C][C]1.59613511828254[/C][C]80.053301917391[/C][/ROW]
[ROW][C]Winsorized Mean ( 45 / 47 )[/C][C]127.839716312057[/C][C]1.58419111178391[/C][C]80.6971553880897[/C][/ROW]
[ROW][C]Winsorized Mean ( 46 / 47 )[/C][C]127.872340425532[/C][C]1.54473289034567[/C][C]82.7795803563926[/C][/ROW]
[ROW][C]Winsorized Mean ( 47 / 47 )[/C][C]127.672340425532[/C][C]1.52628609591670[/C][C]83.6490227927099[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 47 )[/C][C]129.343884892086[/C][C]2.56955298832382[/C][C]50.3371152413791[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 47 )[/C][C]129.143795620438[/C][C]2.51944772800247[/C][C]51.2587715891326[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 47 )[/C][C]129.054074074074[/C][C]2.49485413197151[/C][C]51.728104028307[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 47 )[/C][C]128.969172932331[/C][C]2.47044046215831[/C][C]52.2049306218279[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 47 )[/C][C]128.875572519084[/C][C]2.44864099823356[/C][C]52.6314688890917[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 47 )[/C][C]128.772093023256[/C][C]2.42558681282701[/C][C]53.0890472945689[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 47 )[/C][C]128.668503937008[/C][C]2.40302290066108[/C][C]53.5444351785455[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 47 )[/C][C]128.5584[/C][C]2.37853334695578[/C][C]54.0494419237547[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 47 )[/C][C]128.447154471545[/C][C]2.35407188473411[/C][C]54.5638199515104[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 47 )[/C][C]128.335537190083[/C][C]2.32844189958817[/C][C]55.1164867857692[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 47 )[/C][C]128.258823529412[/C][C]2.30920496950272[/C][C]55.5424162096065[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 47 )[/C][C]128.194017094017[/C][C]2.29278050757943[/C][C]55.9120319935711[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 47 )[/C][C]128.126956521739[/C][C]2.2784662771832[/C][C]56.2338612622078[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 47 )[/C][C]128.087610619469[/C][C]2.26759698823409[/C][C]56.4860560690807[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 47 )[/C][C]128.054054054054[/C][C]2.25628970140828[/C][C]56.7542607556682[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 47 )[/C][C]128.031192660550[/C][C]2.24523382276132[/C][C]57.0235453263796[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 47 )[/C][C]128.032710280374[/C][C]2.23871364544078[/C][C]57.1903023600706[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 47 )[/C][C]128.024761904762[/C][C]2.23227400151986[/C][C]57.3517237658079[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 47 )[/C][C]128.007766990291[/C][C]2.22634216746680[/C][C]57.4968973147297[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 47 )[/C][C]127.990099009901[/C][C]2.21932980025011[/C][C]57.6706080346764[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 47 )[/C][C]127.975757575758[/C][C]2.21144075063907[/C][C]57.8698559022099[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 47 )[/C][C]127.960824742268[/C][C]2.20222745167894[/C][C]58.1051810269247[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 47 )[/C][C]127.946315789474[/C][C]2.19135776352546[/C][C]58.3867764173904[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 47 )[/C][C]127.946236559140[/C][C]2.18615568277535[/C][C]58.5256748031369[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 47 )[/C][C]127.950549450549[/C][C]2.18010113555233[/C][C]58.6901898099938[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 47 )[/C][C]127.946067415730[/C][C]2.17489979350709[/C][C]58.8284884653989[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 47 )[/C][C]127.940229885057[/C][C]2.16933900120262[/C][C]58.9765960111035[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 47 )[/C][C]127.94[/C][C]2.16337362334241[/C][C]59.1391143071869[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 47 )[/C][C]127.946987951807[/C][C]2.15673356466829[/C][C]59.3244293351023[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 47 )[/C][C]127.951851851852[/C][C]2.14890950747829[/C][C]59.5426896323807[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 47 )[/C][C]127.950632911392[/C][C]2.14257689389292[/C][C]59.7181054626771[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 47 )[/C][C]127.940259740260[/C][C]2.13655347807223[/C][C]59.8816088870838[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 47 )[/C][C]127.930666666667[/C][C]2.12995450895323[/C][C]60.0626286284106[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 47 )[/C][C]127.916438356164[/C][C]2.12461655032517[/C][C]60.2068351282431[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 47 )[/C][C]127.902816901408[/C][C]2.12170347625934[/C][C]60.2830783531104[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 47 )[/C][C]127.888405797101[/C][C]2.11766464873473[/C][C]60.3912455513259[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 47 )[/C][C]127.880597014925[/C][C]2.11258985748581[/C][C]60.5326190324116[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 47 )[/C][C]127.867692307692[/C][C]2.10797376700159[/C][C]60.6590529300434[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 47 )[/C][C]127.866666666667[/C][C]2.10360673376051[/C][C]60.7844919939411[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 47 )[/C][C]127.860655737705[/C][C]2.09854005807541[/C][C]60.9283845908414[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 47 )[/C][C]127.862711864407[/C][C]2.09395319114728[/C][C]61.0628319701601[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 47 )[/C][C]127.868421052632[/C][C]2.08675281961413[/C][C]61.2762660966603[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 47 )[/C][C]127.881818181818[/C][C]2.07785516667161[/C][C]61.5451068164025[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 47 )[/C][C]127.901886792453[/C][C]2.07356800145247[/C][C]61.6820315045668[/C][/ROW]
[ROW][C]Trimmed Mean ( 45 / 47 )[/C][C]127.909803921569[/C][C]2.07470528008946[/C][C]61.6520356645805[/C][/ROW]
[ROW][C]Trimmed Mean ( 46 / 47 )[/C][C]127.914285714286[/C][C]2.07422020426528[/C][C]61.6686142827322[/C][/ROW]
[ROW][C]Trimmed Mean ( 47 / 47 )[/C][C]127.917021276596[/C][C]2.07571821247128[/C][C]61.6254270488391[/C][/ROW]
[ROW][C]Median[/C][C]128.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]151.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]127.527142857143[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]127.902816901408[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]127.902816901408[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]127.902816901408[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]127.902816901408[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]127.548611111111[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]127.902816901408[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]127.902816901408[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]141[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7689&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7689&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 Mean129.6531914893622.6429234054055449.0567343813989
Geometric Mean125.925004380601
Harmonic Mean122.302162165636
Quadratic Mean133.371122215923
Winsorized Mean ( 1 / 47 )129.5382978723402.6153493724537849.530016615258
Winsorized Mean ( 2 / 47 )129.3156028368792.5623430900511150.4677157945699
Winsorized Mean ( 3 / 47 )129.2943262411352.5557840659061350.5889084942294
Winsorized Mean ( 4 / 47 )129.3170212765962.5391519772102350.9292166980397
Winsorized Mean ( 5 / 47 )129.3489361702132.5352361042668651.0204694357719
Winsorized Mean ( 6 / 47 )129.3319148936172.5220372828083551.2807307708008
Winsorized Mean ( 7 / 47 )129.3517730496452.5196716634569851.3367574536182
Winsorized Mean ( 8 / 47 )129.3347517730502.5047929710006151.6349068647311
Winsorized Mean ( 9 / 47 )129.3092198581562.4958139017416551.8104413826369
Winsorized Mean ( 10 / 47 )128.9829787234042.4355836752939752.9577283801742
Winsorized Mean ( 11 / 47 )128.8503546099292.3997225489984753.6938550099074
Winsorized Mean ( 12 / 47 )128.8503546099292.3682819717217054.4066779836427
Winsorized Mean ( 13 / 47 )128.5368794326242.3260433401836955.2598815387823
Winsorized Mean ( 14 / 47 )128.4574468085112.3162651683986755.4588691144194
Winsorized Mean ( 15 / 47 )128.3191489361702.2995457713872155.8019546872343
Winsorized Mean ( 16 / 47 )128.0127659574472.2432112717237557.0667451483863
Winsorized Mean ( 17 / 47 )128.1333333333332.2297442769734257.4654836684937
Winsorized Mean ( 18 / 47 )128.2482269503552.2114930986248557.9916921423368
Winsorized Mean ( 19 / 47 )128.2482269503552.2085184631934558.06980067756
Winsorized Mean ( 20 / 47 )128.1914893617022.2021637810349758.2116055425518
Winsorized Mean ( 21 / 47 )128.1914893617022.1988908711400658.2982498332165
Winsorized Mean ( 22 / 47 )128.1758865248232.197153427067958.33724898123
Winsorized Mean ( 23 / 47 )127.9475177304962.1194187283926960.3691550029514
Winsorized Mean ( 24 / 47 )127.8794326241132.1122044927947860.5431117395781
Winsorized Mean ( 25 / 47 )128.0212765957452.0860196602158761.3710786323541
Winsorized Mean ( 26 / 47 )128.0397163120572.0725156339876561.7798554627549
Winsorized Mean ( 27 / 47 )127.9439716312062.0585240206667362.1532565793262
Winsorized Mean ( 28 / 47 )127.8248226950352.0462016992839162.4693170471754
Winsorized Mean ( 29 / 47 )127.8659574468082.0376767344082262.750855073164
Winsorized Mean ( 30 / 47 )127.9723404255322.0005204759395763.9695229139948
Winsorized Mean ( 31 / 47 )128.1262411347521.9759802936675764.8418618066983
Winsorized Mean ( 32 / 47 )128.1035460992911.959889688226865.3626307994873
Winsorized Mean ( 33 / 47 )128.1737588652481.9246725389948266.595099305666
Winsorized Mean ( 34 / 47 )128.1496453900711.8790935386414468.1975871636073
Winsorized Mean ( 35 / 47 )128.1496453900711.8692926304652068.5551546619957
Winsorized Mean ( 36 / 47 )128.0219858156031.8566330313142568.9538447589613
Winsorized Mean ( 37 / 47 )128.1007092198581.8283998730305170.0616484989882
Winsorized Mean ( 38 / 47 )127.8851063829791.8020620115819770.9659853884345
Winsorized Mean ( 39 / 47 )127.9680851063831.7833123555893771.7586488453901
Winsorized Mean ( 40 / 47 )127.8262411347521.7532007623950272.910213066603
Winsorized Mean ( 41 / 47 )127.7680851063831.7476231707259173.1096309814385
Winsorized Mean ( 42 / 47 )127.6489361702131.7305358778541173.7626638105297
Winsorized Mean ( 43 / 47 )127.5574468085111.6638145507274376.6656637019684
Winsorized Mean ( 44 / 47 )127.7758865248231.5961351182825480.053301917391
Winsorized Mean ( 45 / 47 )127.8397163120571.5841911117839180.6971553880897
Winsorized Mean ( 46 / 47 )127.8723404255321.5447328903456782.7795803563926
Winsorized Mean ( 47 / 47 )127.6723404255321.5262860959167083.6490227927099
Trimmed Mean ( 1 / 47 )129.3438848920862.5695529883238250.3371152413791
Trimmed Mean ( 2 / 47 )129.1437956204382.5194477280024751.2587715891326
Trimmed Mean ( 3 / 47 )129.0540740740742.4948541319715151.728104028307
Trimmed Mean ( 4 / 47 )128.9691729323312.4704404621583152.2049306218279
Trimmed Mean ( 5 / 47 )128.8755725190842.4486409982335652.6314688890917
Trimmed Mean ( 6 / 47 )128.7720930232562.4255868128270153.0890472945689
Trimmed Mean ( 7 / 47 )128.6685039370082.4030229006610853.5444351785455
Trimmed Mean ( 8 / 47 )128.55842.3785333469557854.0494419237547
Trimmed Mean ( 9 / 47 )128.4471544715452.3540718847341154.5638199515104
Trimmed Mean ( 10 / 47 )128.3355371900832.3284418995881755.1164867857692
Trimmed Mean ( 11 / 47 )128.2588235294122.3092049695027255.5424162096065
Trimmed Mean ( 12 / 47 )128.1940170940172.2927805075794355.9120319935711
Trimmed Mean ( 13 / 47 )128.1269565217392.278466277183256.2338612622078
Trimmed Mean ( 14 / 47 )128.0876106194692.2675969882340956.4860560690807
Trimmed Mean ( 15 / 47 )128.0540540540542.2562897014082856.7542607556682
Trimmed Mean ( 16 / 47 )128.0311926605502.2452338227613257.0235453263796
Trimmed Mean ( 17 / 47 )128.0327102803742.2387136454407857.1903023600706
Trimmed Mean ( 18 / 47 )128.0247619047622.2322740015198657.3517237658079
Trimmed Mean ( 19 / 47 )128.0077669902912.2263421674668057.4968973147297
Trimmed Mean ( 20 / 47 )127.9900990099012.2193298002501157.6706080346764
Trimmed Mean ( 21 / 47 )127.9757575757582.2114407506390757.8698559022099
Trimmed Mean ( 22 / 47 )127.9608247422682.2022274516789458.1051810269247
Trimmed Mean ( 23 / 47 )127.9463157894742.1913577635254658.3867764173904
Trimmed Mean ( 24 / 47 )127.9462365591402.1861556827753558.5256748031369
Trimmed Mean ( 25 / 47 )127.9505494505492.1801011355523358.6901898099938
Trimmed Mean ( 26 / 47 )127.9460674157302.1748997935070958.8284884653989
Trimmed Mean ( 27 / 47 )127.9402298850572.1693390012026258.9765960111035
Trimmed Mean ( 28 / 47 )127.942.1633736233424159.1391143071869
Trimmed Mean ( 29 / 47 )127.9469879518072.1567335646682959.3244293351023
Trimmed Mean ( 30 / 47 )127.9518518518522.1489095074782959.5426896323807
Trimmed Mean ( 31 / 47 )127.9506329113922.1425768938929259.7181054626771
Trimmed Mean ( 32 / 47 )127.9402597402602.1365534780722359.8816088870838
Trimmed Mean ( 33 / 47 )127.9306666666672.1299545089532360.0626286284106
Trimmed Mean ( 34 / 47 )127.9164383561642.1246165503251760.2068351282431
Trimmed Mean ( 35 / 47 )127.9028169014082.1217034762593460.2830783531104
Trimmed Mean ( 36 / 47 )127.8884057971012.1176646487347360.3912455513259
Trimmed Mean ( 37 / 47 )127.8805970149252.1125898574858160.5326190324116
Trimmed Mean ( 38 / 47 )127.8676923076922.1079737670015960.6590529300434
Trimmed Mean ( 39 / 47 )127.8666666666672.1036067337605160.7844919939411
Trimmed Mean ( 40 / 47 )127.8606557377052.0985400580754160.9283845908414
Trimmed Mean ( 41 / 47 )127.8627118644072.0939531911472861.0628319701601
Trimmed Mean ( 42 / 47 )127.8684210526322.0867528196141361.2762660966603
Trimmed Mean ( 43 / 47 )127.8818181818182.0778551666716161.5451068164025
Trimmed Mean ( 44 / 47 )127.9018867924532.0735680014524761.6820315045668
Trimmed Mean ( 45 / 47 )127.9098039215692.0747052800894661.6520356645805
Trimmed Mean ( 46 / 47 )127.9142857142862.0742202042652861.6686142827322
Trimmed Mean ( 47 / 47 )127.9170212765962.0757182124712861.6254270488391
Median128.1
Midrange151.15
Midmean - Weighted Average at Xnp127.527142857143
Midmean - Weighted Average at X(n+1)p127.902816901408
Midmean - Empirical Distribution Function127.902816901408
Midmean - Empirical Distribution Function - Averaging127.902816901408
Midmean - Empirical Distribution Function - Interpolation127.902816901408
Midmean - Closest Observation127.548611111111
Midmean - True Basic - Statistics Graphics Toolkit127.902816901408
Midmean - MS Excel (old versions)127.902816901408
Number of observations141



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')