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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 computationWed, 20 Oct 2010 15:06:31 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Oct/20/t1287587841lr04e4qqr8u8zlo.htm/, Retrieved Sat, 18 May 2024 13:03:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=87233, Retrieved Sat, 18 May 2024 13:03:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact102
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [gemiddelde eigen ...] [2010-10-20 15:06:31] [465c6c9df074117d1de4b3f3c25f0c87] [Current]
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Dataseries X:
132
131,4
132,7
130,9
126
109,7
68,3
70,6
75,3
74,1
74,9
74
74,2
76
76,2
74,9
74,1
76,5
57,8
59,2
57,3
57,5
60,4
59,9
59,9
60
60,2
65,4
62,4
78,8
65,6
64,4
67,4
65,3
66,7
66,8
69,4
71,7
77,1
81,1
82,1
92,1
77,1
78,2
77,7
77,3
78,5
78,8
78,7
79,8
82,2
84
81,7
77,6
64,3
72,6
73,8
73,8
70,1
70
72,3
72,1
73,3
79,1
77
76,1
66,4
72,7
73,2
70,7
73,6
74,2
72,6
73,6
79,1
79,6
78
85,4
82
91,9
89,4
92,1
93,8
93,6
95,6
99,9
103,7
99,2
93,7
93,5
80,7
91,8
105,8
111,3
110,3
109,4
111,4
111,6
111,8
106,6
104,3
105,5
98,5
108,5
106
101,8
101,3
92,4
88,9
84,9
86,4
90,7
86,8
90,6
88,3
95,4
93,6
91,3
91,3
89,3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87233&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=87233&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87233&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean83.83666666666671.5694407170493653.4181799643153
Geometric Mean82.2104030770412
Harmonic Mean80.69581733859
Quadratic Mean85.5669377349297
Winsorized Mean ( 1 / 40 )83.83251.5676885170258053.4752274380665
Winsorized Mean ( 2 / 40 )83.82751.5644174341470753.583844164779
Winsorized Mean ( 3 / 40 )83.851.5564566884334453.872363184352
Winsorized Mean ( 4 / 40 )83.711.513417302918555.3119089087802
Winsorized Mean ( 5 / 40 )83.11833333333331.3919632183743959.7130241921216
Winsorized Mean ( 6 / 40 )83.11333333333331.3895361927632859.813723288525
Winsorized Mean ( 7 / 40 )83.11333333333331.3859049028077459.9704447000311
Winsorized Mean ( 8 / 40 )83.121.3829157683709360.1048899007891
Winsorized Mean ( 9 / 40 )83.1951.3500969204756661.6215019368305
Winsorized Mean ( 10 / 40 )83.30333333333331.3218657413981163.0195115316515
Winsorized Mean ( 11 / 40 )83.2851.3161593445202963.2788122097448
Winsorized Mean ( 12 / 40 )83.2851.2905694626075464.5335275729568
Winsorized Mean ( 13 / 40 )83.091.2562016466438966.143839424177
Winsorized Mean ( 14 / 40 )83.04333333333331.2425056759663566.8353754350033
Winsorized Mean ( 15 / 40 )83.11833333333331.2269984461038967.7411887498802
Winsorized Mean ( 16 / 40 )83.11833333333331.2162398909983468.3404104309607
Winsorized Mean ( 17 / 40 )82.96251.1886567416372969.795170543285
Winsorized Mean ( 18 / 40 )82.96251.1649419399220571.2159955418474
Winsorized Mean ( 19 / 40 )82.80416666666671.1048254205306074.9477384643265
Winsorized Mean ( 20 / 40 )82.90416666666671.0729885721465377.2647247312389
Winsorized Mean ( 21 / 40 )82.76416666666671.0271188360691480.5789590846285
Winsorized Mean ( 22 / 40 )82.65416666666671.0073475834230282.0512879832435
Winsorized Mean ( 23 / 40 )82.61583333333330.97897862787100684.3898232109507
Winsorized Mean ( 24 / 40 )82.05583333333330.9005769982286791.1147336593402
Winsorized Mean ( 25 / 40 )82.22250.87371631527620794.1066322814484
Winsorized Mean ( 26 / 40 )81.96250.82198610204843899.7127564514104
Winsorized Mean ( 27 / 40 )81.9850.814749063463448100.626074550472
Winsorized Mean ( 28 / 40 )82.03166666666670.804987937113486101.90421854123
Winsorized Mean ( 29 / 40 )82.03166666666670.804987937113486101.90421854123
Winsorized Mean ( 30 / 40 )82.03166666666670.79951489435356102.601799223506
Winsorized Mean ( 31 / 40 )81.87666666666670.753101647523937108.719277053586
Winsorized Mean ( 32 / 40 )81.82333333333330.741164324889739110.398369950559
Winsorized Mean ( 33 / 40 )81.90583333333330.733251169162039111.702288080816
Winsorized Mean ( 34 / 40 )81.84916666666670.72664764562133112.639416311162
Winsorized Mean ( 35 / 40 )81.87833333333330.71771714750882114.081617831664
Winsorized Mean ( 36 / 40 )81.72833333333330.700390230697694116.689710608784
Winsorized Mean ( 37 / 40 )81.790.694551020766782117.759527456607
Winsorized Mean ( 38 / 40 )81.63166666666670.669821648711879121.870749958069
Winsorized Mean ( 39 / 40 )81.59916666666670.666127753993574122.497773403769
Winsorized Mean ( 40 / 40 )81.23250.618018613233065131.440215975123
Trimmed Mean ( 1 / 40 )83.64745762711861.5242891784177354.8763704495676
Trimmed Mean ( 2 / 40 )83.45603448275861.4757344060402856.552204882645
Trimmed Mean ( 3 / 40 )83.26052631578951.4231472010794158.5045076522226
Trimmed Mean ( 4 / 40 )83.051.3671647003522760.7461558790984
Trimmed Mean ( 5 / 40 )82.871.3187855193466362.8381179382804
Trimmed Mean ( 6 / 40 )82.81481481481481.2986152427329663.7716331132303
Trimmed Mean ( 7 / 40 )82.75849056603771.2765990222681364.8273178362625
Trimmed Mean ( 8 / 40 )82.71.2526685481050166.0190599700981
Trimmed Mean ( 9 / 40 )82.63823529411761.2263448349775767.3858061265691
Trimmed Mean ( 10 / 40 )82.5641.2026103930931968.6539884190092
Trimmed Mean ( 11 / 40 )82.47346938775511.1804989825146469.8632278463083
Trimmed Mean ( 12 / 40 )82.381251.1563538360203471.2422508006028
Trimmed Mean ( 13 / 40 )82.28510638297871.1328995335490172.6323067017305
Trimmed Mean ( 14 / 40 )82.2043478260871.1115031950956373.9578151361182
Trimmed Mean ( 15 / 40 )82.12444444444441.0890778964092675.4073190863689
Trimmed Mean ( 16 / 40 )82.03409090909091.0655181165748976.9898602689077
Trimmed Mean ( 17 / 40 )81.9395348837211.0399361748669578.7928498536984
Trimmed Mean ( 18 / 40 )81.85357142857141.0145038926010280.6833488028446
Trimmed Mean ( 19 / 40 )81.76341463414630.9884053995962382.7225495404489
Trimmed Mean ( 20 / 40 )81.681250.96665954525057684.4984673262878
Trimmed Mean ( 21 / 40 )81.58717948717950.94550016359341586.2899686628332
Trimmed Mean ( 22 / 40 )81.49868421052630.92707518463639587.9094657705574
Trimmed Mean ( 23 / 40 )81.41351351351350.90814391865359289.6482505044097
Trimmed Mean ( 24 / 40 )81.32638888888890.88961798578054891.4172040008087
Trimmed Mean ( 25 / 40 )81.27428571428570.87865105936152292.4989332777271
Trimmed Mean ( 26 / 40 )81.20735294117650.868604979309493.4916963125653
Trimmed Mean ( 27 / 40 )81.15454545454550.86308435309126394.0285212724325
Trimmed Mean ( 28 / 40 )81.0968750.85676569961553694.6546705083914
Trimmed Mean ( 29 / 40 )81.03225806451610.84975118202723495.3599827554216
Trimmed Mean ( 30 / 40 )80.96333333333330.84062784804437896.312932674887
Trimmed Mean ( 31 / 40 )80.88965517241380.82968842195534797.4940146588754
Trimmed Mean ( 32 / 40 )80.82142857142860.822554282287798.2566504263364
Trimmed Mean ( 33 / 40 )80.75185185185190.81475620779001199.1116742404302
Trimmed Mean ( 34 / 40 )80.67115384615380.805244576256312100.182175980874
Trimmed Mean ( 35 / 40 )80.5880.793641259625274101.542099812263
Trimmed Mean ( 36 / 40 )80.49583333333330.779553417877106103.258906301176
Trimmed Mean ( 37 / 40 )80.40652173913040.764252039856146105.209430326500
Trimmed Mean ( 38 / 40 )80.30454545454540.74456419525857107.854428088175
Trimmed Mean ( 39 / 40 )80.20476190476190.723706362230896110.825005956177
Trimmed Mean ( 40 / 40 )80.09750.696193749741756115.050587612588
Median78.8
Midrange95
Midmean - Weighted Average at Xnp80.6935483870968
Midmean - Weighted Average at X(n+1)p80.9633333333334
Midmean - Empirical Distribution Function80.6935483870968
Midmean - Empirical Distribution Function - Averaging80.9633333333334
Midmean - Empirical Distribution Function - Interpolation80.9633333333334
Midmean - Closest Observation80.6935483870968
Midmean - True Basic - Statistics Graphics Toolkit80.9633333333334
Midmean - MS Excel (old versions)81.096875
Number of observations120

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 83.8366666666667 & 1.56944071704936 & 53.4181799643153 \tabularnewline
Geometric Mean & 82.2104030770412 &  &  \tabularnewline
Harmonic Mean & 80.69581733859 &  &  \tabularnewline
Quadratic Mean & 85.5669377349297 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 83.8325 & 1.56768851702580 & 53.4752274380665 \tabularnewline
Winsorized Mean ( 2 / 40 ) & 83.8275 & 1.56441743414707 & 53.583844164779 \tabularnewline
Winsorized Mean ( 3 / 40 ) & 83.85 & 1.55645668843344 & 53.872363184352 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 83.71 & 1.5134173029185 & 55.3119089087802 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 83.1183333333333 & 1.39196321837439 & 59.7130241921216 \tabularnewline
Winsorized Mean ( 6 / 40 ) & 83.1133333333333 & 1.38953619276328 & 59.813723288525 \tabularnewline
Winsorized Mean ( 7 / 40 ) & 83.1133333333333 & 1.38590490280774 & 59.9704447000311 \tabularnewline
Winsorized Mean ( 8 / 40 ) & 83.12 & 1.38291576837093 & 60.1048899007891 \tabularnewline
Winsorized Mean ( 9 / 40 ) & 83.195 & 1.35009692047566 & 61.6215019368305 \tabularnewline
Winsorized Mean ( 10 / 40 ) & 83.3033333333333 & 1.32186574139811 & 63.0195115316515 \tabularnewline
Winsorized Mean ( 11 / 40 ) & 83.285 & 1.31615934452029 & 63.2788122097448 \tabularnewline
Winsorized Mean ( 12 / 40 ) & 83.285 & 1.29056946260754 & 64.5335275729568 \tabularnewline
Winsorized Mean ( 13 / 40 ) & 83.09 & 1.25620164664389 & 66.143839424177 \tabularnewline
Winsorized Mean ( 14 / 40 ) & 83.0433333333333 & 1.24250567596635 & 66.8353754350033 \tabularnewline
Winsorized Mean ( 15 / 40 ) & 83.1183333333333 & 1.22699844610389 & 67.7411887498802 \tabularnewline
Winsorized Mean ( 16 / 40 ) & 83.1183333333333 & 1.21623989099834 & 68.3404104309607 \tabularnewline
Winsorized Mean ( 17 / 40 ) & 82.9625 & 1.18865674163729 & 69.795170543285 \tabularnewline
Winsorized Mean ( 18 / 40 ) & 82.9625 & 1.16494193992205 & 71.2159955418474 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 82.8041666666667 & 1.10482542053060 & 74.9477384643265 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 82.9041666666667 & 1.07298857214653 & 77.2647247312389 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 82.7641666666667 & 1.02711883606914 & 80.5789590846285 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 82.6541666666667 & 1.00734758342302 & 82.0512879832435 \tabularnewline
Winsorized Mean ( 23 / 40 ) & 82.6158333333333 & 0.978978627871006 & 84.3898232109507 \tabularnewline
Winsorized Mean ( 24 / 40 ) & 82.0558333333333 & 0.90057699822867 & 91.1147336593402 \tabularnewline
Winsorized Mean ( 25 / 40 ) & 82.2225 & 0.873716315276207 & 94.1066322814484 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 81.9625 & 0.821986102048438 & 99.7127564514104 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 81.985 & 0.814749063463448 & 100.626074550472 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 82.0316666666667 & 0.804987937113486 & 101.90421854123 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 82.0316666666667 & 0.804987937113486 & 101.90421854123 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 82.0316666666667 & 0.79951489435356 & 102.601799223506 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 81.8766666666667 & 0.753101647523937 & 108.719277053586 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 81.8233333333333 & 0.741164324889739 & 110.398369950559 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 81.9058333333333 & 0.733251169162039 & 111.702288080816 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 81.8491666666667 & 0.72664764562133 & 112.639416311162 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 81.8783333333333 & 0.71771714750882 & 114.081617831664 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 81.7283333333333 & 0.700390230697694 & 116.689710608784 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 81.79 & 0.694551020766782 & 117.759527456607 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 81.6316666666667 & 0.669821648711879 & 121.870749958069 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 81.5991666666667 & 0.666127753993574 & 122.497773403769 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 81.2325 & 0.618018613233065 & 131.440215975123 \tabularnewline
Trimmed Mean ( 1 / 40 ) & 83.6474576271186 & 1.52428917841773 & 54.8763704495676 \tabularnewline
Trimmed Mean ( 2 / 40 ) & 83.4560344827586 & 1.47573440604028 & 56.552204882645 \tabularnewline
Trimmed Mean ( 3 / 40 ) & 83.2605263157895 & 1.42314720107941 & 58.5045076522226 \tabularnewline
Trimmed Mean ( 4 / 40 ) & 83.05 & 1.36716470035227 & 60.7461558790984 \tabularnewline
Trimmed Mean ( 5 / 40 ) & 82.87 & 1.31878551934663 & 62.8381179382804 \tabularnewline
Trimmed Mean ( 6 / 40 ) & 82.8148148148148 & 1.29861524273296 & 63.7716331132303 \tabularnewline
Trimmed Mean ( 7 / 40 ) & 82.7584905660377 & 1.27659902226813 & 64.8273178362625 \tabularnewline
Trimmed Mean ( 8 / 40 ) & 82.7 & 1.25266854810501 & 66.0190599700981 \tabularnewline
Trimmed Mean ( 9 / 40 ) & 82.6382352941176 & 1.22634483497757 & 67.3858061265691 \tabularnewline
Trimmed Mean ( 10 / 40 ) & 82.564 & 1.20261039309319 & 68.6539884190092 \tabularnewline
Trimmed Mean ( 11 / 40 ) & 82.4734693877551 & 1.18049898251464 & 69.8632278463083 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 82.38125 & 1.15635383602034 & 71.2422508006028 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 82.2851063829787 & 1.13289953354901 & 72.6323067017305 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 82.204347826087 & 1.11150319509563 & 73.9578151361182 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 82.1244444444444 & 1.08907789640926 & 75.4073190863689 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 82.0340909090909 & 1.06551811657489 & 76.9898602689077 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 81.939534883721 & 1.03993617486695 & 78.7928498536984 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 81.8535714285714 & 1.01450389260102 & 80.6833488028446 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 81.7634146341463 & 0.98840539959623 & 82.7225495404489 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 81.68125 & 0.966659545250576 & 84.4984673262878 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 81.5871794871795 & 0.945500163593415 & 86.2899686628332 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 81.4986842105263 & 0.927075184636395 & 87.9094657705574 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 81.4135135135135 & 0.908143918653592 & 89.6482505044097 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 81.3263888888889 & 0.889617985780548 & 91.4172040008087 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 81.2742857142857 & 0.878651059361522 & 92.4989332777271 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 81.2073529411765 & 0.8686049793094 & 93.4916963125653 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 81.1545454545455 & 0.863084353091263 & 94.0285212724325 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 81.096875 & 0.856765699615536 & 94.6546705083914 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 81.0322580645161 & 0.849751182027234 & 95.3599827554216 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 80.9633333333333 & 0.840627848044378 & 96.312932674887 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 80.8896551724138 & 0.829688421955347 & 97.4940146588754 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 80.8214285714286 & 0.8225542822877 & 98.2566504263364 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 80.7518518518519 & 0.814756207790011 & 99.1116742404302 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 80.6711538461538 & 0.805244576256312 & 100.182175980874 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 80.588 & 0.793641259625274 & 101.542099812263 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 80.4958333333333 & 0.779553417877106 & 103.258906301176 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 80.4065217391304 & 0.764252039856146 & 105.209430326500 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 80.3045454545454 & 0.74456419525857 & 107.854428088175 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 80.2047619047619 & 0.723706362230896 & 110.825005956177 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 80.0975 & 0.696193749741756 & 115.050587612588 \tabularnewline
Median & 78.8 &  &  \tabularnewline
Midrange & 95 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 80.6935483870968 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 80.9633333333334 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 80.6935483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 80.9633333333334 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 80.9633333333334 &  &  \tabularnewline
Midmean - Closest Observation & 80.6935483870968 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 80.9633333333334 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 81.096875 &  &  \tabularnewline
Number of observations & 120 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=87233&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]83.8366666666667[/C][C]1.56944071704936[/C][C]53.4181799643153[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]82.2104030770412[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]80.69581733859[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]85.5669377349297[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]83.8325[/C][C]1.56768851702580[/C][C]53.4752274380665[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]83.8275[/C][C]1.56441743414707[/C][C]53.583844164779[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]83.85[/C][C]1.55645668843344[/C][C]53.872363184352[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]83.71[/C][C]1.5134173029185[/C][C]55.3119089087802[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]83.1183333333333[/C][C]1.39196321837439[/C][C]59.7130241921216[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]83.1133333333333[/C][C]1.38953619276328[/C][C]59.813723288525[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]83.1133333333333[/C][C]1.38590490280774[/C][C]59.9704447000311[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]83.12[/C][C]1.38291576837093[/C][C]60.1048899007891[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]83.195[/C][C]1.35009692047566[/C][C]61.6215019368305[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]83.3033333333333[/C][C]1.32186574139811[/C][C]63.0195115316515[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]83.285[/C][C]1.31615934452029[/C][C]63.2788122097448[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]83.285[/C][C]1.29056946260754[/C][C]64.5335275729568[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]83.09[/C][C]1.25620164664389[/C][C]66.143839424177[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]83.0433333333333[/C][C]1.24250567596635[/C][C]66.8353754350033[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]83.1183333333333[/C][C]1.22699844610389[/C][C]67.7411887498802[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]83.1183333333333[/C][C]1.21623989099834[/C][C]68.3404104309607[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]82.9625[/C][C]1.18865674163729[/C][C]69.795170543285[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]82.9625[/C][C]1.16494193992205[/C][C]71.2159955418474[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]82.8041666666667[/C][C]1.10482542053060[/C][C]74.9477384643265[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]82.9041666666667[/C][C]1.07298857214653[/C][C]77.2647247312389[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]82.7641666666667[/C][C]1.02711883606914[/C][C]80.5789590846285[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]82.6541666666667[/C][C]1.00734758342302[/C][C]82.0512879832435[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]82.6158333333333[/C][C]0.978978627871006[/C][C]84.3898232109507[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]82.0558333333333[/C][C]0.90057699822867[/C][C]91.1147336593402[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]82.2225[/C][C]0.873716315276207[/C][C]94.1066322814484[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]81.9625[/C][C]0.821986102048438[/C][C]99.7127564514104[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]81.985[/C][C]0.814749063463448[/C][C]100.626074550472[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]82.0316666666667[/C][C]0.804987937113486[/C][C]101.90421854123[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]82.0316666666667[/C][C]0.804987937113486[/C][C]101.90421854123[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]82.0316666666667[/C][C]0.79951489435356[/C][C]102.601799223506[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]81.8766666666667[/C][C]0.753101647523937[/C][C]108.719277053586[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]81.8233333333333[/C][C]0.741164324889739[/C][C]110.398369950559[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]81.9058333333333[/C][C]0.733251169162039[/C][C]111.702288080816[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]81.8491666666667[/C][C]0.72664764562133[/C][C]112.639416311162[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]81.8783333333333[/C][C]0.71771714750882[/C][C]114.081617831664[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]81.7283333333333[/C][C]0.700390230697694[/C][C]116.689710608784[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]81.79[/C][C]0.694551020766782[/C][C]117.759527456607[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]81.6316666666667[/C][C]0.669821648711879[/C][C]121.870749958069[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]81.5991666666667[/C][C]0.666127753993574[/C][C]122.497773403769[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]81.2325[/C][C]0.618018613233065[/C][C]131.440215975123[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]83.6474576271186[/C][C]1.52428917841773[/C][C]54.8763704495676[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]83.4560344827586[/C][C]1.47573440604028[/C][C]56.552204882645[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]83.2605263157895[/C][C]1.42314720107941[/C][C]58.5045076522226[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]83.05[/C][C]1.36716470035227[/C][C]60.7461558790984[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]82.87[/C][C]1.31878551934663[/C][C]62.8381179382804[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]82.8148148148148[/C][C]1.29861524273296[/C][C]63.7716331132303[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]82.7584905660377[/C][C]1.27659902226813[/C][C]64.8273178362625[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]82.7[/C][C]1.25266854810501[/C][C]66.0190599700981[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]82.6382352941176[/C][C]1.22634483497757[/C][C]67.3858061265691[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]82.564[/C][C]1.20261039309319[/C][C]68.6539884190092[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]82.4734693877551[/C][C]1.18049898251464[/C][C]69.8632278463083[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]82.38125[/C][C]1.15635383602034[/C][C]71.2422508006028[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]82.2851063829787[/C][C]1.13289953354901[/C][C]72.6323067017305[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]82.204347826087[/C][C]1.11150319509563[/C][C]73.9578151361182[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]82.1244444444444[/C][C]1.08907789640926[/C][C]75.4073190863689[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]82.0340909090909[/C][C]1.06551811657489[/C][C]76.9898602689077[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]81.939534883721[/C][C]1.03993617486695[/C][C]78.7928498536984[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]81.8535714285714[/C][C]1.01450389260102[/C][C]80.6833488028446[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]81.7634146341463[/C][C]0.98840539959623[/C][C]82.7225495404489[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]81.68125[/C][C]0.966659545250576[/C][C]84.4984673262878[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]81.5871794871795[/C][C]0.945500163593415[/C][C]86.2899686628332[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]81.4986842105263[/C][C]0.927075184636395[/C][C]87.9094657705574[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]81.4135135135135[/C][C]0.908143918653592[/C][C]89.6482505044097[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]81.3263888888889[/C][C]0.889617985780548[/C][C]91.4172040008087[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]81.2742857142857[/C][C]0.878651059361522[/C][C]92.4989332777271[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]81.2073529411765[/C][C]0.8686049793094[/C][C]93.4916963125653[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]81.1545454545455[/C][C]0.863084353091263[/C][C]94.0285212724325[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]81.096875[/C][C]0.856765699615536[/C][C]94.6546705083914[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]81.0322580645161[/C][C]0.849751182027234[/C][C]95.3599827554216[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]80.9633333333333[/C][C]0.840627848044378[/C][C]96.312932674887[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]80.8896551724138[/C][C]0.829688421955347[/C][C]97.4940146588754[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]80.8214285714286[/C][C]0.8225542822877[/C][C]98.2566504263364[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]80.7518518518519[/C][C]0.814756207790011[/C][C]99.1116742404302[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]80.6711538461538[/C][C]0.805244576256312[/C][C]100.182175980874[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]80.588[/C][C]0.793641259625274[/C][C]101.542099812263[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]80.4958333333333[/C][C]0.779553417877106[/C][C]103.258906301176[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]80.4065217391304[/C][C]0.764252039856146[/C][C]105.209430326500[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]80.3045454545454[/C][C]0.74456419525857[/C][C]107.854428088175[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]80.2047619047619[/C][C]0.723706362230896[/C][C]110.825005956177[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]80.0975[/C][C]0.696193749741756[/C][C]115.050587612588[/C][/ROW]
[ROW][C]Median[/C][C]78.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]95[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]80.6935483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]80.9633333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]80.6935483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]80.9633333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]80.9633333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]80.6935483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]80.9633333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]81.096875[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]120[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=87233&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=87233&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 Mean83.83666666666671.5694407170493653.4181799643153
Geometric Mean82.2104030770412
Harmonic Mean80.69581733859
Quadratic Mean85.5669377349297
Winsorized Mean ( 1 / 40 )83.83251.5676885170258053.4752274380665
Winsorized Mean ( 2 / 40 )83.82751.5644174341470753.583844164779
Winsorized Mean ( 3 / 40 )83.851.5564566884334453.872363184352
Winsorized Mean ( 4 / 40 )83.711.513417302918555.3119089087802
Winsorized Mean ( 5 / 40 )83.11833333333331.3919632183743959.7130241921216
Winsorized Mean ( 6 / 40 )83.11333333333331.3895361927632859.813723288525
Winsorized Mean ( 7 / 40 )83.11333333333331.3859049028077459.9704447000311
Winsorized Mean ( 8 / 40 )83.121.3829157683709360.1048899007891
Winsorized Mean ( 9 / 40 )83.1951.3500969204756661.6215019368305
Winsorized Mean ( 10 / 40 )83.30333333333331.3218657413981163.0195115316515
Winsorized Mean ( 11 / 40 )83.2851.3161593445202963.2788122097448
Winsorized Mean ( 12 / 40 )83.2851.2905694626075464.5335275729568
Winsorized Mean ( 13 / 40 )83.091.2562016466438966.143839424177
Winsorized Mean ( 14 / 40 )83.04333333333331.2425056759663566.8353754350033
Winsorized Mean ( 15 / 40 )83.11833333333331.2269984461038967.7411887498802
Winsorized Mean ( 16 / 40 )83.11833333333331.2162398909983468.3404104309607
Winsorized Mean ( 17 / 40 )82.96251.1886567416372969.795170543285
Winsorized Mean ( 18 / 40 )82.96251.1649419399220571.2159955418474
Winsorized Mean ( 19 / 40 )82.80416666666671.1048254205306074.9477384643265
Winsorized Mean ( 20 / 40 )82.90416666666671.0729885721465377.2647247312389
Winsorized Mean ( 21 / 40 )82.76416666666671.0271188360691480.5789590846285
Winsorized Mean ( 22 / 40 )82.65416666666671.0073475834230282.0512879832435
Winsorized Mean ( 23 / 40 )82.61583333333330.97897862787100684.3898232109507
Winsorized Mean ( 24 / 40 )82.05583333333330.9005769982286791.1147336593402
Winsorized Mean ( 25 / 40 )82.22250.87371631527620794.1066322814484
Winsorized Mean ( 26 / 40 )81.96250.82198610204843899.7127564514104
Winsorized Mean ( 27 / 40 )81.9850.814749063463448100.626074550472
Winsorized Mean ( 28 / 40 )82.03166666666670.804987937113486101.90421854123
Winsorized Mean ( 29 / 40 )82.03166666666670.804987937113486101.90421854123
Winsorized Mean ( 30 / 40 )82.03166666666670.79951489435356102.601799223506
Winsorized Mean ( 31 / 40 )81.87666666666670.753101647523937108.719277053586
Winsorized Mean ( 32 / 40 )81.82333333333330.741164324889739110.398369950559
Winsorized Mean ( 33 / 40 )81.90583333333330.733251169162039111.702288080816
Winsorized Mean ( 34 / 40 )81.84916666666670.72664764562133112.639416311162
Winsorized Mean ( 35 / 40 )81.87833333333330.71771714750882114.081617831664
Winsorized Mean ( 36 / 40 )81.72833333333330.700390230697694116.689710608784
Winsorized Mean ( 37 / 40 )81.790.694551020766782117.759527456607
Winsorized Mean ( 38 / 40 )81.63166666666670.669821648711879121.870749958069
Winsorized Mean ( 39 / 40 )81.59916666666670.666127753993574122.497773403769
Winsorized Mean ( 40 / 40 )81.23250.618018613233065131.440215975123
Trimmed Mean ( 1 / 40 )83.64745762711861.5242891784177354.8763704495676
Trimmed Mean ( 2 / 40 )83.45603448275861.4757344060402856.552204882645
Trimmed Mean ( 3 / 40 )83.26052631578951.4231472010794158.5045076522226
Trimmed Mean ( 4 / 40 )83.051.3671647003522760.7461558790984
Trimmed Mean ( 5 / 40 )82.871.3187855193466362.8381179382804
Trimmed Mean ( 6 / 40 )82.81481481481481.2986152427329663.7716331132303
Trimmed Mean ( 7 / 40 )82.75849056603771.2765990222681364.8273178362625
Trimmed Mean ( 8 / 40 )82.71.2526685481050166.0190599700981
Trimmed Mean ( 9 / 40 )82.63823529411761.2263448349775767.3858061265691
Trimmed Mean ( 10 / 40 )82.5641.2026103930931968.6539884190092
Trimmed Mean ( 11 / 40 )82.47346938775511.1804989825146469.8632278463083
Trimmed Mean ( 12 / 40 )82.381251.1563538360203471.2422508006028
Trimmed Mean ( 13 / 40 )82.28510638297871.1328995335490172.6323067017305
Trimmed Mean ( 14 / 40 )82.2043478260871.1115031950956373.9578151361182
Trimmed Mean ( 15 / 40 )82.12444444444441.0890778964092675.4073190863689
Trimmed Mean ( 16 / 40 )82.03409090909091.0655181165748976.9898602689077
Trimmed Mean ( 17 / 40 )81.9395348837211.0399361748669578.7928498536984
Trimmed Mean ( 18 / 40 )81.85357142857141.0145038926010280.6833488028446
Trimmed Mean ( 19 / 40 )81.76341463414630.9884053995962382.7225495404489
Trimmed Mean ( 20 / 40 )81.681250.96665954525057684.4984673262878
Trimmed Mean ( 21 / 40 )81.58717948717950.94550016359341586.2899686628332
Trimmed Mean ( 22 / 40 )81.49868421052630.92707518463639587.9094657705574
Trimmed Mean ( 23 / 40 )81.41351351351350.90814391865359289.6482505044097
Trimmed Mean ( 24 / 40 )81.32638888888890.88961798578054891.4172040008087
Trimmed Mean ( 25 / 40 )81.27428571428570.87865105936152292.4989332777271
Trimmed Mean ( 26 / 40 )81.20735294117650.868604979309493.4916963125653
Trimmed Mean ( 27 / 40 )81.15454545454550.86308435309126394.0285212724325
Trimmed Mean ( 28 / 40 )81.0968750.85676569961553694.6546705083914
Trimmed Mean ( 29 / 40 )81.03225806451610.84975118202723495.3599827554216
Trimmed Mean ( 30 / 40 )80.96333333333330.84062784804437896.312932674887
Trimmed Mean ( 31 / 40 )80.88965517241380.82968842195534797.4940146588754
Trimmed Mean ( 32 / 40 )80.82142857142860.822554282287798.2566504263364
Trimmed Mean ( 33 / 40 )80.75185185185190.81475620779001199.1116742404302
Trimmed Mean ( 34 / 40 )80.67115384615380.805244576256312100.182175980874
Trimmed Mean ( 35 / 40 )80.5880.793641259625274101.542099812263
Trimmed Mean ( 36 / 40 )80.49583333333330.779553417877106103.258906301176
Trimmed Mean ( 37 / 40 )80.40652173913040.764252039856146105.209430326500
Trimmed Mean ( 38 / 40 )80.30454545454540.74456419525857107.854428088175
Trimmed Mean ( 39 / 40 )80.20476190476190.723706362230896110.825005956177
Trimmed Mean ( 40 / 40 )80.09750.696193749741756115.050587612588
Median78.8
Midrange95
Midmean - Weighted Average at Xnp80.6935483870968
Midmean - Weighted Average at X(n+1)p80.9633333333334
Midmean - Empirical Distribution Function80.6935483870968
Midmean - Empirical Distribution Function - Averaging80.9633333333334
Midmean - Empirical Distribution Function - Interpolation80.9633333333334
Midmean - Closest Observation80.6935483870968
Midmean - True Basic - Statistics Graphics Toolkit80.9633333333334
Midmean - MS Excel (old versions)81.096875
Number of observations120



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')