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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 01 Mar 2012 09:45:49 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/01/t13306132114il2l6vogpgl54i.htm/, Retrieved Sat, 27 Apr 2024 14:01:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163376, Retrieved Sat, 27 Apr 2024 14:01:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [robuustheid Gem. ...] [2012-03-01 14:45:49] [54d49d8a22bca19e9398641fe7fc5cc7] [Current]
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Dataseries X:
402,55
403,04
399,25
401,26
402,76
402,27
402,27
406,11
406,39
407,88
407,77
407,77
407,77
408,06
403,74
403,44
404,3
403,29
403,29
400,66
400,84
401,31
402
402
402
403,33
403,79
403,04
402,91
406,55
406,55
404,69
404,74
404,2
404,18
404,18
404,18
404,82
406,46
407,25
407,34
404,3
404,3
404,7
406,82
406,82
406,76
406,76
406,76
407,67
406,03
401,97
401,84
402,24
402,24
401,57
401,63
402,06
402,11
402,43




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163376&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163376&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163376&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean404.1540.2930091493143531379.32211654731
Geometric Mean404.147737298245
Harmonic Mean404.141478629363
Quadratic Mean404.160266631114
Winsorized Mean ( 1 / 20 )404.17450.286555762116661410.45671884084
Winsorized Mean ( 2 / 20 )404.1768333333330.2845415076674881420.44946850303
Winsorized Mean ( 3 / 20 )404.1978333333330.2805895822255061440.53043640261
Winsorized Mean ( 4 / 20 )404.2011666666670.2800021278840311443.56462474483
Winsorized Mean ( 5 / 20 )404.21450.2745472312797741472.29494217004
Winsorized Mean ( 6 / 20 )404.18750.2667417576125581515.27643672155
Winsorized Mean ( 7 / 20 )404.20150.2607776099752561549.9854456
Winsorized Mean ( 8 / 20 )404.16150.2472277735892511634.7738530036
Winsorized Mean ( 9 / 20 )404.1660.2465547005006861639.2548962938
Winsorized Mean ( 10 / 20 )404.1560.2447407483405751651.36375017366
Winsorized Mean ( 11 / 20 )404.1560.2447407483405751651.36375017366
Winsorized Mean ( 12 / 20 )404.1680.2429625066980841663.49946538145
Winsorized Mean ( 13 / 20 )404.1333333333330.2332586240364591732.55473405419
Winsorized Mean ( 14 / 20 )404.1636666666670.2288675099261831765.92853567123
Winsorized Mean ( 15 / 20 )404.1411666666670.2249133030291271796.87533473433
Winsorized Mean ( 16 / 20 )404.13050.2205162695613251832.65616094423
Winsorized Mean ( 17 / 20 )404.0511666666670.2069320000302891952.57942999404
Winsorized Mean ( 18 / 20 )404.0751666666670.1959608360022572062.02001843885
Winsorized Mean ( 19 / 20 )403.730.1296411823387613114.21103014185
Winsorized Mean ( 20 / 20 )403.7733333333330.1152172270808323504.45279376548
Trimmed Mean ( 1 / 20 )404.1712068965520.2829075207744041428.63366018058
Trimmed Mean ( 2 / 20 )404.1676785714290.2782813664274741452.37061237718
Trimmed Mean ( 3 / 20 )404.1625925925930.2737433884322231476.42869077972
Trimmed Mean ( 4 / 20 )404.1490384615380.269780965232471498.06357951638
Trimmed Mean ( 5 / 20 )404.13340.264832270368571525.99756607291
Trimmed Mean ( 6 / 20 )404.1131250.2601956704128561553.11241097436
Trimmed Mean ( 7 / 20 )404.0969565217390.2564572587427711575.68929225377
Trimmed Mean ( 8 / 20 )404.0765909090910.2529851258656971597.23457861947
Trimmed Mean ( 9 / 20 )404.0614285714290.2517270361853091605.15705700352
Trimmed Mean ( 10 / 20 )404.0440.2496738385194281618.28729191649
Trimmed Mean ( 11 / 20 )404.0263157894740.2468568906756671636.68234937101
Trimmed Mean ( 12 / 20 )404.0066666666670.2424844946769381666.1134032711
Trimmed Mean ( 13 / 20 )403.9829411764710.236388652986061708.97771984129
Trimmed Mean ( 14 / 20 )403.961250.2302351313892091754.55955640892
Trimmed Mean ( 15 / 20 )403.9323333333330.2220457047978111819.14049497667
Trimmed Mean ( 16 / 20 )403.90250.2108709734892811915.40112570557
Trimmed Mean ( 17 / 20 )403.8696153846150.1950774842263222070.30358724568
Trimmed Mean ( 18 / 20 )403.8429166666670.1762157348403192291.75287344582
Trimmed Mean ( 19 / 20 )403.8077272727270.1495576910479482700.01311496087
Trimmed Mean ( 20 / 20 )403.820.1425722346926742832.38879484822
Median403.985
Midrange403.655
Midmean - Weighted Average at Xnp403.877741935484
Midmean - Weighted Average at X(n+1)p403.877741935484
Midmean - Empirical Distribution Function403.877741935484
Midmean - Empirical Distribution Function - Averaging403.877741935484
Midmean - Empirical Distribution Function - Interpolation403.877741935484
Midmean - Closest Observation403.877741935484
Midmean - True Basic - Statistics Graphics Toolkit403.877741935484
Midmean - MS Excel (old versions)404.039696969697
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 404.154 & 0.293009149314353 & 1379.32211654731 \tabularnewline
Geometric Mean & 404.147737298245 &  &  \tabularnewline
Harmonic Mean & 404.141478629363 &  &  \tabularnewline
Quadratic Mean & 404.160266631114 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 404.1745 & 0.28655576211666 & 1410.45671884084 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 404.176833333333 & 0.284541507667488 & 1420.44946850303 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 404.197833333333 & 0.280589582225506 & 1440.53043640261 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 404.201166666667 & 0.280002127884031 & 1443.56462474483 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 404.2145 & 0.274547231279774 & 1472.29494217004 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 404.1875 & 0.266741757612558 & 1515.27643672155 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 404.2015 & 0.260777609975256 & 1549.9854456 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 404.1615 & 0.247227773589251 & 1634.7738530036 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 404.166 & 0.246554700500686 & 1639.2548962938 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 404.156 & 0.244740748340575 & 1651.36375017366 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 404.156 & 0.244740748340575 & 1651.36375017366 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 404.168 & 0.242962506698084 & 1663.49946538145 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 404.133333333333 & 0.233258624036459 & 1732.55473405419 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 404.163666666667 & 0.228867509926183 & 1765.92853567123 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 404.141166666667 & 0.224913303029127 & 1796.87533473433 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 404.1305 & 0.220516269561325 & 1832.65616094423 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 404.051166666667 & 0.206932000030289 & 1952.57942999404 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 404.075166666667 & 0.195960836002257 & 2062.02001843885 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 403.73 & 0.129641182338761 & 3114.21103014185 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 403.773333333333 & 0.115217227080832 & 3504.45279376548 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 404.171206896552 & 0.282907520774404 & 1428.63366018058 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 404.167678571429 & 0.278281366427474 & 1452.37061237718 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 404.162592592593 & 0.273743388432223 & 1476.42869077972 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 404.149038461538 & 0.26978096523247 & 1498.06357951638 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 404.1334 & 0.26483227036857 & 1525.99756607291 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 404.113125 & 0.260195670412856 & 1553.11241097436 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 404.096956521739 & 0.256457258742771 & 1575.68929225377 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 404.076590909091 & 0.252985125865697 & 1597.23457861947 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 404.061428571429 & 0.251727036185309 & 1605.15705700352 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 404.044 & 0.249673838519428 & 1618.28729191649 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 404.026315789474 & 0.246856890675667 & 1636.68234937101 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 404.006666666667 & 0.242484494676938 & 1666.1134032711 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 403.982941176471 & 0.23638865298606 & 1708.97771984129 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 403.96125 & 0.230235131389209 & 1754.55955640892 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 403.932333333333 & 0.222045704797811 & 1819.14049497667 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 403.9025 & 0.210870973489281 & 1915.40112570557 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 403.869615384615 & 0.195077484226322 & 2070.30358724568 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 403.842916666667 & 0.176215734840319 & 2291.75287344582 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 403.807727272727 & 0.149557691047948 & 2700.01311496087 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 403.82 & 0.142572234692674 & 2832.38879484822 \tabularnewline
Median & 403.985 &  &  \tabularnewline
Midrange & 403.655 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 403.877741935484 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 403.877741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 403.877741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 403.877741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 403.877741935484 &  &  \tabularnewline
Midmean - Closest Observation & 403.877741935484 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 403.877741935484 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 404.039696969697 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163376&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]404.154[/C][C]0.293009149314353[/C][C]1379.32211654731[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]404.147737298245[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]404.141478629363[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]404.160266631114[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]404.1745[/C][C]0.28655576211666[/C][C]1410.45671884084[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]404.176833333333[/C][C]0.284541507667488[/C][C]1420.44946850303[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]404.197833333333[/C][C]0.280589582225506[/C][C]1440.53043640261[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]404.201166666667[/C][C]0.280002127884031[/C][C]1443.56462474483[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]404.2145[/C][C]0.274547231279774[/C][C]1472.29494217004[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]404.1875[/C][C]0.266741757612558[/C][C]1515.27643672155[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]404.2015[/C][C]0.260777609975256[/C][C]1549.9854456[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]404.1615[/C][C]0.247227773589251[/C][C]1634.7738530036[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]404.166[/C][C]0.246554700500686[/C][C]1639.2548962938[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]404.156[/C][C]0.244740748340575[/C][C]1651.36375017366[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]404.156[/C][C]0.244740748340575[/C][C]1651.36375017366[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]404.168[/C][C]0.242962506698084[/C][C]1663.49946538145[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]404.133333333333[/C][C]0.233258624036459[/C][C]1732.55473405419[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]404.163666666667[/C][C]0.228867509926183[/C][C]1765.92853567123[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]404.141166666667[/C][C]0.224913303029127[/C][C]1796.87533473433[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]404.1305[/C][C]0.220516269561325[/C][C]1832.65616094423[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]404.051166666667[/C][C]0.206932000030289[/C][C]1952.57942999404[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]404.075166666667[/C][C]0.195960836002257[/C][C]2062.02001843885[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]403.73[/C][C]0.129641182338761[/C][C]3114.21103014185[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]403.773333333333[/C][C]0.115217227080832[/C][C]3504.45279376548[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]404.171206896552[/C][C]0.282907520774404[/C][C]1428.63366018058[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]404.167678571429[/C][C]0.278281366427474[/C][C]1452.37061237718[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]404.162592592593[/C][C]0.273743388432223[/C][C]1476.42869077972[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]404.149038461538[/C][C]0.26978096523247[/C][C]1498.06357951638[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]404.1334[/C][C]0.26483227036857[/C][C]1525.99756607291[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]404.113125[/C][C]0.260195670412856[/C][C]1553.11241097436[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]404.096956521739[/C][C]0.256457258742771[/C][C]1575.68929225377[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]404.076590909091[/C][C]0.252985125865697[/C][C]1597.23457861947[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]404.061428571429[/C][C]0.251727036185309[/C][C]1605.15705700352[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]404.044[/C][C]0.249673838519428[/C][C]1618.28729191649[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]404.026315789474[/C][C]0.246856890675667[/C][C]1636.68234937101[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]404.006666666667[/C][C]0.242484494676938[/C][C]1666.1134032711[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]403.982941176471[/C][C]0.23638865298606[/C][C]1708.97771984129[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]403.96125[/C][C]0.230235131389209[/C][C]1754.55955640892[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]403.932333333333[/C][C]0.222045704797811[/C][C]1819.14049497667[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]403.9025[/C][C]0.210870973489281[/C][C]1915.40112570557[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]403.869615384615[/C][C]0.195077484226322[/C][C]2070.30358724568[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]403.842916666667[/C][C]0.176215734840319[/C][C]2291.75287344582[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]403.807727272727[/C][C]0.149557691047948[/C][C]2700.01311496087[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]403.82[/C][C]0.142572234692674[/C][C]2832.38879484822[/C][/ROW]
[ROW][C]Median[/C][C]403.985[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]403.655[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]403.877741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]403.877741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]403.877741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]403.877741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]403.877741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]403.877741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]403.877741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]404.039696969697[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163376&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163376&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 Mean404.1540.2930091493143531379.32211654731
Geometric Mean404.147737298245
Harmonic Mean404.141478629363
Quadratic Mean404.160266631114
Winsorized Mean ( 1 / 20 )404.17450.286555762116661410.45671884084
Winsorized Mean ( 2 / 20 )404.1768333333330.2845415076674881420.44946850303
Winsorized Mean ( 3 / 20 )404.1978333333330.2805895822255061440.53043640261
Winsorized Mean ( 4 / 20 )404.2011666666670.2800021278840311443.56462474483
Winsorized Mean ( 5 / 20 )404.21450.2745472312797741472.29494217004
Winsorized Mean ( 6 / 20 )404.18750.2667417576125581515.27643672155
Winsorized Mean ( 7 / 20 )404.20150.2607776099752561549.9854456
Winsorized Mean ( 8 / 20 )404.16150.2472277735892511634.7738530036
Winsorized Mean ( 9 / 20 )404.1660.2465547005006861639.2548962938
Winsorized Mean ( 10 / 20 )404.1560.2447407483405751651.36375017366
Winsorized Mean ( 11 / 20 )404.1560.2447407483405751651.36375017366
Winsorized Mean ( 12 / 20 )404.1680.2429625066980841663.49946538145
Winsorized Mean ( 13 / 20 )404.1333333333330.2332586240364591732.55473405419
Winsorized Mean ( 14 / 20 )404.1636666666670.2288675099261831765.92853567123
Winsorized Mean ( 15 / 20 )404.1411666666670.2249133030291271796.87533473433
Winsorized Mean ( 16 / 20 )404.13050.2205162695613251832.65616094423
Winsorized Mean ( 17 / 20 )404.0511666666670.2069320000302891952.57942999404
Winsorized Mean ( 18 / 20 )404.0751666666670.1959608360022572062.02001843885
Winsorized Mean ( 19 / 20 )403.730.1296411823387613114.21103014185
Winsorized Mean ( 20 / 20 )403.7733333333330.1152172270808323504.45279376548
Trimmed Mean ( 1 / 20 )404.1712068965520.2829075207744041428.63366018058
Trimmed Mean ( 2 / 20 )404.1676785714290.2782813664274741452.37061237718
Trimmed Mean ( 3 / 20 )404.1625925925930.2737433884322231476.42869077972
Trimmed Mean ( 4 / 20 )404.1490384615380.269780965232471498.06357951638
Trimmed Mean ( 5 / 20 )404.13340.264832270368571525.99756607291
Trimmed Mean ( 6 / 20 )404.1131250.2601956704128561553.11241097436
Trimmed Mean ( 7 / 20 )404.0969565217390.2564572587427711575.68929225377
Trimmed Mean ( 8 / 20 )404.0765909090910.2529851258656971597.23457861947
Trimmed Mean ( 9 / 20 )404.0614285714290.2517270361853091605.15705700352
Trimmed Mean ( 10 / 20 )404.0440.2496738385194281618.28729191649
Trimmed Mean ( 11 / 20 )404.0263157894740.2468568906756671636.68234937101
Trimmed Mean ( 12 / 20 )404.0066666666670.2424844946769381666.1134032711
Trimmed Mean ( 13 / 20 )403.9829411764710.236388652986061708.97771984129
Trimmed Mean ( 14 / 20 )403.961250.2302351313892091754.55955640892
Trimmed Mean ( 15 / 20 )403.9323333333330.2220457047978111819.14049497667
Trimmed Mean ( 16 / 20 )403.90250.2108709734892811915.40112570557
Trimmed Mean ( 17 / 20 )403.8696153846150.1950774842263222070.30358724568
Trimmed Mean ( 18 / 20 )403.8429166666670.1762157348403192291.75287344582
Trimmed Mean ( 19 / 20 )403.8077272727270.1495576910479482700.01311496087
Trimmed Mean ( 20 / 20 )403.820.1425722346926742832.38879484822
Median403.985
Midrange403.655
Midmean - Weighted Average at Xnp403.877741935484
Midmean - Weighted Average at X(n+1)p403.877741935484
Midmean - Empirical Distribution Function403.877741935484
Midmean - Empirical Distribution Function - Averaging403.877741935484
Midmean - Empirical Distribution Function - Interpolation403.877741935484
Midmean - Closest Observation403.877741935484
Midmean - True Basic - Statistics Graphics Toolkit403.877741935484
Midmean - MS Excel (old versions)404.039696969697
Number of observations60



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')