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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, 19 Oct 2011 07:33:26 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Oct/19/t1319024085ohe6xa0mxkj447z.htm/, Retrieved Wed, 15 May 2024 04:54:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=132762, Retrieved Wed, 15 May 2024 04:54:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact118
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Opgave 5 IKO Opdr 1] [2011-10-19 11:33:26] [76bda0bb7d6f469fbad64fdea2dd989f] [Current]
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Dataseries X:
105,46
105,1
105,09
105,04
104,87
104,67
104,54
104,9
104,9
104,89
104,8
104,41
104,31
103,88
103,88
103,86
103,89
103,98
103,98
104,29
104,29
104,24
103,98
103,54
103,44
103,32
103,3
103,26
103,14
103,11
102,91
103,23
103,23
103,14
102,91
102,42
102,1
102,07
102,06
101,98
101,83
101,75
101,56
101,66
101,65
101,61
101,52
101,31
101,19
101,11
101,1
101,07
100,98
100,93
100,92
101,02
101,01
100,97
100,89
100,62
100,53
100,48
100,48
100,47
100,52
100,49
100,47
100,44
100,35
100,38
100,33
100,32




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132762&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=132762&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132762&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean102.5329166666670.192157713237463533.587306693015
Geometric Mean102.520150017081
Harmonic Mean102.507402609229
Quadratic Mean102.545700279599
Winsorized Mean ( 1 / 24 )102.5280555555560.19112483516523536.445488452188
Winsorized Mean ( 2 / 24 )102.5283333333330.190982653719937536.846312145627
Winsorized Mean ( 3 / 24 )102.52750.190392555309736538.505824627466
Winsorized Mean ( 4 / 24 )102.5230555555560.18845447087682544.020288181797
Winsorized Mean ( 5 / 24 )102.5251388888890.188132032626396544.963754750313
Winsorized Mean ( 6 / 24 )102.5243055555560.187984098733688545.388180416253
Winsorized Mean ( 7 / 24 )102.5233333333330.187490949181658546.817506556007
Winsorized Mean ( 8 / 24 )102.5155555555560.186133112473394550.764741390166
Winsorized Mean ( 9 / 24 )102.5005555555560.183180035021273559.561829670204
Winsorized Mean ( 10 / 24 )102.4866666666670.179576314090026570.713722385946
Winsorized Mean ( 11 / 24 )102.4683333333330.176199000101966581.548892298112
Winsorized Mean ( 12 / 24 )102.4666666666670.171341594766206598.025638820986
Winsorized Mean ( 13 / 24 )102.5118055555560.163683313648687626.281343348023
Winsorized Mean ( 14 / 24 )102.5176388888890.162873321390091629.431744953203
Winsorized Mean ( 15 / 24 )102.5093055555560.160998610787862636.70925515392
Winsorized Mean ( 16 / 24 )102.4604166666670.151298557241362677.206832205376
Winsorized Mean ( 17 / 24 )102.4627777777780.150971452884838678.689751074575
Winsorized Mean ( 18 / 24 )102.4702777777780.149938298762938683.416302727227
Winsorized Mean ( 19 / 24 )102.4491666666670.146243353847623700.53895764325
Winsorized Mean ( 20 / 24 )102.4602777777780.143957176652606711.74136753899
Winsorized Mean ( 21 / 24 )102.4690277777780.142771192639346717.715008773685
Winsorized Mean ( 22 / 24 )102.4659722222220.141509393468549724.093077573651
Winsorized Mean ( 23 / 24 )102.3893055555560.124263452272864823.969587861794
Winsorized Mean ( 24 / 24 )102.3959722222220.114558016361855893.835066930488
Trimmed Mean ( 1 / 24 )102.5227142857140.19050243271609538.17010535769
Trimmed Mean ( 2 / 24 )102.5170588235290.189631251015954540.61268000022
Trimmed Mean ( 3 / 24 )102.5109090909090.188550566047335543.678606964107
Trimmed Mean ( 4 / 24 )102.50468750.187384616448755547.028296359817
Trimmed Mean ( 5 / 24 )102.499354838710.186519071088825549.538201323642
Trimmed Mean ( 6 / 24 )102.4931666666670.185406636877208552.802037688362
Trimmed Mean ( 7 / 24 )102.4867241379310.183935334768359557.188885251434
Trimmed Mean ( 8 / 24 )102.480.182105114500589562.751904475854
Trimmed Mean ( 9 / 24 )102.4740740740740.180025916008106569.218456688536
Trimmed Mean ( 10 / 24 )102.470.177968255172574575.776842339865
Trimmed Mean ( 11 / 24 )102.46760.176019841182169582.136646140664
Trimmed Mean ( 12 / 24 )102.46750.174099888789728588.555803868184
Trimmed Mean ( 13 / 24 )102.4676086956520.172468630427134594.123165713566
Trimmed Mean ( 14 / 24 )102.4620454545450.171675174974366596.836703209095
Trimmed Mean ( 15 / 24 )102.4552380952380.170468452773093601.021693037914
Trimmed Mean ( 16 / 24 )102.448750.168946656541082606.397025531476
Trimmed Mean ( 17 / 24 )102.4473684210530.16866039181803607.418062514549
Trimmed Mean ( 18 / 24 )102.4455555555560.167837054597439610.386995894761
Trimmed Mean ( 19 / 24 )102.4426470588240.166428515497443615.535425240258
Trimmed Mean ( 20 / 24 )102.4418750.16485235176686621.415914920504
Trimmed Mean ( 21 / 24 )102.4396666666670.162623946246303629.917481595954
Trimmed Mean ( 22 / 24 )102.4360714285710.159109907843599643.806993649092
Trimmed Mean ( 23 / 24 )102.4323076923080.153685300525565666.506863974727
Trimmed Mean ( 24 / 24 )102.4379166666670.150971466694997678.525014754071
Median102.26
Midrange102.89
Midmean - Weighted Average at Xnp102.486666666667
Midmean - Weighted Average at X(n+1)p102.526315789474
Midmean - Empirical Distribution Function102.486666666667
Midmean - Empirical Distribution Function - Averaging102.526315789474
Midmean - Empirical Distribution Function - Interpolation102.526315789474
Midmean - Closest Observation102.486666666667
Midmean - True Basic - Statistics Graphics Toolkit102.526315789474
Midmean - MS Excel (old versions)102.486666666667
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 102.532916666667 & 0.192157713237463 & 533.587306693015 \tabularnewline
Geometric Mean & 102.520150017081 &  &  \tabularnewline
Harmonic Mean & 102.507402609229 &  &  \tabularnewline
Quadratic Mean & 102.545700279599 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 102.528055555556 & 0.19112483516523 & 536.445488452188 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 102.528333333333 & 0.190982653719937 & 536.846312145627 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 102.5275 & 0.190392555309736 & 538.505824627466 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 102.523055555556 & 0.18845447087682 & 544.020288181797 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 102.525138888889 & 0.188132032626396 & 544.963754750313 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 102.524305555556 & 0.187984098733688 & 545.388180416253 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 102.523333333333 & 0.187490949181658 & 546.817506556007 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 102.515555555556 & 0.186133112473394 & 550.764741390166 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 102.500555555556 & 0.183180035021273 & 559.561829670204 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 102.486666666667 & 0.179576314090026 & 570.713722385946 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 102.468333333333 & 0.176199000101966 & 581.548892298112 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 102.466666666667 & 0.171341594766206 & 598.025638820986 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 102.511805555556 & 0.163683313648687 & 626.281343348023 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 102.517638888889 & 0.162873321390091 & 629.431744953203 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 102.509305555556 & 0.160998610787862 & 636.70925515392 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 102.460416666667 & 0.151298557241362 & 677.206832205376 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 102.462777777778 & 0.150971452884838 & 678.689751074575 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 102.470277777778 & 0.149938298762938 & 683.416302727227 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 102.449166666667 & 0.146243353847623 & 700.53895764325 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 102.460277777778 & 0.143957176652606 & 711.74136753899 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 102.469027777778 & 0.142771192639346 & 717.715008773685 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 102.465972222222 & 0.141509393468549 & 724.093077573651 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 102.389305555556 & 0.124263452272864 & 823.969587861794 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 102.395972222222 & 0.114558016361855 & 893.835066930488 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 102.522714285714 & 0.19050243271609 & 538.17010535769 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 102.517058823529 & 0.189631251015954 & 540.61268000022 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 102.510909090909 & 0.188550566047335 & 543.678606964107 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 102.5046875 & 0.187384616448755 & 547.028296359817 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 102.49935483871 & 0.186519071088825 & 549.538201323642 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 102.493166666667 & 0.185406636877208 & 552.802037688362 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 102.486724137931 & 0.183935334768359 & 557.188885251434 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 102.48 & 0.182105114500589 & 562.751904475854 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 102.474074074074 & 0.180025916008106 & 569.218456688536 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 102.47 & 0.177968255172574 & 575.776842339865 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 102.4676 & 0.176019841182169 & 582.136646140664 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 102.4675 & 0.174099888789728 & 588.555803868184 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 102.467608695652 & 0.172468630427134 & 594.123165713566 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 102.462045454545 & 0.171675174974366 & 596.836703209095 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 102.455238095238 & 0.170468452773093 & 601.021693037914 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 102.44875 & 0.168946656541082 & 606.397025531476 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 102.447368421053 & 0.16866039181803 & 607.418062514549 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 102.445555555556 & 0.167837054597439 & 610.386995894761 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 102.442647058824 & 0.166428515497443 & 615.535425240258 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 102.441875 & 0.16485235176686 & 621.415914920504 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 102.439666666667 & 0.162623946246303 & 629.917481595954 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 102.436071428571 & 0.159109907843599 & 643.806993649092 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 102.432307692308 & 0.153685300525565 & 666.506863974727 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 102.437916666667 & 0.150971466694997 & 678.525014754071 \tabularnewline
Median & 102.26 &  &  \tabularnewline
Midrange & 102.89 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 102.486666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 102.526315789474 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 102.486666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 102.526315789474 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 102.526315789474 &  &  \tabularnewline
Midmean - Closest Observation & 102.486666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 102.526315789474 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 102.486666666667 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132762&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]102.532916666667[/C][C]0.192157713237463[/C][C]533.587306693015[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]102.520150017081[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]102.507402609229[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]102.545700279599[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]102.528055555556[/C][C]0.19112483516523[/C][C]536.445488452188[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]102.528333333333[/C][C]0.190982653719937[/C][C]536.846312145627[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]102.5275[/C][C]0.190392555309736[/C][C]538.505824627466[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]102.523055555556[/C][C]0.18845447087682[/C][C]544.020288181797[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]102.525138888889[/C][C]0.188132032626396[/C][C]544.963754750313[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]102.524305555556[/C][C]0.187984098733688[/C][C]545.388180416253[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]102.523333333333[/C][C]0.187490949181658[/C][C]546.817506556007[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]102.515555555556[/C][C]0.186133112473394[/C][C]550.764741390166[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]102.500555555556[/C][C]0.183180035021273[/C][C]559.561829670204[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]102.486666666667[/C][C]0.179576314090026[/C][C]570.713722385946[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]102.468333333333[/C][C]0.176199000101966[/C][C]581.548892298112[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]102.466666666667[/C][C]0.171341594766206[/C][C]598.025638820986[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]102.511805555556[/C][C]0.163683313648687[/C][C]626.281343348023[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]102.517638888889[/C][C]0.162873321390091[/C][C]629.431744953203[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]102.509305555556[/C][C]0.160998610787862[/C][C]636.70925515392[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]102.460416666667[/C][C]0.151298557241362[/C][C]677.206832205376[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]102.462777777778[/C][C]0.150971452884838[/C][C]678.689751074575[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]102.470277777778[/C][C]0.149938298762938[/C][C]683.416302727227[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]102.449166666667[/C][C]0.146243353847623[/C][C]700.53895764325[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]102.460277777778[/C][C]0.143957176652606[/C][C]711.74136753899[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]102.469027777778[/C][C]0.142771192639346[/C][C]717.715008773685[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]102.465972222222[/C][C]0.141509393468549[/C][C]724.093077573651[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]102.389305555556[/C][C]0.124263452272864[/C][C]823.969587861794[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]102.395972222222[/C][C]0.114558016361855[/C][C]893.835066930488[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]102.522714285714[/C][C]0.19050243271609[/C][C]538.17010535769[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]102.517058823529[/C][C]0.189631251015954[/C][C]540.61268000022[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]102.510909090909[/C][C]0.188550566047335[/C][C]543.678606964107[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]102.5046875[/C][C]0.187384616448755[/C][C]547.028296359817[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]102.49935483871[/C][C]0.186519071088825[/C][C]549.538201323642[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]102.493166666667[/C][C]0.185406636877208[/C][C]552.802037688362[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]102.486724137931[/C][C]0.183935334768359[/C][C]557.188885251434[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]102.48[/C][C]0.182105114500589[/C][C]562.751904475854[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]102.474074074074[/C][C]0.180025916008106[/C][C]569.218456688536[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]102.47[/C][C]0.177968255172574[/C][C]575.776842339865[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]102.4676[/C][C]0.176019841182169[/C][C]582.136646140664[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]102.4675[/C][C]0.174099888789728[/C][C]588.555803868184[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]102.467608695652[/C][C]0.172468630427134[/C][C]594.123165713566[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]102.462045454545[/C][C]0.171675174974366[/C][C]596.836703209095[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]102.455238095238[/C][C]0.170468452773093[/C][C]601.021693037914[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]102.44875[/C][C]0.168946656541082[/C][C]606.397025531476[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]102.447368421053[/C][C]0.16866039181803[/C][C]607.418062514549[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]102.445555555556[/C][C]0.167837054597439[/C][C]610.386995894761[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]102.442647058824[/C][C]0.166428515497443[/C][C]615.535425240258[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]102.441875[/C][C]0.16485235176686[/C][C]621.415914920504[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]102.439666666667[/C][C]0.162623946246303[/C][C]629.917481595954[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]102.436071428571[/C][C]0.159109907843599[/C][C]643.806993649092[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]102.432307692308[/C][C]0.153685300525565[/C][C]666.506863974727[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]102.437916666667[/C][C]0.150971466694997[/C][C]678.525014754071[/C][/ROW]
[ROW][C]Median[/C][C]102.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]102.89[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]102.486666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]102.526315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]102.486666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]102.526315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]102.526315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]102.486666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]102.526315789474[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]102.486666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=132762&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132762&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 Mean102.5329166666670.192157713237463533.587306693015
Geometric Mean102.520150017081
Harmonic Mean102.507402609229
Quadratic Mean102.545700279599
Winsorized Mean ( 1 / 24 )102.5280555555560.19112483516523536.445488452188
Winsorized Mean ( 2 / 24 )102.5283333333330.190982653719937536.846312145627
Winsorized Mean ( 3 / 24 )102.52750.190392555309736538.505824627466
Winsorized Mean ( 4 / 24 )102.5230555555560.18845447087682544.020288181797
Winsorized Mean ( 5 / 24 )102.5251388888890.188132032626396544.963754750313
Winsorized Mean ( 6 / 24 )102.5243055555560.187984098733688545.388180416253
Winsorized Mean ( 7 / 24 )102.5233333333330.187490949181658546.817506556007
Winsorized Mean ( 8 / 24 )102.5155555555560.186133112473394550.764741390166
Winsorized Mean ( 9 / 24 )102.5005555555560.183180035021273559.561829670204
Winsorized Mean ( 10 / 24 )102.4866666666670.179576314090026570.713722385946
Winsorized Mean ( 11 / 24 )102.4683333333330.176199000101966581.548892298112
Winsorized Mean ( 12 / 24 )102.4666666666670.171341594766206598.025638820986
Winsorized Mean ( 13 / 24 )102.5118055555560.163683313648687626.281343348023
Winsorized Mean ( 14 / 24 )102.5176388888890.162873321390091629.431744953203
Winsorized Mean ( 15 / 24 )102.5093055555560.160998610787862636.70925515392
Winsorized Mean ( 16 / 24 )102.4604166666670.151298557241362677.206832205376
Winsorized Mean ( 17 / 24 )102.4627777777780.150971452884838678.689751074575
Winsorized Mean ( 18 / 24 )102.4702777777780.149938298762938683.416302727227
Winsorized Mean ( 19 / 24 )102.4491666666670.146243353847623700.53895764325
Winsorized Mean ( 20 / 24 )102.4602777777780.143957176652606711.74136753899
Winsorized Mean ( 21 / 24 )102.4690277777780.142771192639346717.715008773685
Winsorized Mean ( 22 / 24 )102.4659722222220.141509393468549724.093077573651
Winsorized Mean ( 23 / 24 )102.3893055555560.124263452272864823.969587861794
Winsorized Mean ( 24 / 24 )102.3959722222220.114558016361855893.835066930488
Trimmed Mean ( 1 / 24 )102.5227142857140.19050243271609538.17010535769
Trimmed Mean ( 2 / 24 )102.5170588235290.189631251015954540.61268000022
Trimmed Mean ( 3 / 24 )102.5109090909090.188550566047335543.678606964107
Trimmed Mean ( 4 / 24 )102.50468750.187384616448755547.028296359817
Trimmed Mean ( 5 / 24 )102.499354838710.186519071088825549.538201323642
Trimmed Mean ( 6 / 24 )102.4931666666670.185406636877208552.802037688362
Trimmed Mean ( 7 / 24 )102.4867241379310.183935334768359557.188885251434
Trimmed Mean ( 8 / 24 )102.480.182105114500589562.751904475854
Trimmed Mean ( 9 / 24 )102.4740740740740.180025916008106569.218456688536
Trimmed Mean ( 10 / 24 )102.470.177968255172574575.776842339865
Trimmed Mean ( 11 / 24 )102.46760.176019841182169582.136646140664
Trimmed Mean ( 12 / 24 )102.46750.174099888789728588.555803868184
Trimmed Mean ( 13 / 24 )102.4676086956520.172468630427134594.123165713566
Trimmed Mean ( 14 / 24 )102.4620454545450.171675174974366596.836703209095
Trimmed Mean ( 15 / 24 )102.4552380952380.170468452773093601.021693037914
Trimmed Mean ( 16 / 24 )102.448750.168946656541082606.397025531476
Trimmed Mean ( 17 / 24 )102.4473684210530.16866039181803607.418062514549
Trimmed Mean ( 18 / 24 )102.4455555555560.167837054597439610.386995894761
Trimmed Mean ( 19 / 24 )102.4426470588240.166428515497443615.535425240258
Trimmed Mean ( 20 / 24 )102.4418750.16485235176686621.415914920504
Trimmed Mean ( 21 / 24 )102.4396666666670.162623946246303629.917481595954
Trimmed Mean ( 22 / 24 )102.4360714285710.159109907843599643.806993649092
Trimmed Mean ( 23 / 24 )102.4323076923080.153685300525565666.506863974727
Trimmed Mean ( 24 / 24 )102.4379166666670.150971466694997678.525014754071
Median102.26
Midrange102.89
Midmean - Weighted Average at Xnp102.486666666667
Midmean - Weighted Average at X(n+1)p102.526315789474
Midmean - Empirical Distribution Function102.486666666667
Midmean - Empirical Distribution Function - Averaging102.526315789474
Midmean - Empirical Distribution Function - Interpolation102.526315789474
Midmean - Closest Observation102.486666666667
Midmean - True Basic - Statistics Graphics Toolkit102.526315789474
Midmean - MS Excel (old versions)102.486666666667
Number of observations72



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')