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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 computationTue, 14 Mar 2017 20:37:23 +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/2017/Mar/14/t14895240287d01cgxfn354om4.htm/, Retrieved Tue, 14 May 2024 01:56:45 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 01:56:45 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
97,96
98,36
98,36
98,51
98,77
98,78
98,89
98,87
99,05
99,09
99,1
99,12
99,37
99,46
99,6
99,87
99,88
100,01
100,02
100,19
100,2
100,35
100,47
100,57
101,41
101,67
101,82
101,86
101,98
102,06
102,17
102,2
102,35
102,47
102,55
102,62
102,81
102,88
102,94
102,95
102,94
103,05
103,09
103,1
103,14
103,19
103,36
103,43
103,62
103,79
103,9
103,92
103,94
103,98
104,04
104,09
104,16
104,22
104,28
104,32




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean101.5858333333330.257023080551086395.240120519613
Geometric Mean101.566578706398
Harmonic Mean101.547256394663
Quadratic Mean101.605015255154
Winsorized Mean ( 1 / 20 )101.5918333333330.255391301816085397.788932555318
Winsorized Mean ( 2 / 20 )101.5898333333330.255038104128459398.331981334695
Winsorized Mean ( 3 / 20 )101.5943333333330.252937919927202401.657186722232
Winsorized Mean ( 4 / 20 )101.6070.248673804444596408.595510198332
Winsorized Mean ( 5 / 20 )101.6036666666670.247813029422969410.001309871601
Winsorized Mean ( 6 / 20 )101.6066666666670.245099964233052414.551944079659
Winsorized Mean ( 7 / 20 )101.6043333333330.243897422944607416.58633415085
Winsorized Mean ( 8 / 20 )101.6230.239509420925074424.296462358325
Winsorized Mean ( 9 / 20 )101.6260.237934402012439427.117722954107
Winsorized Mean ( 10 / 20 )101.6093333333330.234704149227881432.925168419915
Winsorized Mean ( 11 / 20 )101.5818333333330.229234601127423443.13481836395
Winsorized Mean ( 12 / 20 )101.5938333333330.21466780165156473.260696535368
Winsorized Mean ( 13 / 20 )101.5981666666670.209082944056401485.922785931598
Winsorized Mean ( 14 / 20 )101.5911666666670.197913993142811513.309670799075
Winsorized Mean ( 15 / 20 )101.6461666666670.184944959237253549.602255102675
Winsorized Mean ( 16 / 20 )101.6381666666670.183058832762459555.221319468121
Winsorized Mean ( 17 / 20 )101.6721666666670.176739792722098575.264716002774
Winsorized Mean ( 18 / 20 )101.6631666666670.17463804241022582.136430663043
Winsorized Mean ( 19 / 20 )101.6853333333330.161900169189002628.074287029471
Winsorized Mean ( 20 / 20 )101.6853333333330.160937659732427631.830570311473
Trimmed Mean ( 1 / 20 )101.6012068965520.253958030075243400.070857639151
Trimmed Mean ( 2 / 20 )101.611250.25196140480833403.281010745661
Trimmed Mean ( 3 / 20 )101.6231481481480.249491841911871407.320525470507
Trimmed Mean ( 4 / 20 )101.6342307692310.247167108753595411.196422055297
Trimmed Mean ( 5 / 20 )101.64240.24559541310614413.861149581294
Trimmed Mean ( 6 / 20 )101.6520833333330.243561225925293417.357413714582
Trimmed Mean ( 7 / 20 )101.6619565217390.241439847494137421.065360904057
Trimmed Mean ( 8 / 20 )101.6731818181820.238684903952839425.972401833469
Trimmed Mean ( 9 / 20 )101.6821428571430.235934777034746430.975645621622
Trimmed Mean ( 10 / 20 )101.69150.232343012894784437.678321947434
Trimmed Mean ( 11 / 20 )101.7044736842110.227997559746446.077027304651
Trimmed Mean ( 12 / 20 )101.7230555555560.223121370432244455.909065807957
Trimmed Mean ( 13 / 20 )101.7420588235290.21991725044456462.637917752514
Trimmed Mean ( 14 / 20 )101.76281250.216330855840095470.403595940191
Trimmed Mean ( 15 / 20 )101.7873333333330.213595349153666476.542835490789
Trimmed Mean ( 16 / 20 )101.80750.212613881716159478.837501945963
Trimmed Mean ( 17 / 20 )101.8319230769230.210396708975994483.999600433589
Trimmed Mean ( 18 / 20 )101.8554166666670.20789662562063489.932996086874
Trimmed Mean ( 19 / 20 )101.8845454545450.203026587806029501.828585879037
Trimmed Mean ( 20 / 20 )101.9160.198792936441282512.674151428431
Median102.115
Midrange101.14
Midmean - Weighted Average at Xnp101.716774193548
Midmean - Weighted Average at X(n+1)p101.787333333333
Midmean - Empirical Distribution Function101.716774193548
Midmean - Empirical Distribution Function - Averaging101.787333333333
Midmean - Empirical Distribution Function - Interpolation101.787333333333
Midmean - Closest Observation101.716774193548
Midmean - True Basic - Statistics Graphics Toolkit101.787333333333
Midmean - MS Excel (old versions)101.7628125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 101.585833333333 & 0.257023080551086 & 395.240120519613 \tabularnewline
Geometric Mean & 101.566578706398 &  &  \tabularnewline
Harmonic Mean & 101.547256394663 &  &  \tabularnewline
Quadratic Mean & 101.605015255154 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 101.591833333333 & 0.255391301816085 & 397.788932555318 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 101.589833333333 & 0.255038104128459 & 398.331981334695 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 101.594333333333 & 0.252937919927202 & 401.657186722232 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 101.607 & 0.248673804444596 & 408.595510198332 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 101.603666666667 & 0.247813029422969 & 410.001309871601 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 101.606666666667 & 0.245099964233052 & 414.551944079659 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 101.604333333333 & 0.243897422944607 & 416.58633415085 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 101.623 & 0.239509420925074 & 424.296462358325 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 101.626 & 0.237934402012439 & 427.117722954107 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 101.609333333333 & 0.234704149227881 & 432.925168419915 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 101.581833333333 & 0.229234601127423 & 443.13481836395 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 101.593833333333 & 0.21466780165156 & 473.260696535368 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 101.598166666667 & 0.209082944056401 & 485.922785931598 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 101.591166666667 & 0.197913993142811 & 513.309670799075 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 101.646166666667 & 0.184944959237253 & 549.602255102675 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 101.638166666667 & 0.183058832762459 & 555.221319468121 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 101.672166666667 & 0.176739792722098 & 575.264716002774 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 101.663166666667 & 0.17463804241022 & 582.136430663043 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 101.685333333333 & 0.161900169189002 & 628.074287029471 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 101.685333333333 & 0.160937659732427 & 631.830570311473 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 101.601206896552 & 0.253958030075243 & 400.070857639151 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 101.61125 & 0.25196140480833 & 403.281010745661 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 101.623148148148 & 0.249491841911871 & 407.320525470507 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 101.634230769231 & 0.247167108753595 & 411.196422055297 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 101.6424 & 0.24559541310614 & 413.861149581294 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 101.652083333333 & 0.243561225925293 & 417.357413714582 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 101.661956521739 & 0.241439847494137 & 421.065360904057 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 101.673181818182 & 0.238684903952839 & 425.972401833469 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 101.682142857143 & 0.235934777034746 & 430.975645621622 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 101.6915 & 0.232343012894784 & 437.678321947434 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 101.704473684211 & 0.227997559746 & 446.077027304651 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 101.723055555556 & 0.223121370432244 & 455.909065807957 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 101.742058823529 & 0.21991725044456 & 462.637917752514 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 101.7628125 & 0.216330855840095 & 470.403595940191 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 101.787333333333 & 0.213595349153666 & 476.542835490789 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 101.8075 & 0.212613881716159 & 478.837501945963 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 101.831923076923 & 0.210396708975994 & 483.999600433589 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 101.855416666667 & 0.20789662562063 & 489.932996086874 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 101.884545454545 & 0.203026587806029 & 501.828585879037 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 101.916 & 0.198792936441282 & 512.674151428431 \tabularnewline
Median & 102.115 &  &  \tabularnewline
Midrange & 101.14 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 101.716774193548 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 101.787333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 101.716774193548 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 101.787333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 101.787333333333 &  &  \tabularnewline
Midmean - Closest Observation & 101.716774193548 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 101.787333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 101.7628125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]101.585833333333[/C][C]0.257023080551086[/C][C]395.240120519613[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]101.566578706398[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]101.547256394663[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]101.605015255154[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]101.591833333333[/C][C]0.255391301816085[/C][C]397.788932555318[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]101.589833333333[/C][C]0.255038104128459[/C][C]398.331981334695[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]101.594333333333[/C][C]0.252937919927202[/C][C]401.657186722232[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]101.607[/C][C]0.248673804444596[/C][C]408.595510198332[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]101.603666666667[/C][C]0.247813029422969[/C][C]410.001309871601[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]101.606666666667[/C][C]0.245099964233052[/C][C]414.551944079659[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]101.604333333333[/C][C]0.243897422944607[/C][C]416.58633415085[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]101.623[/C][C]0.239509420925074[/C][C]424.296462358325[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]101.626[/C][C]0.237934402012439[/C][C]427.117722954107[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]101.609333333333[/C][C]0.234704149227881[/C][C]432.925168419915[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]101.581833333333[/C][C]0.229234601127423[/C][C]443.13481836395[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]101.593833333333[/C][C]0.21466780165156[/C][C]473.260696535368[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]101.598166666667[/C][C]0.209082944056401[/C][C]485.922785931598[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]101.591166666667[/C][C]0.197913993142811[/C][C]513.309670799075[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]101.646166666667[/C][C]0.184944959237253[/C][C]549.602255102675[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]101.638166666667[/C][C]0.183058832762459[/C][C]555.221319468121[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]101.672166666667[/C][C]0.176739792722098[/C][C]575.264716002774[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]101.663166666667[/C][C]0.17463804241022[/C][C]582.136430663043[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]101.685333333333[/C][C]0.161900169189002[/C][C]628.074287029471[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]101.685333333333[/C][C]0.160937659732427[/C][C]631.830570311473[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]101.601206896552[/C][C]0.253958030075243[/C][C]400.070857639151[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]101.61125[/C][C]0.25196140480833[/C][C]403.281010745661[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]101.623148148148[/C][C]0.249491841911871[/C][C]407.320525470507[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]101.634230769231[/C][C]0.247167108753595[/C][C]411.196422055297[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]101.6424[/C][C]0.24559541310614[/C][C]413.861149581294[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]101.652083333333[/C][C]0.243561225925293[/C][C]417.357413714582[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]101.661956521739[/C][C]0.241439847494137[/C][C]421.065360904057[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]101.673181818182[/C][C]0.238684903952839[/C][C]425.972401833469[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]101.682142857143[/C][C]0.235934777034746[/C][C]430.975645621622[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]101.6915[/C][C]0.232343012894784[/C][C]437.678321947434[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]101.704473684211[/C][C]0.227997559746[/C][C]446.077027304651[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]101.723055555556[/C][C]0.223121370432244[/C][C]455.909065807957[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]101.742058823529[/C][C]0.21991725044456[/C][C]462.637917752514[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]101.7628125[/C][C]0.216330855840095[/C][C]470.403595940191[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]101.787333333333[/C][C]0.213595349153666[/C][C]476.542835490789[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]101.8075[/C][C]0.212613881716159[/C][C]478.837501945963[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]101.831923076923[/C][C]0.210396708975994[/C][C]483.999600433589[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]101.855416666667[/C][C]0.20789662562063[/C][C]489.932996086874[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]101.884545454545[/C][C]0.203026587806029[/C][C]501.828585879037[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]101.916[/C][C]0.198792936441282[/C][C]512.674151428431[/C][/ROW]
[ROW][C]Median[/C][C]102.115[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]101.14[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]101.716774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]101.787333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]101.716774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]101.787333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]101.787333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]101.716774193548[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]101.787333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]101.7628125[/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=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Mean101.5858333333330.257023080551086395.240120519613
Geometric Mean101.566578706398
Harmonic Mean101.547256394663
Quadratic Mean101.605015255154
Winsorized Mean ( 1 / 20 )101.5918333333330.255391301816085397.788932555318
Winsorized Mean ( 2 / 20 )101.5898333333330.255038104128459398.331981334695
Winsorized Mean ( 3 / 20 )101.5943333333330.252937919927202401.657186722232
Winsorized Mean ( 4 / 20 )101.6070.248673804444596408.595510198332
Winsorized Mean ( 5 / 20 )101.6036666666670.247813029422969410.001309871601
Winsorized Mean ( 6 / 20 )101.6066666666670.245099964233052414.551944079659
Winsorized Mean ( 7 / 20 )101.6043333333330.243897422944607416.58633415085
Winsorized Mean ( 8 / 20 )101.6230.239509420925074424.296462358325
Winsorized Mean ( 9 / 20 )101.6260.237934402012439427.117722954107
Winsorized Mean ( 10 / 20 )101.6093333333330.234704149227881432.925168419915
Winsorized Mean ( 11 / 20 )101.5818333333330.229234601127423443.13481836395
Winsorized Mean ( 12 / 20 )101.5938333333330.21466780165156473.260696535368
Winsorized Mean ( 13 / 20 )101.5981666666670.209082944056401485.922785931598
Winsorized Mean ( 14 / 20 )101.5911666666670.197913993142811513.309670799075
Winsorized Mean ( 15 / 20 )101.6461666666670.184944959237253549.602255102675
Winsorized Mean ( 16 / 20 )101.6381666666670.183058832762459555.221319468121
Winsorized Mean ( 17 / 20 )101.6721666666670.176739792722098575.264716002774
Winsorized Mean ( 18 / 20 )101.6631666666670.17463804241022582.136430663043
Winsorized Mean ( 19 / 20 )101.6853333333330.161900169189002628.074287029471
Winsorized Mean ( 20 / 20 )101.6853333333330.160937659732427631.830570311473
Trimmed Mean ( 1 / 20 )101.6012068965520.253958030075243400.070857639151
Trimmed Mean ( 2 / 20 )101.611250.25196140480833403.281010745661
Trimmed Mean ( 3 / 20 )101.6231481481480.249491841911871407.320525470507
Trimmed Mean ( 4 / 20 )101.6342307692310.247167108753595411.196422055297
Trimmed Mean ( 5 / 20 )101.64240.24559541310614413.861149581294
Trimmed Mean ( 6 / 20 )101.6520833333330.243561225925293417.357413714582
Trimmed Mean ( 7 / 20 )101.6619565217390.241439847494137421.065360904057
Trimmed Mean ( 8 / 20 )101.6731818181820.238684903952839425.972401833469
Trimmed Mean ( 9 / 20 )101.6821428571430.235934777034746430.975645621622
Trimmed Mean ( 10 / 20 )101.69150.232343012894784437.678321947434
Trimmed Mean ( 11 / 20 )101.7044736842110.227997559746446.077027304651
Trimmed Mean ( 12 / 20 )101.7230555555560.223121370432244455.909065807957
Trimmed Mean ( 13 / 20 )101.7420588235290.21991725044456462.637917752514
Trimmed Mean ( 14 / 20 )101.76281250.216330855840095470.403595940191
Trimmed Mean ( 15 / 20 )101.7873333333330.213595349153666476.542835490789
Trimmed Mean ( 16 / 20 )101.80750.212613881716159478.837501945963
Trimmed Mean ( 17 / 20 )101.8319230769230.210396708975994483.999600433589
Trimmed Mean ( 18 / 20 )101.8554166666670.20789662562063489.932996086874
Trimmed Mean ( 19 / 20 )101.8845454545450.203026587806029501.828585879037
Trimmed Mean ( 20 / 20 )101.9160.198792936441282512.674151428431
Median102.115
Midrange101.14
Midmean - Weighted Average at Xnp101.716774193548
Midmean - Weighted Average at X(n+1)p101.787333333333
Midmean - Empirical Distribution Function101.716774193548
Midmean - Empirical Distribution Function - Averaging101.787333333333
Midmean - Empirical Distribution Function - Interpolation101.787333333333
Midmean - Closest Observation101.716774193548
Midmean - True Basic - Statistics Graphics Toolkit101.787333333333
Midmean - MS Excel (old versions)101.7628125
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')