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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 computationThu, 18 Oct 2007 01:16:43 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Oct/18/j1eukuqf0wj19mu1192695364.htm/, Retrieved Sun, 28 Apr 2024 19:13:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=947, Retrieved Sun, 28 Apr 2024 19:13:14 +0000
QR Codes:

Original text written by user:De centrale tendens van de productie van kledij.
IsPrivate?No (this computation is public)
User-defined keywordsCentral tendency for the production of clothing, central tendency, clothing, Q1, industrial production
Estimated Impact198
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Industrial produc...] [2007-10-18 08:16:43] [2cdb7403ed3391afb545b8c0d20da37e] [Current]
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Dataseries X:
109,20
88,60
94,30
98,30
86,40
80,60
104,10
108,20
93,40
71,90
94,10
94,90
96,40
91,10
84,40
86,40
88,00
75,10
109,70
103,00
82,10
68,00
96,40
94,30
90,00
88,00
76,10
82,50
81,40
66,50
97,20
94,10
80,70
70,50
87,80
89,50
99,60
84,20
75,10
92,00
80,80
73,10
99,80
90,00
83,10
72,40
78,80
87,30
91,00
80,10
73,60
86,40
74,50
71,20
92,40
81,50
85,30
69,90
84,20
90,70
100,30




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=947&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=947&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=947&T=0

As an alternative you can also use a QR Code:  

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

Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean86.89344262295081.3533400673857264.2066578216406
Geometric Mean86.2576130505509
Harmonic Mean85.6188757284786
Quadratic Mean87.5234947379705
Winsorized Mean ( 1 / 20 )86.90983606557381.3450876115005364.6127696980425
Winsorized Mean ( 2 / 20 )86.9393442622951.3221717493994465.7549552860928
Winsorized Mean ( 3 / 20 )86.76721311475411.2657245302203468.5514193990136
Winsorized Mean ( 4 / 20 )86.74098360655741.2398955029325069.958301648328
Winsorized Mean ( 5 / 20 )86.57704918032791.1823090158567273.227090396154
Winsorized Mean ( 6 / 20 )86.57704918032791.1628056174864574.4553069561832
Winsorized Mean ( 7 / 20 )86.63442622950821.1423656914177875.8377346942089
Winsorized Mean ( 8 / 20 )86.52950819672131.0980841345091178.800435665527
Winsorized Mean ( 9 / 20 )86.51.0439521375876282.8582047831092
Winsorized Mean ( 10 / 20 )86.46721311475411.0032099337132686.1905471716237
Winsorized Mean ( 11 / 20 )86.46721311475411.0032099337132686.1905471716237
Winsorized Mean ( 12 / 20 )86.36885245901640.91906801505865893.9743860561876
Winsorized Mean ( 13 / 20 )86.8163934426230.79699291509377108.929943790540
Winsorized Mean ( 14 / 20 )87.11475409836060.74863385983806116.364966603574
Winsorized Mean ( 15 / 20 )87.1885245901640.721818810653629120.790042186920
Winsorized Mean ( 16 / 20 )87.21475409836070.717839944660839121.496100554236
Winsorized Mean ( 17 / 20 )87.04754098360660.682880457249123127.471126255778
Winsorized Mean ( 18 / 20 )86.92950819672130.611087645696527142.253748392569
Winsorized Mean ( 19 / 20 )86.83606557377050.587966918453831147.688692762039
Winsorized Mean ( 20 / 20 )86.73770491803280.515901057646733168.128565802296
Trimmed Mean ( 1 / 20 )86.85254237288141.2982102411059066.9017541402961
Trimmed Mean ( 2 / 20 )86.79122807017541.2405312567135069.9629514375226
Trimmed Mean ( 3 / 20 )86.70909090909091.184667117793773.1927894399366
Trimmed Mean ( 4 / 20 )86.68679245283021.1433852092951475.8159120374397
Trimmed Mean ( 5 / 20 )86.67058823529411.1020526093902778.6446921832945
Trimmed Mean ( 6 / 20 )86.69387755102041.0700523231026781.018353662975
Trimmed Mean ( 7 / 20 )86.71914893617021.0352154508036283.7691795160628
Trimmed Mean ( 8 / 20 )86.73555555555550.99634258212986687.0539482214464
Trimmed Mean ( 9 / 20 )86.77209302325580.9584983039560190.5292087269443
Trimmed Mean ( 10 / 20 )86.81707317073170.92386319359302793.9717847542865
Trimmed Mean ( 11 / 20 )86.87179487179490.88872794747025597.7484674799229
Trimmed Mean ( 12 / 20 )86.93243243243240.840527987701135103.425981888116
Trimmed Mean ( 13 / 20 )87.01428571428570.79915020892356108.883517444727
Trimmed Mean ( 14 / 20 )87.04242424242420.778134305993157111.860412234787
Trimmed Mean ( 15 / 20 )87.03225806451610.760961292118509114.371465363526
Trimmed Mean ( 16 / 20 )87.01034482758620.742106986225427117.247710158540
Trimmed Mean ( 17 / 20 )86.98148148148150.713205456966791121.95851929037
Trimmed Mean ( 18 / 20 )86.9720.680282294345517127.84692578788
Trimmed Mean ( 19 / 20 )86.97826086956520.655109335886746132.769075488495
Trimmed Mean ( 20 / 20 )870.620905636569527140.117909833563
Median87.3
Midrange88.1
Midmean - Weighted Average at Xnp87.0322580645161
Midmean - Weighted Average at X(n+1)p87.0322580645161
Midmean - Empirical Distribution Function87.0322580645161
Midmean - Empirical Distribution Function - Averaging87.0322580645161
Midmean - Empirical Distribution Function - Interpolation87.0322580645161
Midmean - Closest Observation86.815625
Midmean - True Basic - Statistics Graphics Toolkit87.0322580645161
Midmean - MS Excel (old versions)87.0322580645161
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 86.8934426229508 & 1.35334006738572 & 64.2066578216406 \tabularnewline
Geometric Mean & 86.2576130505509 &  &  \tabularnewline
Harmonic Mean & 85.6188757284786 &  &  \tabularnewline
Quadratic Mean & 87.5234947379705 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 86.9098360655738 & 1.34508761150053 & 64.6127696980425 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 86.939344262295 & 1.32217174939944 & 65.7549552860928 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 86.7672131147541 & 1.26572453022034 & 68.5514193990136 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 86.7409836065574 & 1.23989550293250 & 69.958301648328 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 86.5770491803279 & 1.18230901585672 & 73.227090396154 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 86.5770491803279 & 1.16280561748645 & 74.4553069561832 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 86.6344262295082 & 1.14236569141778 & 75.8377346942089 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 86.5295081967213 & 1.09808413450911 & 78.800435665527 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 86.5 & 1.04395213758762 & 82.8582047831092 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 86.4672131147541 & 1.00320993371326 & 86.1905471716237 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 86.4672131147541 & 1.00320993371326 & 86.1905471716237 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 86.3688524590164 & 0.919068015058658 & 93.9743860561876 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 86.816393442623 & 0.79699291509377 & 108.929943790540 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 87.1147540983606 & 0.74863385983806 & 116.364966603574 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 87.188524590164 & 0.721818810653629 & 120.790042186920 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 87.2147540983607 & 0.717839944660839 & 121.496100554236 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 87.0475409836066 & 0.682880457249123 & 127.471126255778 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 86.9295081967213 & 0.611087645696527 & 142.253748392569 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 86.8360655737705 & 0.587966918453831 & 147.688692762039 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 86.7377049180328 & 0.515901057646733 & 168.128565802296 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 86.8525423728814 & 1.29821024110590 & 66.9017541402961 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 86.7912280701754 & 1.24053125671350 & 69.9629514375226 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 86.7090909090909 & 1.1846671177937 & 73.1927894399366 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 86.6867924528302 & 1.14338520929514 & 75.8159120374397 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 86.6705882352941 & 1.10205260939027 & 78.6446921832945 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 86.6938775510204 & 1.07005232310267 & 81.018353662975 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 86.7191489361702 & 1.03521545080362 & 83.7691795160628 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 86.7355555555555 & 0.996342582129866 & 87.0539482214464 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 86.7720930232558 & 0.95849830395601 & 90.5292087269443 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 86.8170731707317 & 0.923863193593027 & 93.9717847542865 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 86.8717948717949 & 0.888727947470255 & 97.7484674799229 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 86.9324324324324 & 0.840527987701135 & 103.425981888116 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 87.0142857142857 & 0.79915020892356 & 108.883517444727 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 87.0424242424242 & 0.778134305993157 & 111.860412234787 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 87.0322580645161 & 0.760961292118509 & 114.371465363526 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 87.0103448275862 & 0.742106986225427 & 117.247710158540 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 86.9814814814815 & 0.713205456966791 & 121.95851929037 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 86.972 & 0.680282294345517 & 127.84692578788 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 86.9782608695652 & 0.655109335886746 & 132.769075488495 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 87 & 0.620905636569527 & 140.117909833563 \tabularnewline
Median & 87.3 &  &  \tabularnewline
Midrange & 88.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 87.0322580645161 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 87.0322580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 87.0322580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 87.0322580645161 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 87.0322580645161 &  &  \tabularnewline
Midmean - Closest Observation & 86.815625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 87.0322580645161 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 87.0322580645161 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=947&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]86.8934426229508[/C][C]1.35334006738572[/C][C]64.2066578216406[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]86.2576130505509[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]85.6188757284786[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]87.5234947379705[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]86.9098360655738[/C][C]1.34508761150053[/C][C]64.6127696980425[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]86.939344262295[/C][C]1.32217174939944[/C][C]65.7549552860928[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]86.7672131147541[/C][C]1.26572453022034[/C][C]68.5514193990136[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]86.7409836065574[/C][C]1.23989550293250[/C][C]69.958301648328[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]86.5770491803279[/C][C]1.18230901585672[/C][C]73.227090396154[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]86.5770491803279[/C][C]1.16280561748645[/C][C]74.4553069561832[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]86.6344262295082[/C][C]1.14236569141778[/C][C]75.8377346942089[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]86.5295081967213[/C][C]1.09808413450911[/C][C]78.800435665527[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]86.5[/C][C]1.04395213758762[/C][C]82.8582047831092[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]86.4672131147541[/C][C]1.00320993371326[/C][C]86.1905471716237[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]86.4672131147541[/C][C]1.00320993371326[/C][C]86.1905471716237[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]86.3688524590164[/C][C]0.919068015058658[/C][C]93.9743860561876[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]86.816393442623[/C][C]0.79699291509377[/C][C]108.929943790540[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]87.1147540983606[/C][C]0.74863385983806[/C][C]116.364966603574[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]87.188524590164[/C][C]0.721818810653629[/C][C]120.790042186920[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]87.2147540983607[/C][C]0.717839944660839[/C][C]121.496100554236[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]87.0475409836066[/C][C]0.682880457249123[/C][C]127.471126255778[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]86.9295081967213[/C][C]0.611087645696527[/C][C]142.253748392569[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]86.8360655737705[/C][C]0.587966918453831[/C][C]147.688692762039[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]86.7377049180328[/C][C]0.515901057646733[/C][C]168.128565802296[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]86.8525423728814[/C][C]1.29821024110590[/C][C]66.9017541402961[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]86.7912280701754[/C][C]1.24053125671350[/C][C]69.9629514375226[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]86.7090909090909[/C][C]1.1846671177937[/C][C]73.1927894399366[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]86.6867924528302[/C][C]1.14338520929514[/C][C]75.8159120374397[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]86.6705882352941[/C][C]1.10205260939027[/C][C]78.6446921832945[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]86.6938775510204[/C][C]1.07005232310267[/C][C]81.018353662975[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]86.7191489361702[/C][C]1.03521545080362[/C][C]83.7691795160628[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]86.7355555555555[/C][C]0.996342582129866[/C][C]87.0539482214464[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]86.7720930232558[/C][C]0.95849830395601[/C][C]90.5292087269443[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]86.8170731707317[/C][C]0.923863193593027[/C][C]93.9717847542865[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]86.8717948717949[/C][C]0.888727947470255[/C][C]97.7484674799229[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]86.9324324324324[/C][C]0.840527987701135[/C][C]103.425981888116[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]87.0142857142857[/C][C]0.79915020892356[/C][C]108.883517444727[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]87.0424242424242[/C][C]0.778134305993157[/C][C]111.860412234787[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]87.0322580645161[/C][C]0.760961292118509[/C][C]114.371465363526[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]87.0103448275862[/C][C]0.742106986225427[/C][C]117.247710158540[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]86.9814814814815[/C][C]0.713205456966791[/C][C]121.95851929037[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]86.972[/C][C]0.680282294345517[/C][C]127.84692578788[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]86.9782608695652[/C][C]0.655109335886746[/C][C]132.769075488495[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]87[/C][C]0.620905636569527[/C][C]140.117909833563[/C][/ROW]
[ROW][C]Median[/C][C]87.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]88.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]87.0322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]87.0322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]87.0322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]87.0322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]87.0322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]86.815625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]87.0322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]87.0322580645161[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=947&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=947&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 Mean86.89344262295081.3533400673857264.2066578216406
Geometric Mean86.2576130505509
Harmonic Mean85.6188757284786
Quadratic Mean87.5234947379705
Winsorized Mean ( 1 / 20 )86.90983606557381.3450876115005364.6127696980425
Winsorized Mean ( 2 / 20 )86.9393442622951.3221717493994465.7549552860928
Winsorized Mean ( 3 / 20 )86.76721311475411.2657245302203468.5514193990136
Winsorized Mean ( 4 / 20 )86.74098360655741.2398955029325069.958301648328
Winsorized Mean ( 5 / 20 )86.57704918032791.1823090158567273.227090396154
Winsorized Mean ( 6 / 20 )86.57704918032791.1628056174864574.4553069561832
Winsorized Mean ( 7 / 20 )86.63442622950821.1423656914177875.8377346942089
Winsorized Mean ( 8 / 20 )86.52950819672131.0980841345091178.800435665527
Winsorized Mean ( 9 / 20 )86.51.0439521375876282.8582047831092
Winsorized Mean ( 10 / 20 )86.46721311475411.0032099337132686.1905471716237
Winsorized Mean ( 11 / 20 )86.46721311475411.0032099337132686.1905471716237
Winsorized Mean ( 12 / 20 )86.36885245901640.91906801505865893.9743860561876
Winsorized Mean ( 13 / 20 )86.8163934426230.79699291509377108.929943790540
Winsorized Mean ( 14 / 20 )87.11475409836060.74863385983806116.364966603574
Winsorized Mean ( 15 / 20 )87.1885245901640.721818810653629120.790042186920
Winsorized Mean ( 16 / 20 )87.21475409836070.717839944660839121.496100554236
Winsorized Mean ( 17 / 20 )87.04754098360660.682880457249123127.471126255778
Winsorized Mean ( 18 / 20 )86.92950819672130.611087645696527142.253748392569
Winsorized Mean ( 19 / 20 )86.83606557377050.587966918453831147.688692762039
Winsorized Mean ( 20 / 20 )86.73770491803280.515901057646733168.128565802296
Trimmed Mean ( 1 / 20 )86.85254237288141.2982102411059066.9017541402961
Trimmed Mean ( 2 / 20 )86.79122807017541.2405312567135069.9629514375226
Trimmed Mean ( 3 / 20 )86.70909090909091.184667117793773.1927894399366
Trimmed Mean ( 4 / 20 )86.68679245283021.1433852092951475.8159120374397
Trimmed Mean ( 5 / 20 )86.67058823529411.1020526093902778.6446921832945
Trimmed Mean ( 6 / 20 )86.69387755102041.0700523231026781.018353662975
Trimmed Mean ( 7 / 20 )86.71914893617021.0352154508036283.7691795160628
Trimmed Mean ( 8 / 20 )86.73555555555550.99634258212986687.0539482214464
Trimmed Mean ( 9 / 20 )86.77209302325580.9584983039560190.5292087269443
Trimmed Mean ( 10 / 20 )86.81707317073170.92386319359302793.9717847542865
Trimmed Mean ( 11 / 20 )86.87179487179490.88872794747025597.7484674799229
Trimmed Mean ( 12 / 20 )86.93243243243240.840527987701135103.425981888116
Trimmed Mean ( 13 / 20 )87.01428571428570.79915020892356108.883517444727
Trimmed Mean ( 14 / 20 )87.04242424242420.778134305993157111.860412234787
Trimmed Mean ( 15 / 20 )87.03225806451610.760961292118509114.371465363526
Trimmed Mean ( 16 / 20 )87.01034482758620.742106986225427117.247710158540
Trimmed Mean ( 17 / 20 )86.98148148148150.713205456966791121.95851929037
Trimmed Mean ( 18 / 20 )86.9720.680282294345517127.84692578788
Trimmed Mean ( 19 / 20 )86.97826086956520.655109335886746132.769075488495
Trimmed Mean ( 20 / 20 )870.620905636569527140.117909833563
Median87.3
Midrange88.1
Midmean - Weighted Average at Xnp87.0322580645161
Midmean - Weighted Average at X(n+1)p87.0322580645161
Midmean - Empirical Distribution Function87.0322580645161
Midmean - Empirical Distribution Function - Averaging87.0322580645161
Midmean - Empirical Distribution Function - Interpolation87.0322580645161
Midmean - Closest Observation86.815625
Midmean - True Basic - Statistics Graphics Toolkit87.0322580645161
Midmean - MS Excel (old versions)87.0322580645161
Number of observations61



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')