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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 17 Oct 2009 07:13:42 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/17/t1255785700of6u5p9ccd0kie5.htm/, Retrieved Mon, 06 May 2024 01:29:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47168, Retrieved Mon, 06 May 2024 01:29:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [WS3] [2009-10-17 13:13:42] [9f6463b67b1eb7bae5c03a796abf0348] [Current]
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Post a new message
Dataseries X:
500.9
359.82
375.90
449.78
503.70
420.63
448.75
436.11
486.70
586.40
547.67
569.80
542.91
408.14
516.88
566.09
511.29
477.77
609.79
622.93
560.00
678.00
544.89
547.86
557.80
471.33
508.71
556.78
588.78
455.60
508.24
520.44
458.59
581.36
506.63
490.60
630.00
558.44
579.49
482.15
690.75
537.59
503.95
618.87
709.71
678.31
662.17
500.73
551.03
471.57
480.13
587.33
515.64
493.98
570.00
385.73
465.58
542.08
572.33
476.91
454.12




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47168&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47168&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47168&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean527.8059016393449.7546808642709154.1079620116094
Geometric Mean522.378216908588
Harmonic Mean516.903286656945
Quadratic Mean533.18692569412
Winsorized Mean ( 1 / 20 )527.758688524599.5896771898335455.0340410920288
Winsorized Mean ( 2 / 20 )527.6731147540989.394239784168756.1698580063221
Winsorized Mean ( 3 / 20 )528.769.1297623069508657.9160751641292
Winsorized Mean ( 4 / 20 )528.5409836065578.6798191719754360.8930869565878
Winsorized Mean ( 5 / 20 )527.1729508196727.7935652676842167.6420781392028
Winsorized Mean ( 6 / 20 )527.7208196721317.4108747457367771.208978397012
Winsorized Mean ( 7 / 20 )527.3731147540987.2912868823786372.3292229837559
Winsorized Mean ( 8 / 20 )526.7514754098366.947933485419875.8141217838687
Winsorized Mean ( 9 / 20 )523.876.3338288474549582.709844647997
Winsorized Mean ( 10 / 20 )524.1224590163936.2061850369956284.451632668387
Winsorized Mean ( 11 / 20 )525.2152459016395.9615013448385188.1011704134518
Winsorized Mean ( 12 / 20 )525.3549180327875.6089402465865893.6638464552195
Winsorized Mean ( 13 / 20 )525.0075409836075.5348655492120694.854615042699
Winsorized Mean ( 14 / 20 )524.5898360655745.07637852548235103.339385239348
Winsorized Mean ( 15 / 20 )524.2283606557384.9542768694807105.813295152131
Winsorized Mean ( 16 / 20 )524.7949180327874.85029672137769108.198518189568
Winsorized Mean ( 17 / 20 )524.323934426234.60601240645886113.834676973728
Winsorized Mean ( 18 / 20 )523.8695081967214.1360382526837126.659734797376
Winsorized Mean ( 19 / 20 )524.5983606557383.88578115713055135.004607681799
Winsorized Mean ( 20 / 20 )525.4967213114753.69566079719723142.192898685401
Trimmed Mean ( 1 / 20 )527.579.1572287350688457.6124082146818
Trimmed Mean ( 2 / 20 )527.3680701754398.6225034614239561.1618275985415
Trimmed Mean ( 3 / 20 )527.1989090909098.0918766169133265.1516247774933
Trimmed Mean ( 4 / 20 )526.67.5604972728691969.6515032006826
Trimmed Mean ( 5 / 20 )526.0196078431377.0824278154902674.2710863487601
Trimmed Mean ( 6 / 20 )525.7324489795926.8079303779867477.2235348762575
Trimmed Mean ( 7 / 20 )525.3023404255326.5807424613436779.824175389212
Trimmed Mean ( 8 / 20 )524.9013333333336.3230448856751583.0140134735556
Trimmed Mean ( 9 / 20 )524.5732558139536.0881974733149686.1623260600857
Trimmed Mean ( 10 / 20 )524.6895121951225.9500509318502688.1823564545458
Trimmed Mean ( 11 / 20 )524.7782051282055.7949563308178390.5577497344392
Trimmed Mean ( 12 / 20 )524.7127027027035.6463586241940392.9293970904303
Trimmed Mean ( 13 / 20 )524.6194285714295.5311984043890194.8473351010412
Trimmed Mean ( 14 / 20 )524.5642424242425.3814639960319197.4761222617185
Trimmed Mean ( 15 / 20 )524.560645161295.2904284220988599.152772386094
Trimmed Mean ( 16 / 20 )524.607241379315.17849691224072101.30492501391
Trimmed Mean ( 17 / 20 )524.5807407407415.02906605564112104.309773412564
Trimmed Mean ( 18 / 20 )524.61764.87018419501083107.72027894498
Trimmed Mean ( 19 / 20 )524.7278260869564.77586123915889109.870827440407
Trimmed Mean ( 20 / 20 )524.7476190476194.6904286993003111.876259653174
Median516.88
Midrange534.765
Midmean - Weighted Average at Xnp523.046
Midmean - Weighted Average at X(n+1)p524.56064516129
Midmean - Empirical Distribution Function524.56064516129
Midmean - Empirical Distribution Function - Averaging524.56064516129
Midmean - Empirical Distribution Function - Interpolation524.56064516129
Midmean - Closest Observation523.0715625
Midmean - True Basic - Statistics Graphics Toolkit524.56064516129
Midmean - MS Excel (old versions)524.56064516129
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 527.805901639344 & 9.75468086427091 & 54.1079620116094 \tabularnewline
Geometric Mean & 522.378216908588 &  &  \tabularnewline
Harmonic Mean & 516.903286656945 &  &  \tabularnewline
Quadratic Mean & 533.18692569412 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 527.75868852459 & 9.58967718983354 & 55.0340410920288 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 527.673114754098 & 9.3942397841687 & 56.1698580063221 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 528.76 & 9.12976230695086 & 57.9160751641292 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 528.540983606557 & 8.67981917197543 & 60.8930869565878 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 527.172950819672 & 7.79356526768421 & 67.6420781392028 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 527.720819672131 & 7.41087474573677 & 71.208978397012 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 527.373114754098 & 7.29128688237863 & 72.3292229837559 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 526.751475409836 & 6.9479334854198 & 75.8141217838687 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 523.87 & 6.33382884745495 & 82.709844647997 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 524.122459016393 & 6.20618503699562 & 84.451632668387 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 525.215245901639 & 5.96150134483851 & 88.1011704134518 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 525.354918032787 & 5.60894024658658 & 93.6638464552195 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 525.007540983607 & 5.53486554921206 & 94.854615042699 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 524.589836065574 & 5.07637852548235 & 103.339385239348 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 524.228360655738 & 4.9542768694807 & 105.813295152131 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 524.794918032787 & 4.85029672137769 & 108.198518189568 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 524.32393442623 & 4.60601240645886 & 113.834676973728 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 523.869508196721 & 4.1360382526837 & 126.659734797376 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 524.598360655738 & 3.88578115713055 & 135.004607681799 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 525.496721311475 & 3.69566079719723 & 142.192898685401 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 527.57 & 9.15722873506884 & 57.6124082146818 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 527.368070175439 & 8.62250346142395 & 61.1618275985415 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 527.198909090909 & 8.09187661691332 & 65.1516247774933 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 526.6 & 7.56049727286919 & 69.6515032006826 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 526.019607843137 & 7.08242781549026 & 74.2710863487601 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 525.732448979592 & 6.80793037798674 & 77.2235348762575 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 525.302340425532 & 6.58074246134367 & 79.824175389212 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 524.901333333333 & 6.32304488567515 & 83.0140134735556 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 524.573255813953 & 6.08819747331496 & 86.1623260600857 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 524.689512195122 & 5.95005093185026 & 88.1823564545458 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 524.778205128205 & 5.79495633081783 & 90.5577497344392 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 524.712702702703 & 5.64635862419403 & 92.9293970904303 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 524.619428571429 & 5.53119840438901 & 94.8473351010412 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 524.564242424242 & 5.38146399603191 & 97.4761222617185 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 524.56064516129 & 5.29042842209885 & 99.152772386094 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 524.60724137931 & 5.17849691224072 & 101.30492501391 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 524.580740740741 & 5.02906605564112 & 104.309773412564 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 524.6176 & 4.87018419501083 & 107.72027894498 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 524.727826086956 & 4.77586123915889 & 109.870827440407 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 524.747619047619 & 4.6904286993003 & 111.876259653174 \tabularnewline
Median & 516.88 &  &  \tabularnewline
Midrange & 534.765 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 523.046 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 524.56064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 524.56064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 524.56064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 524.56064516129 &  &  \tabularnewline
Midmean - Closest Observation & 523.0715625 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 524.56064516129 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 524.56064516129 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47168&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]527.805901639344[/C][C]9.75468086427091[/C][C]54.1079620116094[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]522.378216908588[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]516.903286656945[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]533.18692569412[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]527.75868852459[/C][C]9.58967718983354[/C][C]55.0340410920288[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]527.673114754098[/C][C]9.3942397841687[/C][C]56.1698580063221[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]528.76[/C][C]9.12976230695086[/C][C]57.9160751641292[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]528.540983606557[/C][C]8.67981917197543[/C][C]60.8930869565878[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]527.172950819672[/C][C]7.79356526768421[/C][C]67.6420781392028[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]527.720819672131[/C][C]7.41087474573677[/C][C]71.208978397012[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]527.373114754098[/C][C]7.29128688237863[/C][C]72.3292229837559[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]526.751475409836[/C][C]6.9479334854198[/C][C]75.8141217838687[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]523.87[/C][C]6.33382884745495[/C][C]82.709844647997[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]524.122459016393[/C][C]6.20618503699562[/C][C]84.451632668387[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]525.215245901639[/C][C]5.96150134483851[/C][C]88.1011704134518[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]525.354918032787[/C][C]5.60894024658658[/C][C]93.6638464552195[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]525.007540983607[/C][C]5.53486554921206[/C][C]94.854615042699[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]524.589836065574[/C][C]5.07637852548235[/C][C]103.339385239348[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]524.228360655738[/C][C]4.9542768694807[/C][C]105.813295152131[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]524.794918032787[/C][C]4.85029672137769[/C][C]108.198518189568[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]524.32393442623[/C][C]4.60601240645886[/C][C]113.834676973728[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]523.869508196721[/C][C]4.1360382526837[/C][C]126.659734797376[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]524.598360655738[/C][C]3.88578115713055[/C][C]135.004607681799[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]525.496721311475[/C][C]3.69566079719723[/C][C]142.192898685401[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]527.57[/C][C]9.15722873506884[/C][C]57.6124082146818[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]527.368070175439[/C][C]8.62250346142395[/C][C]61.1618275985415[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]527.198909090909[/C][C]8.09187661691332[/C][C]65.1516247774933[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]526.6[/C][C]7.56049727286919[/C][C]69.6515032006826[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]526.019607843137[/C][C]7.08242781549026[/C][C]74.2710863487601[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]525.732448979592[/C][C]6.80793037798674[/C][C]77.2235348762575[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]525.302340425532[/C][C]6.58074246134367[/C][C]79.824175389212[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]524.901333333333[/C][C]6.32304488567515[/C][C]83.0140134735556[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]524.573255813953[/C][C]6.08819747331496[/C][C]86.1623260600857[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]524.689512195122[/C][C]5.95005093185026[/C][C]88.1823564545458[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]524.778205128205[/C][C]5.79495633081783[/C][C]90.5577497344392[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]524.712702702703[/C][C]5.64635862419403[/C][C]92.9293970904303[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]524.619428571429[/C][C]5.53119840438901[/C][C]94.8473351010412[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]524.564242424242[/C][C]5.38146399603191[/C][C]97.4761222617185[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]524.56064516129[/C][C]5.29042842209885[/C][C]99.152772386094[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]524.60724137931[/C][C]5.17849691224072[/C][C]101.30492501391[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]524.580740740741[/C][C]5.02906605564112[/C][C]104.309773412564[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]524.6176[/C][C]4.87018419501083[/C][C]107.72027894498[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]524.727826086956[/C][C]4.77586123915889[/C][C]109.870827440407[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]524.747619047619[/C][C]4.6904286993003[/C][C]111.876259653174[/C][/ROW]
[ROW][C]Median[/C][C]516.88[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]534.765[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]523.046[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]524.56064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]524.56064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]524.56064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]524.56064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]523.0715625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]524.56064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]524.56064516129[/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=47168&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47168&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 Mean527.8059016393449.7546808642709154.1079620116094
Geometric Mean522.378216908588
Harmonic Mean516.903286656945
Quadratic Mean533.18692569412
Winsorized Mean ( 1 / 20 )527.758688524599.5896771898335455.0340410920288
Winsorized Mean ( 2 / 20 )527.6731147540989.394239784168756.1698580063221
Winsorized Mean ( 3 / 20 )528.769.1297623069508657.9160751641292
Winsorized Mean ( 4 / 20 )528.5409836065578.6798191719754360.8930869565878
Winsorized Mean ( 5 / 20 )527.1729508196727.7935652676842167.6420781392028
Winsorized Mean ( 6 / 20 )527.7208196721317.4108747457367771.208978397012
Winsorized Mean ( 7 / 20 )527.3731147540987.2912868823786372.3292229837559
Winsorized Mean ( 8 / 20 )526.7514754098366.947933485419875.8141217838687
Winsorized Mean ( 9 / 20 )523.876.3338288474549582.709844647997
Winsorized Mean ( 10 / 20 )524.1224590163936.2061850369956284.451632668387
Winsorized Mean ( 11 / 20 )525.2152459016395.9615013448385188.1011704134518
Winsorized Mean ( 12 / 20 )525.3549180327875.6089402465865893.6638464552195
Winsorized Mean ( 13 / 20 )525.0075409836075.5348655492120694.854615042699
Winsorized Mean ( 14 / 20 )524.5898360655745.07637852548235103.339385239348
Winsorized Mean ( 15 / 20 )524.2283606557384.9542768694807105.813295152131
Winsorized Mean ( 16 / 20 )524.7949180327874.85029672137769108.198518189568
Winsorized Mean ( 17 / 20 )524.323934426234.60601240645886113.834676973728
Winsorized Mean ( 18 / 20 )523.8695081967214.1360382526837126.659734797376
Winsorized Mean ( 19 / 20 )524.5983606557383.88578115713055135.004607681799
Winsorized Mean ( 20 / 20 )525.4967213114753.69566079719723142.192898685401
Trimmed Mean ( 1 / 20 )527.579.1572287350688457.6124082146818
Trimmed Mean ( 2 / 20 )527.3680701754398.6225034614239561.1618275985415
Trimmed Mean ( 3 / 20 )527.1989090909098.0918766169133265.1516247774933
Trimmed Mean ( 4 / 20 )526.67.5604972728691969.6515032006826
Trimmed Mean ( 5 / 20 )526.0196078431377.0824278154902674.2710863487601
Trimmed Mean ( 6 / 20 )525.7324489795926.8079303779867477.2235348762575
Trimmed Mean ( 7 / 20 )525.3023404255326.5807424613436779.824175389212
Trimmed Mean ( 8 / 20 )524.9013333333336.3230448856751583.0140134735556
Trimmed Mean ( 9 / 20 )524.5732558139536.0881974733149686.1623260600857
Trimmed Mean ( 10 / 20 )524.6895121951225.9500509318502688.1823564545458
Trimmed Mean ( 11 / 20 )524.7782051282055.7949563308178390.5577497344392
Trimmed Mean ( 12 / 20 )524.7127027027035.6463586241940392.9293970904303
Trimmed Mean ( 13 / 20 )524.6194285714295.5311984043890194.8473351010412
Trimmed Mean ( 14 / 20 )524.5642424242425.3814639960319197.4761222617185
Trimmed Mean ( 15 / 20 )524.560645161295.2904284220988599.152772386094
Trimmed Mean ( 16 / 20 )524.607241379315.17849691224072101.30492501391
Trimmed Mean ( 17 / 20 )524.5807407407415.02906605564112104.309773412564
Trimmed Mean ( 18 / 20 )524.61764.87018419501083107.72027894498
Trimmed Mean ( 19 / 20 )524.7278260869564.77586123915889109.870827440407
Trimmed Mean ( 20 / 20 )524.7476190476194.6904286993003111.876259653174
Median516.88
Midrange534.765
Midmean - Weighted Average at Xnp523.046
Midmean - Weighted Average at X(n+1)p524.56064516129
Midmean - Empirical Distribution Function524.56064516129
Midmean - Empirical Distribution Function - Averaging524.56064516129
Midmean - Empirical Distribution Function - Interpolation524.56064516129
Midmean - Closest Observation523.0715625
Midmean - True Basic - Statistics Graphics Toolkit524.56064516129
Midmean - MS Excel (old versions)524.56064516129
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')