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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 computationMon, 22 Oct 2007 02:29:58 -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/22/w6r583u9iadgb6p1193045161.htm/, Retrieved Sun, 05 May 2024 21:33:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1620, Retrieved Sun, 05 May 2024 21:33:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsinvestigating associations, q8
Estimated Impact190
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendancy ...] [2007-10-22 09:29:58] [e2f7a6e26aa7cf06a3d27eb5298a4843] [Current]
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Dataseries X:
100
100,1
100
100
99,8
100
99,9
99,2
98,7
98,7
98,9
99,2
99,8
100,5
100,1
100,5
98,4
98,6
99
99,1
98,9
98,5
96,9
96,8
97
97
96,9
97,1
97,2
97,9
98,9
99,2
99,5
99,3
99,9
100
100,3
100,5
100,7
100,9
100,8
100,9
101
100,3
100,1
99,8
99,9
99,9
100,2
99,7
100,4
100,9
101,3
101,4
101,3
100,9
100,9
100,9
101,1
101,1
101,3




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 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=1620&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]2 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=1620&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1620&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean99.6393442622950.162195973492175614.314536403102
Geometric Mean99.6313676683
Harmonic Mean99.6233350608848
Quadratic Mean99.6472647745495
Winsorized Mean ( 1 / 20 )99.6393442622950.16143615511319617.205880506963
Winsorized Mean ( 2 / 20 )99.6393442622950.16143615511319617.205880506963
Winsorized Mean ( 3 / 20 )99.6442622950820.160063590337451622.529221573804
Winsorized Mean ( 4 / 20 )99.63114754098360.157915744699759630.913324889861
Winsorized Mean ( 5 / 20 )99.6393442622950.155663197592860640.095705363213
Winsorized Mean ( 6 / 20 )99.6393442622950.151500305479044657.684114545086
Winsorized Mean ( 7 / 20 )99.70819672131150.129528254654802769.779512485812
Winsorized Mean ( 8 / 20 )99.77377049180330.115325664785274865.14801954598
Winsorized Mean ( 9 / 20 )99.7885245901640.112451528371523887.391447988838
Winsorized Mean ( 10 / 20 )99.80491803278690.109380426753947912.456835237076
Winsorized Mean ( 11 / 20 )99.82295081967210.106134089912975940.536173641497
Winsorized Mean ( 12 / 20 )99.82295081967210.106134089912975940.536173641496
Winsorized Mean ( 13 / 20 )99.8442622950820.09525704627104351048.15618585302
Winsorized Mean ( 14 / 20 )99.82131147540980.09149979109828211090.94578552851
Winsorized Mean ( 15 / 20 )99.7721311475410.08399619909241461187.81721346426
Winsorized Mean ( 16 / 20 )99.79836065573770.07953044587574631254.84472715841
Winsorized Mean ( 17 / 20 )99.82622950819670.07494630643918211331.96996958355
Winsorized Mean ( 18 / 20 )99.82622950819670.0658654714117011515.60791061859
Winsorized Mean ( 19 / 20 )99.79508196721310.0614677590867651623.53538586541
Winsorized Mean ( 20 / 20 )99.79508196721310.0614677590867651623.53538586541
Trimmed Mean ( 1 / 20 )99.6576271186440.157701257678779631.93933000608
Trimmed Mean ( 2 / 20 )99.67719298245610.153060211092472651.228639180668
Trimmed Mean ( 3 / 20 )99.69818181818180.147264413449501677.001180956522
Trimmed Mean ( 4 / 20 )99.71886792452830.140676795670632708.850862355447
Trimmed Mean ( 5 / 20 )99.74509803921570.133146351013306749.138803129857
Trimmed Mean ( 6 / 20 )99.77142857142860.124300765372176802.661417833566
Trimmed Mean ( 7 / 20 )99.80.114167541652904874.153884327434
Trimmed Mean ( 8 / 20 )99.81777777777780.108585435752054919.255672608831
Trimmed Mean ( 9 / 20 )99.82558139534880.105658983790050944.790284882043
Trimmed Mean ( 10 / 20 )99.83170731707320.102555102642091973.44456536188
Trimmed Mean ( 11 / 20 )99.83589743589740.0992201154107431006.20622161751
Trimmed Mean ( 12 / 20 )99.83783783783780.09557407951398331044.61207835364
Trimmed Mean ( 13 / 20 )99.840.09048886834366761103.34013263176
Trimmed Mean ( 14 / 20 )99.8393939393940.0867051991052581151.48105268972
Trimmed Mean ( 15 / 20 )99.8419354838710.08240657056332531211.57736332623
Trimmed Mean ( 16 / 20 )99.8517241379310.07841105055188051273.43943787444
Trimmed Mean ( 17 / 20 )99.85925925925930.07400994374925621349.26814155649
Trimmed Mean ( 18 / 20 )99.8640.06901207623790671447.05108792462
Trimmed Mean ( 19 / 20 )99.86956521739130.0648606845747541539.75502836836
Trimmed Mean ( 20 / 20 )99.88095238095240.05960946218394691675.58888675649
Median99.9
Midrange99.1
Midmean - Weighted Average at Xnp99.7848484848485
Midmean - Weighted Average at X(n+1)p99.7848484848485
Midmean - Empirical Distribution Function99.7848484848485
Midmean - Empirical Distribution Function - Averaging99.7848484848485
Midmean - Empirical Distribution Function - Interpolation99.7848484848485
Midmean - Closest Observation99.7848484848485
Midmean - True Basic - Statistics Graphics Toolkit99.7848484848485
Midmean - MS Excel (old versions)99.7848484848485
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 99.639344262295 & 0.162195973492175 & 614.314536403102 \tabularnewline
Geometric Mean & 99.6313676683 &  &  \tabularnewline
Harmonic Mean & 99.6233350608848 &  &  \tabularnewline
Quadratic Mean & 99.6472647745495 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 99.639344262295 & 0.16143615511319 & 617.205880506963 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 99.639344262295 & 0.16143615511319 & 617.205880506963 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 99.644262295082 & 0.160063590337451 & 622.529221573804 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 99.6311475409836 & 0.157915744699759 & 630.913324889861 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 99.639344262295 & 0.155663197592860 & 640.095705363213 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 99.639344262295 & 0.151500305479044 & 657.684114545086 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 99.7081967213115 & 0.129528254654802 & 769.779512485812 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 99.7737704918033 & 0.115325664785274 & 865.14801954598 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 99.788524590164 & 0.112451528371523 & 887.391447988838 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 99.8049180327869 & 0.109380426753947 & 912.456835237076 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 99.8229508196721 & 0.106134089912975 & 940.536173641497 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 99.8229508196721 & 0.106134089912975 & 940.536173641496 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 99.844262295082 & 0.0952570462710435 & 1048.15618585302 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 99.8213114754098 & 0.0914997910982821 & 1090.94578552851 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 99.772131147541 & 0.0839961990924146 & 1187.81721346426 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 99.7983606557377 & 0.0795304458757463 & 1254.84472715841 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 99.8262295081967 & 0.0749463064391821 & 1331.96996958355 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 99.8262295081967 & 0.065865471411701 & 1515.60791061859 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 99.7950819672131 & 0.061467759086765 & 1623.53538586541 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 99.7950819672131 & 0.061467759086765 & 1623.53538586541 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 99.657627118644 & 0.157701257678779 & 631.93933000608 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 99.6771929824561 & 0.153060211092472 & 651.228639180668 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 99.6981818181818 & 0.147264413449501 & 677.001180956522 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 99.7188679245283 & 0.140676795670632 & 708.850862355447 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 99.7450980392157 & 0.133146351013306 & 749.138803129857 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 99.7714285714286 & 0.124300765372176 & 802.661417833566 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 99.8 & 0.114167541652904 & 874.153884327434 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 99.8177777777778 & 0.108585435752054 & 919.255672608831 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 99.8255813953488 & 0.105658983790050 & 944.790284882043 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 99.8317073170732 & 0.102555102642091 & 973.44456536188 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 99.8358974358974 & 0.099220115410743 & 1006.20622161751 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 99.8378378378378 & 0.0955740795139833 & 1044.61207835364 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 99.84 & 0.0904888683436676 & 1103.34013263176 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 99.839393939394 & 0.086705199105258 & 1151.48105268972 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 99.841935483871 & 0.0824065705633253 & 1211.57736332623 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 99.851724137931 & 0.0784110505518805 & 1273.43943787444 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 99.8592592592593 & 0.0740099437492562 & 1349.26814155649 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 99.864 & 0.0690120762379067 & 1447.05108792462 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 99.8695652173913 & 0.064860684574754 & 1539.75502836836 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 99.8809523809524 & 0.0596094621839469 & 1675.58888675649 \tabularnewline
Median & 99.9 &  &  \tabularnewline
Midrange & 99.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 99.7848484848485 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 99.7848484848485 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 99.7848484848485 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 99.7848484848485 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 99.7848484848485 &  &  \tabularnewline
Midmean - Closest Observation & 99.7848484848485 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 99.7848484848485 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 99.7848484848485 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1620&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]99.639344262295[/C][C]0.162195973492175[/C][C]614.314536403102[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]99.6313676683[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]99.6233350608848[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]99.6472647745495[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]99.639344262295[/C][C]0.16143615511319[/C][C]617.205880506963[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]99.639344262295[/C][C]0.16143615511319[/C][C]617.205880506963[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]99.644262295082[/C][C]0.160063590337451[/C][C]622.529221573804[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]99.6311475409836[/C][C]0.157915744699759[/C][C]630.913324889861[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]99.639344262295[/C][C]0.155663197592860[/C][C]640.095705363213[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]99.639344262295[/C][C]0.151500305479044[/C][C]657.684114545086[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]99.7081967213115[/C][C]0.129528254654802[/C][C]769.779512485812[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]99.7737704918033[/C][C]0.115325664785274[/C][C]865.14801954598[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]99.788524590164[/C][C]0.112451528371523[/C][C]887.391447988838[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]99.8049180327869[/C][C]0.109380426753947[/C][C]912.456835237076[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]99.8229508196721[/C][C]0.106134089912975[/C][C]940.536173641497[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]99.8229508196721[/C][C]0.106134089912975[/C][C]940.536173641496[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]99.844262295082[/C][C]0.0952570462710435[/C][C]1048.15618585302[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]99.8213114754098[/C][C]0.0914997910982821[/C][C]1090.94578552851[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]99.772131147541[/C][C]0.0839961990924146[/C][C]1187.81721346426[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]99.7983606557377[/C][C]0.0795304458757463[/C][C]1254.84472715841[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]99.8262295081967[/C][C]0.0749463064391821[/C][C]1331.96996958355[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]99.8262295081967[/C][C]0.065865471411701[/C][C]1515.60791061859[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]99.7950819672131[/C][C]0.061467759086765[/C][C]1623.53538586541[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]99.7950819672131[/C][C]0.061467759086765[/C][C]1623.53538586541[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]99.657627118644[/C][C]0.157701257678779[/C][C]631.93933000608[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]99.6771929824561[/C][C]0.153060211092472[/C][C]651.228639180668[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]99.6981818181818[/C][C]0.147264413449501[/C][C]677.001180956522[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]99.7188679245283[/C][C]0.140676795670632[/C][C]708.850862355447[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]99.7450980392157[/C][C]0.133146351013306[/C][C]749.138803129857[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]99.7714285714286[/C][C]0.124300765372176[/C][C]802.661417833566[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]99.8[/C][C]0.114167541652904[/C][C]874.153884327434[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]99.8177777777778[/C][C]0.108585435752054[/C][C]919.255672608831[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]99.8255813953488[/C][C]0.105658983790050[/C][C]944.790284882043[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]99.8317073170732[/C][C]0.102555102642091[/C][C]973.44456536188[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]99.8358974358974[/C][C]0.099220115410743[/C][C]1006.20622161751[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]99.8378378378378[/C][C]0.0955740795139833[/C][C]1044.61207835364[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]99.84[/C][C]0.0904888683436676[/C][C]1103.34013263176[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]99.839393939394[/C][C]0.086705199105258[/C][C]1151.48105268972[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]99.841935483871[/C][C]0.0824065705633253[/C][C]1211.57736332623[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]99.851724137931[/C][C]0.0784110505518805[/C][C]1273.43943787444[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]99.8592592592593[/C][C]0.0740099437492562[/C][C]1349.26814155649[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]99.864[/C][C]0.0690120762379067[/C][C]1447.05108792462[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]99.8695652173913[/C][C]0.064860684574754[/C][C]1539.75502836836[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]99.8809523809524[/C][C]0.0596094621839469[/C][C]1675.58888675649[/C][/ROW]
[ROW][C]Median[/C][C]99.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]99.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]99.7848484848485[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]99.7848484848485[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]99.7848484848485[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]99.7848484848485[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]99.7848484848485[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]99.7848484848485[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]99.7848484848485[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]99.7848484848485[/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=1620&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1620&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 Mean99.6393442622950.162195973492175614.314536403102
Geometric Mean99.6313676683
Harmonic Mean99.6233350608848
Quadratic Mean99.6472647745495
Winsorized Mean ( 1 / 20 )99.6393442622950.16143615511319617.205880506963
Winsorized Mean ( 2 / 20 )99.6393442622950.16143615511319617.205880506963
Winsorized Mean ( 3 / 20 )99.6442622950820.160063590337451622.529221573804
Winsorized Mean ( 4 / 20 )99.63114754098360.157915744699759630.913324889861
Winsorized Mean ( 5 / 20 )99.6393442622950.155663197592860640.095705363213
Winsorized Mean ( 6 / 20 )99.6393442622950.151500305479044657.684114545086
Winsorized Mean ( 7 / 20 )99.70819672131150.129528254654802769.779512485812
Winsorized Mean ( 8 / 20 )99.77377049180330.115325664785274865.14801954598
Winsorized Mean ( 9 / 20 )99.7885245901640.112451528371523887.391447988838
Winsorized Mean ( 10 / 20 )99.80491803278690.109380426753947912.456835237076
Winsorized Mean ( 11 / 20 )99.82295081967210.106134089912975940.536173641497
Winsorized Mean ( 12 / 20 )99.82295081967210.106134089912975940.536173641496
Winsorized Mean ( 13 / 20 )99.8442622950820.09525704627104351048.15618585302
Winsorized Mean ( 14 / 20 )99.82131147540980.09149979109828211090.94578552851
Winsorized Mean ( 15 / 20 )99.7721311475410.08399619909241461187.81721346426
Winsorized Mean ( 16 / 20 )99.79836065573770.07953044587574631254.84472715841
Winsorized Mean ( 17 / 20 )99.82622950819670.07494630643918211331.96996958355
Winsorized Mean ( 18 / 20 )99.82622950819670.0658654714117011515.60791061859
Winsorized Mean ( 19 / 20 )99.79508196721310.0614677590867651623.53538586541
Winsorized Mean ( 20 / 20 )99.79508196721310.0614677590867651623.53538586541
Trimmed Mean ( 1 / 20 )99.6576271186440.157701257678779631.93933000608
Trimmed Mean ( 2 / 20 )99.67719298245610.153060211092472651.228639180668
Trimmed Mean ( 3 / 20 )99.69818181818180.147264413449501677.001180956522
Trimmed Mean ( 4 / 20 )99.71886792452830.140676795670632708.850862355447
Trimmed Mean ( 5 / 20 )99.74509803921570.133146351013306749.138803129857
Trimmed Mean ( 6 / 20 )99.77142857142860.124300765372176802.661417833566
Trimmed Mean ( 7 / 20 )99.80.114167541652904874.153884327434
Trimmed Mean ( 8 / 20 )99.81777777777780.108585435752054919.255672608831
Trimmed Mean ( 9 / 20 )99.82558139534880.105658983790050944.790284882043
Trimmed Mean ( 10 / 20 )99.83170731707320.102555102642091973.44456536188
Trimmed Mean ( 11 / 20 )99.83589743589740.0992201154107431006.20622161751
Trimmed Mean ( 12 / 20 )99.83783783783780.09557407951398331044.61207835364
Trimmed Mean ( 13 / 20 )99.840.09048886834366761103.34013263176
Trimmed Mean ( 14 / 20 )99.8393939393940.0867051991052581151.48105268972
Trimmed Mean ( 15 / 20 )99.8419354838710.08240657056332531211.57736332623
Trimmed Mean ( 16 / 20 )99.8517241379310.07841105055188051273.43943787444
Trimmed Mean ( 17 / 20 )99.85925925925930.07400994374925621349.26814155649
Trimmed Mean ( 18 / 20 )99.8640.06901207623790671447.05108792462
Trimmed Mean ( 19 / 20 )99.86956521739130.0648606845747541539.75502836836
Trimmed Mean ( 20 / 20 )99.88095238095240.05960946218394691675.58888675649
Median99.9
Midrange99.1
Midmean - Weighted Average at Xnp99.7848484848485
Midmean - Weighted Average at X(n+1)p99.7848484848485
Midmean - Empirical Distribution Function99.7848484848485
Midmean - Empirical Distribution Function - Averaging99.7848484848485
Midmean - Empirical Distribution Function - Interpolation99.7848484848485
Midmean - Closest Observation99.7848484848485
Midmean - True Basic - Statistics Graphics Toolkit99.7848484848485
Midmean - MS Excel (old versions)99.7848484848485
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')