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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 11:15:30 -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/vyr03xew9mtuoks1193076653.htm/, Retrieved Mon, 06 May 2024 04:59:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=1618, Retrieved Mon, 06 May 2024 04:59:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsQ8
Estimated Impact206
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 18:15:30] [1329bc68d11d0852ec1dfd239c736a2c] [Current]
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Dataseries X:
680.2
668.9
611.4
640.8
549.8
541.8
628.6
686.5
611.8
588.4
566.9
563.7
569.9
635.4
590.8
634.3
576.1
351.6
507.5
586.2
666.4
693.6
650.6
654.8
733.5
648.1
678.1
816.2
591.0
563.5
742.5
694.4
728.6
749.0
538.9
568.5
692.8
580.5
506.9
612.8
442.9
523.3
596.7
533.7
523.1
559.2
430.7
538.2
612.4
428.0
522.4
531.1
425.9
410.3
551.0
555.6
460.2
288.9
392.3
400.5
399.0




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=1618&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=1618&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1618&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 Mean574.20819672131113.562591652145742.3376454477613
Geometric Mean563.676969469522
Harmonic Mean551.987105778083
Quadratic Mean583.739399665049
Winsorized Mean ( 1 / 20 )574.13442622950812.945663004642144.349557533178
Winsorized Mean ( 2 / 20 )575.25573770491812.544192596334645.8583311191354
Winsorized Mean ( 3 / 20 )575.1426229508212.368617183536646.5001555482185
Winsorized Mean ( 4 / 20 )574.91967213114812.277498815177246.8271005997119
Winsorized Mean ( 5 / 20 )572.91967213114811.548542552208749.6096948633205
Winsorized Mean ( 6 / 20 )574.37540983606611.184689636811251.3537191005887
Winsorized Mean ( 7 / 20 )574.52459016393411.115262400324851.6879016861666
Winsorized Mean ( 8 / 20 )574.05245901639310.893169416039752.6983871352562
Winsorized Mean ( 9 / 20 )574.92295081967210.345382115306755.5729062891773
Winsorized Mean ( 10 / 20 )577.4147540983619.6986737406836859.5354343838003
Winsorized Mean ( 11 / 20 )584.1770491803287.8510986991528474.4070443597101
Winsorized Mean ( 12 / 20 )583.8032786885257.7437815585346475.3899466656699
Winsorized Mean ( 13 / 20 )584.5065573770496.8074673194371485.8625579748472
Winsorized Mean ( 14 / 20 )583.7032786885256.6188371550686788.1881915226646
Winsorized Mean ( 15 / 20 )583.1377049180336.5083998536798189.5977072749041
Winsorized Mean ( 16 / 20 )583.2688524590165.8848065653329599.1143627209463
Winsorized Mean ( 17 / 20 )582.4885245901645.53548715325297105.228051021284
Winsorized Mean ( 18 / 20 )583.4918032786895.29135199963624110.272724876138
Winsorized Mean ( 19 / 20 )581.9344262295084.97927446886757116.871329320767
Winsorized Mean ( 20 / 20 )577.7049180327874.05993918110353142.293983299464
Trimmed Mean ( 1 / 20 )574.94237288135612.483092528884346.0576873519934
Trimmed Mean ( 2 / 20 )575.8070175438611.913187933532248.3335796225568
Trimmed Mean ( 3 / 20 )576.11272727272711.482016990582450.1752198890889
Trimmed Mean ( 4 / 20 )576.48490566037711.031818802782952.2565604064267
Trimmed Mean ( 5 / 20 )576.95294117647110.502794531182954.9332788967254
Trimmed Mean ( 6 / 20 )577.95714285714310.094593841751757.2541255168369
Trimmed Mean ( 7 / 20 )578.7319148936179.6934484423627859.7034087853003
Trimmed Mean ( 8 / 20 )579.5466666666679.1944859408871663.0319813845674
Trimmed Mean ( 9 / 20 )580.5209302325588.6057750306125467.4571352571412
Trimmed Mean ( 10 / 20 )581.4463414634157.9954507625952672.722146471537
Trimmed Mean ( 11 / 20 )582.0769230769237.3830307144751578.8398349658366
Trimmed Mean ( 12 / 20 )581.7621621621627.1233800132439581.6693986675619
Trimmed Mean ( 13 / 20 )581.4657142857146.7927023902350585.6015295358162
Trimmed Mean ( 14 / 20 )581.0333333333336.6025357655489888.0015427353042
Trimmed Mean ( 15 / 20 )580.6580645161296.3782691793771591.0369330904958
Trimmed Mean ( 16 / 20 )580.3103448275866.0775658386270895.4840079459637
Trimmed Mean ( 17 / 20 )579.8925925925935.8357526751601599.3689460248893
Trimmed Mean ( 18 / 20 )579.525.58107217895152103.836678942373
Trimmed Mean ( 19 / 20 )578.9347826086965.25495290064244110.169357091272
Trimmed Mean ( 20 / 20 )578.476190476194.85482531077957119.154893007531
Median576.1
Midrange552.55
Midmean - Weighted Average at Xnp578.41
Midmean - Weighted Average at X(n+1)p580.658064516129
Midmean - Empirical Distribution Function580.658064516129
Midmean - Empirical Distribution Function - Averaging580.658064516129
Midmean - Empirical Distribution Function - Interpolation580.658064516129
Midmean - Closest Observation578.859375
Midmean - True Basic - Statistics Graphics Toolkit580.658064516129
Midmean - MS Excel (old versions)580.658064516129
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 574.208196721311 & 13.5625916521457 & 42.3376454477613 \tabularnewline
Geometric Mean & 563.676969469522 &  &  \tabularnewline
Harmonic Mean & 551.987105778083 &  &  \tabularnewline
Quadratic Mean & 583.739399665049 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 574.134426229508 & 12.9456630046421 & 44.349557533178 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 575.255737704918 & 12.5441925963346 & 45.8583311191354 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 575.14262295082 & 12.3686171835366 & 46.5001555482185 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 574.919672131148 & 12.2774988151772 & 46.8271005997119 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 572.919672131148 & 11.5485425522087 & 49.6096948633205 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 574.375409836066 & 11.1846896368112 & 51.3537191005887 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 574.524590163934 & 11.1152624003248 & 51.6879016861666 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 574.052459016393 & 10.8931694160397 & 52.6983871352562 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 574.922950819672 & 10.3453821153067 & 55.5729062891773 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 577.414754098361 & 9.69867374068368 & 59.5354343838003 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 584.177049180328 & 7.85109869915284 & 74.4070443597101 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 583.803278688525 & 7.74378155853464 & 75.3899466656699 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 584.506557377049 & 6.80746731943714 & 85.8625579748472 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 583.703278688525 & 6.61883715506867 & 88.1881915226646 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 583.137704918033 & 6.50839985367981 & 89.5977072749041 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 583.268852459016 & 5.88480656533295 & 99.1143627209463 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 582.488524590164 & 5.53548715325297 & 105.228051021284 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 583.491803278689 & 5.29135199963624 & 110.272724876138 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 581.934426229508 & 4.97927446886757 & 116.871329320767 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 577.704918032787 & 4.05993918110353 & 142.293983299464 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 574.942372881356 & 12.4830925288843 & 46.0576873519934 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 575.80701754386 & 11.9131879335322 & 48.3335796225568 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 576.112727272727 & 11.4820169905824 & 50.1752198890889 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 576.484905660377 & 11.0318188027829 & 52.2565604064267 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 576.952941176471 & 10.5027945311829 & 54.9332788967254 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 577.957142857143 & 10.0945938417517 & 57.2541255168369 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 578.731914893617 & 9.69344844236278 & 59.7034087853003 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 579.546666666667 & 9.19448594088716 & 63.0319813845674 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 580.520930232558 & 8.60577503061254 & 67.4571352571412 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 581.446341463415 & 7.99545076259526 & 72.722146471537 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 582.076923076923 & 7.38303071447515 & 78.8398349658366 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 581.762162162162 & 7.12338001324395 & 81.6693986675619 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 581.465714285714 & 6.79270239023505 & 85.6015295358162 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 581.033333333333 & 6.60253576554898 & 88.0015427353042 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 580.658064516129 & 6.37826917937715 & 91.0369330904958 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 580.310344827586 & 6.07756583862708 & 95.4840079459637 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 579.892592592593 & 5.83575267516015 & 99.3689460248893 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 579.52 & 5.58107217895152 & 103.836678942373 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 578.934782608696 & 5.25495290064244 & 110.169357091272 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 578.47619047619 & 4.85482531077957 & 119.154893007531 \tabularnewline
Median & 576.1 &  &  \tabularnewline
Midrange & 552.55 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 578.41 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 580.658064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 580.658064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 580.658064516129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 580.658064516129 &  &  \tabularnewline
Midmean - Closest Observation & 578.859375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 580.658064516129 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 580.658064516129 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=1618&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]574.208196721311[/C][C]13.5625916521457[/C][C]42.3376454477613[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]563.676969469522[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]551.987105778083[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]583.739399665049[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]574.134426229508[/C][C]12.9456630046421[/C][C]44.349557533178[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]575.255737704918[/C][C]12.5441925963346[/C][C]45.8583311191354[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]575.14262295082[/C][C]12.3686171835366[/C][C]46.5001555482185[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]574.919672131148[/C][C]12.2774988151772[/C][C]46.8271005997119[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]572.919672131148[/C][C]11.5485425522087[/C][C]49.6096948633205[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]574.375409836066[/C][C]11.1846896368112[/C][C]51.3537191005887[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]574.524590163934[/C][C]11.1152624003248[/C][C]51.6879016861666[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]574.052459016393[/C][C]10.8931694160397[/C][C]52.6983871352562[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]574.922950819672[/C][C]10.3453821153067[/C][C]55.5729062891773[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]577.414754098361[/C][C]9.69867374068368[/C][C]59.5354343838003[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]584.177049180328[/C][C]7.85109869915284[/C][C]74.4070443597101[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]583.803278688525[/C][C]7.74378155853464[/C][C]75.3899466656699[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]584.506557377049[/C][C]6.80746731943714[/C][C]85.8625579748472[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]583.703278688525[/C][C]6.61883715506867[/C][C]88.1881915226646[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]583.137704918033[/C][C]6.50839985367981[/C][C]89.5977072749041[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]583.268852459016[/C][C]5.88480656533295[/C][C]99.1143627209463[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]582.488524590164[/C][C]5.53548715325297[/C][C]105.228051021284[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]583.491803278689[/C][C]5.29135199963624[/C][C]110.272724876138[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]581.934426229508[/C][C]4.97927446886757[/C][C]116.871329320767[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]577.704918032787[/C][C]4.05993918110353[/C][C]142.293983299464[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]574.942372881356[/C][C]12.4830925288843[/C][C]46.0576873519934[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]575.80701754386[/C][C]11.9131879335322[/C][C]48.3335796225568[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]576.112727272727[/C][C]11.4820169905824[/C][C]50.1752198890889[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]576.484905660377[/C][C]11.0318188027829[/C][C]52.2565604064267[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]576.952941176471[/C][C]10.5027945311829[/C][C]54.9332788967254[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]577.957142857143[/C][C]10.0945938417517[/C][C]57.2541255168369[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]578.731914893617[/C][C]9.69344844236278[/C][C]59.7034087853003[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]579.546666666667[/C][C]9.19448594088716[/C][C]63.0319813845674[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]580.520930232558[/C][C]8.60577503061254[/C][C]67.4571352571412[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]581.446341463415[/C][C]7.99545076259526[/C][C]72.722146471537[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]582.076923076923[/C][C]7.38303071447515[/C][C]78.8398349658366[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]581.762162162162[/C][C]7.12338001324395[/C][C]81.6693986675619[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]581.465714285714[/C][C]6.79270239023505[/C][C]85.6015295358162[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]581.033333333333[/C][C]6.60253576554898[/C][C]88.0015427353042[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]580.658064516129[/C][C]6.37826917937715[/C][C]91.0369330904958[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]580.310344827586[/C][C]6.07756583862708[/C][C]95.4840079459637[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]579.892592592593[/C][C]5.83575267516015[/C][C]99.3689460248893[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]579.52[/C][C]5.58107217895152[/C][C]103.836678942373[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]578.934782608696[/C][C]5.25495290064244[/C][C]110.169357091272[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]578.47619047619[/C][C]4.85482531077957[/C][C]119.154893007531[/C][/ROW]
[ROW][C]Median[/C][C]576.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]552.55[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]578.41[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]580.658064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]580.658064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]580.658064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]580.658064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]578.859375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]580.658064516129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]580.658064516129[/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=1618&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=1618&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 Mean574.20819672131113.562591652145742.3376454477613
Geometric Mean563.676969469522
Harmonic Mean551.987105778083
Quadratic Mean583.739399665049
Winsorized Mean ( 1 / 20 )574.13442622950812.945663004642144.349557533178
Winsorized Mean ( 2 / 20 )575.25573770491812.544192596334645.8583311191354
Winsorized Mean ( 3 / 20 )575.1426229508212.368617183536646.5001555482185
Winsorized Mean ( 4 / 20 )574.91967213114812.277498815177246.8271005997119
Winsorized Mean ( 5 / 20 )572.91967213114811.548542552208749.6096948633205
Winsorized Mean ( 6 / 20 )574.37540983606611.184689636811251.3537191005887
Winsorized Mean ( 7 / 20 )574.52459016393411.115262400324851.6879016861666
Winsorized Mean ( 8 / 20 )574.05245901639310.893169416039752.6983871352562
Winsorized Mean ( 9 / 20 )574.92295081967210.345382115306755.5729062891773
Winsorized Mean ( 10 / 20 )577.4147540983619.6986737406836859.5354343838003
Winsorized Mean ( 11 / 20 )584.1770491803287.8510986991528474.4070443597101
Winsorized Mean ( 12 / 20 )583.8032786885257.7437815585346475.3899466656699
Winsorized Mean ( 13 / 20 )584.5065573770496.8074673194371485.8625579748472
Winsorized Mean ( 14 / 20 )583.7032786885256.6188371550686788.1881915226646
Winsorized Mean ( 15 / 20 )583.1377049180336.5083998536798189.5977072749041
Winsorized Mean ( 16 / 20 )583.2688524590165.8848065653329599.1143627209463
Winsorized Mean ( 17 / 20 )582.4885245901645.53548715325297105.228051021284
Winsorized Mean ( 18 / 20 )583.4918032786895.29135199963624110.272724876138
Winsorized Mean ( 19 / 20 )581.9344262295084.97927446886757116.871329320767
Winsorized Mean ( 20 / 20 )577.7049180327874.05993918110353142.293983299464
Trimmed Mean ( 1 / 20 )574.94237288135612.483092528884346.0576873519934
Trimmed Mean ( 2 / 20 )575.8070175438611.913187933532248.3335796225568
Trimmed Mean ( 3 / 20 )576.11272727272711.482016990582450.1752198890889
Trimmed Mean ( 4 / 20 )576.48490566037711.031818802782952.2565604064267
Trimmed Mean ( 5 / 20 )576.95294117647110.502794531182954.9332788967254
Trimmed Mean ( 6 / 20 )577.95714285714310.094593841751757.2541255168369
Trimmed Mean ( 7 / 20 )578.7319148936179.6934484423627859.7034087853003
Trimmed Mean ( 8 / 20 )579.5466666666679.1944859408871663.0319813845674
Trimmed Mean ( 9 / 20 )580.5209302325588.6057750306125467.4571352571412
Trimmed Mean ( 10 / 20 )581.4463414634157.9954507625952672.722146471537
Trimmed Mean ( 11 / 20 )582.0769230769237.3830307144751578.8398349658366
Trimmed Mean ( 12 / 20 )581.7621621621627.1233800132439581.6693986675619
Trimmed Mean ( 13 / 20 )581.4657142857146.7927023902350585.6015295358162
Trimmed Mean ( 14 / 20 )581.0333333333336.6025357655489888.0015427353042
Trimmed Mean ( 15 / 20 )580.6580645161296.3782691793771591.0369330904958
Trimmed Mean ( 16 / 20 )580.3103448275866.0775658386270895.4840079459637
Trimmed Mean ( 17 / 20 )579.8925925925935.8357526751601599.3689460248893
Trimmed Mean ( 18 / 20 )579.525.58107217895152103.836678942373
Trimmed Mean ( 19 / 20 )578.9347826086965.25495290064244110.169357091272
Trimmed Mean ( 20 / 20 )578.476190476194.85482531077957119.154893007531
Median576.1
Midrange552.55
Midmean - Weighted Average at Xnp578.41
Midmean - Weighted Average at X(n+1)p580.658064516129
Midmean - Empirical Distribution Function580.658064516129
Midmean - Empirical Distribution Function - Averaging580.658064516129
Midmean - Empirical Distribution Function - Interpolation580.658064516129
Midmean - Closest Observation578.859375
Midmean - True Basic - Statistics Graphics Toolkit580.658064516129
Midmean - MS Excel (old versions)580.658064516129
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')