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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 11 Oct 2016 11:47:02 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/11/t14761832928r0udu7hzj8c9n6.htm/, Retrieved Sun, 28 Apr 2024 20:59:35 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 28 Apr 2024 20:59:35 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
70
65
62
58
55
67
64
60
71
71
73
69
81
84
84
80
76
87
83
78
87
85
81
78
87
89
88
84
82
91
93
90
100
98
95
89
99
100
99
94
86
90
86
82
86
84
82
80
86
80
79
78
73
80
79
74
82
81
76
69




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean811.3548406623433659.7856281194727
Geometric Mean80.2962426051924
Harmonic Mean79.5531532297752
Quadratic Mean81.6657823081369
Winsorized Mean ( 1 / 20 )81.051.3394123426819760.5116120086735
Winsorized Mean ( 2 / 20 )81.08333333333331.3127561179577161.765724969141
Winsorized Mean ( 3 / 20 )81.18333333333331.2864991401725863.1040711946709
Winsorized Mean ( 4 / 20 )81.251.2384209464790165.6077404302666
Winsorized Mean ( 5 / 20 )81.08333333333331.1647583262500269.6138688223713
Winsorized Mean ( 6 / 20 )81.18333333333331.0994327419396673.8411093616391
Winsorized Mean ( 7 / 20 )81.31.0273931687352479.1323151389874
Winsorized Mean ( 8 / 20 )81.03333333333330.97857461966492682.8075158551322
Winsorized Mean ( 9 / 20 )81.03333333333330.92240372139069687.8501804081627
Winsorized Mean ( 10 / 20 )81.20.88929604611013591.3081761188263
Winsorized Mean ( 11 / 20 )81.01666666666670.85947417464041594.263061133352
Winsorized Mean ( 12 / 20 )81.41666666666670.783405454066662103.926601792255
Winsorized Mean ( 13 / 20 )81.20.748935214022054108.420592969486
Winsorized Mean ( 14 / 20 )81.20.670946712880705121.023023797774
Winsorized Mean ( 15 / 20 )81.70.583821426145974139.940050743483
Winsorized Mean ( 16 / 20 )81.70.583821426145974139.940050743483
Winsorized Mean ( 17 / 20 )81.98333333333330.450669098713058181.914698761124
Winsorized Mean ( 18 / 20 )81.98333333333330.450669098713058181.914698761124
Winsorized Mean ( 19 / 20 )81.98333333333330.450669098713058181.914698761124
Winsorized Mean ( 20 / 20 )82.31666666666670.402317907483289204.606022092332
Trimmed Mean ( 1 / 20 )81.12068965517241.2851418545561763.1219731639572
Trimmed Mean ( 2 / 20 )81.19642857142861.2179447353959366.6667593460496
Trimmed Mean ( 3 / 20 )81.25925925925931.1526365684072470.4985955560533
Trimmed Mean ( 4 / 20 )81.28846153846151.0840738408217974.9842478228609
Trimmed Mean ( 5 / 20 )81.31.0179010015613579.8702426614129
Trimmed Mean ( 6 / 20 )81.35416666666670.9613495165786584.6249623718523
Trimmed Mean ( 7 / 20 )81.39130434782610.91127042013769889.3163023282676
Trimmed Mean ( 8 / 20 )81.40909090909090.86956902998270193.6200440702338
Trimmed Mean ( 9 / 20 )81.47619047619050.82936670019310198.2390424612182
Trimmed Mean ( 10 / 20 )81.550.792553484404066102.895263985015
Trimmed Mean ( 11 / 20 )81.60526315789470.752935907197541108.382748621504
Trimmed Mean ( 12 / 20 )81.69444444444440.706904098078424115.566516966749
Trimmed Mean ( 13 / 20 )81.73529411764710.667969524865232122.363807142456
Trimmed Mean ( 14 / 20 )81.81250.622879467188606131.345636370491
Trimmed Mean ( 15 / 20 )81.90.583981577413723140.244150102663
Trimmed Mean ( 16 / 20 )81.92857142857140.558552009838505146.680291155446
Trimmed Mean ( 17 / 20 )81.96153846153850.5188174993513157.977590509222
Trimmed Mean ( 18 / 20 )81.95833333333330.508903220585904161.048957872528
Trimmed Mean ( 19 / 20 )81.95454545454550.490062601917059167.232808898191
Trimmed Mean ( 20 / 20 )81.950.455810440747836179.789650859131
Median82
Midrange77.5
Midmean - Weighted Average at Xnp81.8125
Midmean - Weighted Average at X(n+1)p82.0645161290323
Midmean - Empirical Distribution Function81.8125
Midmean - Empirical Distribution Function - Averaging82.0645161290323
Midmean - Empirical Distribution Function - Interpolation82.0645161290323
Midmean - Closest Observation81.8125
Midmean - True Basic - Statistics Graphics Toolkit82.0645161290323
Midmean - MS Excel (old versions)81.8125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 81 & 1.35484066234336 & 59.7856281194727 \tabularnewline
Geometric Mean & 80.2962426051924 &  &  \tabularnewline
Harmonic Mean & 79.5531532297752 &  &  \tabularnewline
Quadratic Mean & 81.6657823081369 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 81.05 & 1.33941234268197 & 60.5116120086735 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 81.0833333333333 & 1.31275611795771 & 61.765724969141 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 81.1833333333333 & 1.28649914017258 & 63.1040711946709 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 81.25 & 1.23842094647901 & 65.6077404302666 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 81.0833333333333 & 1.16475832625002 & 69.6138688223713 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 81.1833333333333 & 1.09943274193966 & 73.8411093616391 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 81.3 & 1.02739316873524 & 79.1323151389874 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 81.0333333333333 & 0.978574619664926 & 82.8075158551322 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 81.0333333333333 & 0.922403721390696 & 87.8501804081627 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 81.2 & 0.889296046110135 & 91.3081761188263 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 81.0166666666667 & 0.859474174640415 & 94.263061133352 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 81.4166666666667 & 0.783405454066662 & 103.926601792255 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 81.2 & 0.748935214022054 & 108.420592969486 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 81.2 & 0.670946712880705 & 121.023023797774 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 81.7 & 0.583821426145974 & 139.940050743483 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 81.7 & 0.583821426145974 & 139.940050743483 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 81.9833333333333 & 0.450669098713058 & 181.914698761124 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 81.9833333333333 & 0.450669098713058 & 181.914698761124 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 81.9833333333333 & 0.450669098713058 & 181.914698761124 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 82.3166666666667 & 0.402317907483289 & 204.606022092332 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 81.1206896551724 & 1.28514185455617 & 63.1219731639572 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 81.1964285714286 & 1.21794473539593 & 66.6667593460496 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 81.2592592592593 & 1.15263656840724 & 70.4985955560533 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 81.2884615384615 & 1.08407384082179 & 74.9842478228609 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 81.3 & 1.01790100156135 & 79.8702426614129 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 81.3541666666667 & 0.96134951657865 & 84.6249623718523 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 81.3913043478261 & 0.911270420137698 & 89.3163023282676 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 81.4090909090909 & 0.869569029982701 & 93.6200440702338 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 81.4761904761905 & 0.829366700193101 & 98.2390424612182 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 81.55 & 0.792553484404066 & 102.895263985015 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 81.6052631578947 & 0.752935907197541 & 108.382748621504 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 81.6944444444444 & 0.706904098078424 & 115.566516966749 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 81.7352941176471 & 0.667969524865232 & 122.363807142456 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 81.8125 & 0.622879467188606 & 131.345636370491 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 81.9 & 0.583981577413723 & 140.244150102663 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 81.9285714285714 & 0.558552009838505 & 146.680291155446 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 81.9615384615385 & 0.5188174993513 & 157.977590509222 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 81.9583333333333 & 0.508903220585904 & 161.048957872528 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 81.9545454545455 & 0.490062601917059 & 167.232808898191 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 81.95 & 0.455810440747836 & 179.789650859131 \tabularnewline
Median & 82 &  &  \tabularnewline
Midrange & 77.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 81.8125 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 82.0645161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 81.8125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 82.0645161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 82.0645161290323 &  &  \tabularnewline
Midmean - Closest Observation & 81.8125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 82.0645161290323 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 81.8125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]81[/C][C]1.35484066234336[/C][C]59.7856281194727[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]80.2962426051924[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]79.5531532297752[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]81.6657823081369[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]81.05[/C][C]1.33941234268197[/C][C]60.5116120086735[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]81.0833333333333[/C][C]1.31275611795771[/C][C]61.765724969141[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]81.1833333333333[/C][C]1.28649914017258[/C][C]63.1040711946709[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]81.25[/C][C]1.23842094647901[/C][C]65.6077404302666[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]81.0833333333333[/C][C]1.16475832625002[/C][C]69.6138688223713[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]81.1833333333333[/C][C]1.09943274193966[/C][C]73.8411093616391[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]81.3[/C][C]1.02739316873524[/C][C]79.1323151389874[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]81.0333333333333[/C][C]0.978574619664926[/C][C]82.8075158551322[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]81.0333333333333[/C][C]0.922403721390696[/C][C]87.8501804081627[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]81.2[/C][C]0.889296046110135[/C][C]91.3081761188263[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]81.0166666666667[/C][C]0.859474174640415[/C][C]94.263061133352[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]81.4166666666667[/C][C]0.783405454066662[/C][C]103.926601792255[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]81.2[/C][C]0.748935214022054[/C][C]108.420592969486[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]81.2[/C][C]0.670946712880705[/C][C]121.023023797774[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]81.7[/C][C]0.583821426145974[/C][C]139.940050743483[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]81.7[/C][C]0.583821426145974[/C][C]139.940050743483[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]81.9833333333333[/C][C]0.450669098713058[/C][C]181.914698761124[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]81.9833333333333[/C][C]0.450669098713058[/C][C]181.914698761124[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]81.9833333333333[/C][C]0.450669098713058[/C][C]181.914698761124[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]82.3166666666667[/C][C]0.402317907483289[/C][C]204.606022092332[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]81.1206896551724[/C][C]1.28514185455617[/C][C]63.1219731639572[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]81.1964285714286[/C][C]1.21794473539593[/C][C]66.6667593460496[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]81.2592592592593[/C][C]1.15263656840724[/C][C]70.4985955560533[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]81.2884615384615[/C][C]1.08407384082179[/C][C]74.9842478228609[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]81.3[/C][C]1.01790100156135[/C][C]79.8702426614129[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]81.3541666666667[/C][C]0.96134951657865[/C][C]84.6249623718523[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]81.3913043478261[/C][C]0.911270420137698[/C][C]89.3163023282676[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]81.4090909090909[/C][C]0.869569029982701[/C][C]93.6200440702338[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]81.4761904761905[/C][C]0.829366700193101[/C][C]98.2390424612182[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]81.55[/C][C]0.792553484404066[/C][C]102.895263985015[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]81.6052631578947[/C][C]0.752935907197541[/C][C]108.382748621504[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]81.6944444444444[/C][C]0.706904098078424[/C][C]115.566516966749[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]81.7352941176471[/C][C]0.667969524865232[/C][C]122.363807142456[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]81.8125[/C][C]0.622879467188606[/C][C]131.345636370491[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]81.9[/C][C]0.583981577413723[/C][C]140.244150102663[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]81.9285714285714[/C][C]0.558552009838505[/C][C]146.680291155446[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]81.9615384615385[/C][C]0.5188174993513[/C][C]157.977590509222[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]81.9583333333333[/C][C]0.508903220585904[/C][C]161.048957872528[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]81.9545454545455[/C][C]0.490062601917059[/C][C]167.232808898191[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]81.95[/C][C]0.455810440747836[/C][C]179.789650859131[/C][/ROW]
[ROW][C]Median[/C][C]82[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]77.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]81.8125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]82.0645161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]81.8125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]82.0645161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]82.0645161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]81.8125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]82.0645161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]81.8125[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=1

As an alternative you can also use a QR Code:  

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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean811.3548406623433659.7856281194727
Geometric Mean80.2962426051924
Harmonic Mean79.5531532297752
Quadratic Mean81.6657823081369
Winsorized Mean ( 1 / 20 )81.051.3394123426819760.5116120086735
Winsorized Mean ( 2 / 20 )81.08333333333331.3127561179577161.765724969141
Winsorized Mean ( 3 / 20 )81.18333333333331.2864991401725863.1040711946709
Winsorized Mean ( 4 / 20 )81.251.2384209464790165.6077404302666
Winsorized Mean ( 5 / 20 )81.08333333333331.1647583262500269.6138688223713
Winsorized Mean ( 6 / 20 )81.18333333333331.0994327419396673.8411093616391
Winsorized Mean ( 7 / 20 )81.31.0273931687352479.1323151389874
Winsorized Mean ( 8 / 20 )81.03333333333330.97857461966492682.8075158551322
Winsorized Mean ( 9 / 20 )81.03333333333330.92240372139069687.8501804081627
Winsorized Mean ( 10 / 20 )81.20.88929604611013591.3081761188263
Winsorized Mean ( 11 / 20 )81.01666666666670.85947417464041594.263061133352
Winsorized Mean ( 12 / 20 )81.41666666666670.783405454066662103.926601792255
Winsorized Mean ( 13 / 20 )81.20.748935214022054108.420592969486
Winsorized Mean ( 14 / 20 )81.20.670946712880705121.023023797774
Winsorized Mean ( 15 / 20 )81.70.583821426145974139.940050743483
Winsorized Mean ( 16 / 20 )81.70.583821426145974139.940050743483
Winsorized Mean ( 17 / 20 )81.98333333333330.450669098713058181.914698761124
Winsorized Mean ( 18 / 20 )81.98333333333330.450669098713058181.914698761124
Winsorized Mean ( 19 / 20 )81.98333333333330.450669098713058181.914698761124
Winsorized Mean ( 20 / 20 )82.31666666666670.402317907483289204.606022092332
Trimmed Mean ( 1 / 20 )81.12068965517241.2851418545561763.1219731639572
Trimmed Mean ( 2 / 20 )81.19642857142861.2179447353959366.6667593460496
Trimmed Mean ( 3 / 20 )81.25925925925931.1526365684072470.4985955560533
Trimmed Mean ( 4 / 20 )81.28846153846151.0840738408217974.9842478228609
Trimmed Mean ( 5 / 20 )81.31.0179010015613579.8702426614129
Trimmed Mean ( 6 / 20 )81.35416666666670.9613495165786584.6249623718523
Trimmed Mean ( 7 / 20 )81.39130434782610.91127042013769889.3163023282676
Trimmed Mean ( 8 / 20 )81.40909090909090.86956902998270193.6200440702338
Trimmed Mean ( 9 / 20 )81.47619047619050.82936670019310198.2390424612182
Trimmed Mean ( 10 / 20 )81.550.792553484404066102.895263985015
Trimmed Mean ( 11 / 20 )81.60526315789470.752935907197541108.382748621504
Trimmed Mean ( 12 / 20 )81.69444444444440.706904098078424115.566516966749
Trimmed Mean ( 13 / 20 )81.73529411764710.667969524865232122.363807142456
Trimmed Mean ( 14 / 20 )81.81250.622879467188606131.345636370491
Trimmed Mean ( 15 / 20 )81.90.583981577413723140.244150102663
Trimmed Mean ( 16 / 20 )81.92857142857140.558552009838505146.680291155446
Trimmed Mean ( 17 / 20 )81.96153846153850.5188174993513157.977590509222
Trimmed Mean ( 18 / 20 )81.95833333333330.508903220585904161.048957872528
Trimmed Mean ( 19 / 20 )81.95454545454550.490062601917059167.232808898191
Trimmed Mean ( 20 / 20 )81.950.455810440747836179.789650859131
Median82
Midrange77.5
Midmean - Weighted Average at Xnp81.8125
Midmean - Weighted Average at X(n+1)p82.0645161290323
Midmean - Empirical Distribution Function81.8125
Midmean - Empirical Distribution Function - Averaging82.0645161290323
Midmean - Empirical Distribution Function - Interpolation82.0645161290323
Midmean - Closest Observation81.8125
Midmean - True Basic - Statistics Graphics Toolkit82.0645161290323
Midmean - MS Excel (old versions)81.8125
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')