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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 14:02:40 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/20/t12245329927dp3vt9735mtx17.htm/, Retrieved Sun, 19 May 2024 13:08:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18039, Retrieved Sun, 19 May 2024 13:08:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Verkeersbelasting] [2008-10-13 21:38:41] [7e0d4664815809d7a7facf71b03d5464]
- RMPD    [Central Tendency] [Centrale tendens ...] [2008-10-20 20:02:40] [84a986a411c52e49a8807521f8b9f7a0] [Current]
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Dataseries X:
107.06
109.98
112.64
112.89
112.9
112.9
112.91
112.99
113.01
113
113.07
113.07
113.21
114.13
114.59
114.88
115.3
115.33
115.36
115.41
115.43
115.43
115.43
115.43
115.56
115.88
116.02
116.09
116.28
116.28
116.28
116.25
116.07
116.08
116.07
115.92
116.07
117.22
117.75
117.78
117.78
117.81
117.81
117.74
117.75
117.76
117.76
117.75
117.8
118.09
118.95
119.03
118.9
118.9
118.9
118.87
118.88
119.36
119.39
119.47




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18039&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18039&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18039&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean115.9441666666670.320134707845945362.173059731035
Geometric Mean115.917724301236
Harmonic Mean115.890902882186
Quadratic Mean115.970239594763
Winsorized Mean ( 1 / 20 )115.99150.300071538080675386.546157432684
Winsorized Mean ( 2 / 20 )116.0791666666670.275185432259886421.821626651520
Winsorized Mean ( 3 / 20 )116.0751666666670.269406178093092430.855622867555
Winsorized Mean ( 4 / 20 )116.07050.268291773986272432.627874777627
Winsorized Mean ( 5 / 20 )116.0663333333330.267538789274524433.829926673685
Winsorized Mean ( 6 / 20 )116.0673333333330.267338405350818434.158845157406
Winsorized Mean ( 7 / 20 )116.0766666666670.26548459760048437.225615782604
Winsorized Mean ( 8 / 20 )116.0753333333330.264742222632591438.446622450634
Winsorized Mean ( 9 / 20 )116.0753333333330.264177913286053439.383186465125
Winsorized Mean ( 10 / 20 )115.9553333333330.240666032833258481.810133188472
Winsorized Mean ( 11 / 20 )115.9040.233247789000124496.913606327639
Winsorized Mean ( 12 / 20 )115.9320.227525350918825509.534430039672
Winsorized Mean ( 13 / 20 )116.1291666666670.188909641459971614.733931890256
Winsorized Mean ( 14 / 20 )116.2318333333330.169730675937053684.801569849633
Winsorized Mean ( 15 / 20 )116.3043333333330.158242709718040734.97435389325
Winsorized Mean ( 16 / 20 )116.4110.141324385443221823.714885685952
Winsorized Mean ( 17 / 20 )116.41950.140198290768694830.391721337562
Winsorized Mean ( 18 / 20 )116.42550.138532752251327840.418587719818
Winsorized Mean ( 19 / 20 )116.4413333333330.136486680434282853.133309146597
Winsorized Mean ( 20 / 20 )116.4480.135635728506384858.534851269067
Trimmed Mean ( 1 / 20 )116.0365517241380.286279464411521405.326145075282
Trimmed Mean ( 2 / 20 )116.0848214285710.269009968321968431.526096050217
Trimmed Mean ( 3 / 20 )116.0879629629630.264544937078234438.821336915747
Trimmed Mean ( 4 / 20 )116.0928846153850.261543789039432443.875517142875
Trimmed Mean ( 5 / 20 )116.09960.257975312851475450.041512564586
Trimmed Mean ( 6 / 20 )116.1079166666670.253492966863795458.03210283563
Trimmed Mean ( 7 / 20 )116.1167391304350.247637738835264468.897590797658
Trimmed Mean ( 8 / 20 )116.1245454545450.240480371649264482.885753453138
Trimmed Mean ( 9 / 20 )116.1333333333330.231213198513537502.278131525151
Trimmed Mean ( 10 / 20 )116.1430.218985188587066530.369203275238
Trimmed Mean ( 11 / 20 )116.1726315789470.209214368752569555.280367556117
Trimmed Mean ( 12 / 20 )116.2133333333330.197553689708546588.26202388214
Trimmed Mean ( 13 / 20 )116.2547058823530.18293275080757635.505153501153
Trimmed Mean ( 14 / 20 )116.27281250.175730752155177661.653188608257
Trimmed Mean ( 15 / 20 )116.2786666666670.171302470497268678.791533648786
Trimmed Mean ( 16 / 20 )116.2750.167928162393530692.409172724206
Trimmed Mean ( 17 / 20 )116.2553846153850.167116938117945695.652911815173
Trimmed Mean ( 18 / 20 )116.231250.164949830427227704.646071468859
Trimmed Mean ( 19 / 20 )116.2018181818180.160722982842204722.994410176571
Trimmed Mean ( 20 / 20 )116.1640.15288351258737759.820323552643
Median116.07
Midrange113.265
Midmean - Weighted Average at Xnp116.2728125
Midmean - Weighted Average at X(n+1)p116.327096774194
Midmean - Empirical Distribution Function116.2728125
Midmean - Empirical Distribution Function - Averaging116.327096774194
Midmean - Empirical Distribution Function - Interpolation116.327096774194
Midmean - Closest Observation116.2728125
Midmean - True Basic - Statistics Graphics Toolkit116.327096774194
Midmean - MS Excel (old versions)116.2728125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 115.944166666667 & 0.320134707845945 & 362.173059731035 \tabularnewline
Geometric Mean & 115.917724301236 &  &  \tabularnewline
Harmonic Mean & 115.890902882186 &  &  \tabularnewline
Quadratic Mean & 115.970239594763 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 115.9915 & 0.300071538080675 & 386.546157432684 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 116.079166666667 & 0.275185432259886 & 421.821626651520 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 116.075166666667 & 0.269406178093092 & 430.855622867555 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 116.0705 & 0.268291773986272 & 432.627874777627 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 116.066333333333 & 0.267538789274524 & 433.829926673685 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 116.067333333333 & 0.267338405350818 & 434.158845157406 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 116.076666666667 & 0.26548459760048 & 437.225615782604 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 116.075333333333 & 0.264742222632591 & 438.446622450634 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 116.075333333333 & 0.264177913286053 & 439.383186465125 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 115.955333333333 & 0.240666032833258 & 481.810133188472 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 115.904 & 0.233247789000124 & 496.913606327639 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 115.932 & 0.227525350918825 & 509.534430039672 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 116.129166666667 & 0.188909641459971 & 614.733931890256 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 116.231833333333 & 0.169730675937053 & 684.801569849633 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 116.304333333333 & 0.158242709718040 & 734.97435389325 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 116.411 & 0.141324385443221 & 823.714885685952 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 116.4195 & 0.140198290768694 & 830.391721337562 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 116.4255 & 0.138532752251327 & 840.418587719818 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 116.441333333333 & 0.136486680434282 & 853.133309146597 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 116.448 & 0.135635728506384 & 858.534851269067 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 116.036551724138 & 0.286279464411521 & 405.326145075282 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 116.084821428571 & 0.269009968321968 & 431.526096050217 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 116.087962962963 & 0.264544937078234 & 438.821336915747 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 116.092884615385 & 0.261543789039432 & 443.875517142875 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 116.0996 & 0.257975312851475 & 450.041512564586 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 116.107916666667 & 0.253492966863795 & 458.03210283563 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 116.116739130435 & 0.247637738835264 & 468.897590797658 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 116.124545454545 & 0.240480371649264 & 482.885753453138 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 116.133333333333 & 0.231213198513537 & 502.278131525151 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 116.143 & 0.218985188587066 & 530.369203275238 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 116.172631578947 & 0.209214368752569 & 555.280367556117 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 116.213333333333 & 0.197553689708546 & 588.26202388214 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 116.254705882353 & 0.18293275080757 & 635.505153501153 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 116.2728125 & 0.175730752155177 & 661.653188608257 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 116.278666666667 & 0.171302470497268 & 678.791533648786 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 116.275 & 0.167928162393530 & 692.409172724206 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 116.255384615385 & 0.167116938117945 & 695.652911815173 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 116.23125 & 0.164949830427227 & 704.646071468859 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 116.201818181818 & 0.160722982842204 & 722.994410176571 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 116.164 & 0.15288351258737 & 759.820323552643 \tabularnewline
Median & 116.07 &  &  \tabularnewline
Midrange & 113.265 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 116.2728125 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 116.327096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 116.2728125 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 116.327096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 116.327096774194 &  &  \tabularnewline
Midmean - Closest Observation & 116.2728125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 116.327096774194 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 116.2728125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18039&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]115.944166666667[/C][C]0.320134707845945[/C][C]362.173059731035[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]115.917724301236[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]115.890902882186[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]115.970239594763[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]115.9915[/C][C]0.300071538080675[/C][C]386.546157432684[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]116.079166666667[/C][C]0.275185432259886[/C][C]421.821626651520[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]116.075166666667[/C][C]0.269406178093092[/C][C]430.855622867555[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]116.0705[/C][C]0.268291773986272[/C][C]432.627874777627[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]116.066333333333[/C][C]0.267538789274524[/C][C]433.829926673685[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]116.067333333333[/C][C]0.267338405350818[/C][C]434.158845157406[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]116.076666666667[/C][C]0.26548459760048[/C][C]437.225615782604[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]116.075333333333[/C][C]0.264742222632591[/C][C]438.446622450634[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]116.075333333333[/C][C]0.264177913286053[/C][C]439.383186465125[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]115.955333333333[/C][C]0.240666032833258[/C][C]481.810133188472[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]115.904[/C][C]0.233247789000124[/C][C]496.913606327639[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]115.932[/C][C]0.227525350918825[/C][C]509.534430039672[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]116.129166666667[/C][C]0.188909641459971[/C][C]614.733931890256[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]116.231833333333[/C][C]0.169730675937053[/C][C]684.801569849633[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]116.304333333333[/C][C]0.158242709718040[/C][C]734.97435389325[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]116.411[/C][C]0.141324385443221[/C][C]823.714885685952[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]116.4195[/C][C]0.140198290768694[/C][C]830.391721337562[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]116.4255[/C][C]0.138532752251327[/C][C]840.418587719818[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]116.441333333333[/C][C]0.136486680434282[/C][C]853.133309146597[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]116.448[/C][C]0.135635728506384[/C][C]858.534851269067[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]116.036551724138[/C][C]0.286279464411521[/C][C]405.326145075282[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]116.084821428571[/C][C]0.269009968321968[/C][C]431.526096050217[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]116.087962962963[/C][C]0.264544937078234[/C][C]438.821336915747[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]116.092884615385[/C][C]0.261543789039432[/C][C]443.875517142875[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]116.0996[/C][C]0.257975312851475[/C][C]450.041512564586[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]116.107916666667[/C][C]0.253492966863795[/C][C]458.03210283563[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]116.116739130435[/C][C]0.247637738835264[/C][C]468.897590797658[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]116.124545454545[/C][C]0.240480371649264[/C][C]482.885753453138[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]116.133333333333[/C][C]0.231213198513537[/C][C]502.278131525151[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]116.143[/C][C]0.218985188587066[/C][C]530.369203275238[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]116.172631578947[/C][C]0.209214368752569[/C][C]555.280367556117[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]116.213333333333[/C][C]0.197553689708546[/C][C]588.26202388214[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]116.254705882353[/C][C]0.18293275080757[/C][C]635.505153501153[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]116.2728125[/C][C]0.175730752155177[/C][C]661.653188608257[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]116.278666666667[/C][C]0.171302470497268[/C][C]678.791533648786[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]116.275[/C][C]0.167928162393530[/C][C]692.409172724206[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]116.255384615385[/C][C]0.167116938117945[/C][C]695.652911815173[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]116.23125[/C][C]0.164949830427227[/C][C]704.646071468859[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]116.201818181818[/C][C]0.160722982842204[/C][C]722.994410176571[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]116.164[/C][C]0.15288351258737[/C][C]759.820323552643[/C][/ROW]
[ROW][C]Median[/C][C]116.07[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]113.265[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]116.2728125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]116.327096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]116.2728125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]116.327096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]116.327096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]116.2728125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]116.327096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]116.2728125[/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=18039&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18039&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 Mean115.9441666666670.320134707845945362.173059731035
Geometric Mean115.917724301236
Harmonic Mean115.890902882186
Quadratic Mean115.970239594763
Winsorized Mean ( 1 / 20 )115.99150.300071538080675386.546157432684
Winsorized Mean ( 2 / 20 )116.0791666666670.275185432259886421.821626651520
Winsorized Mean ( 3 / 20 )116.0751666666670.269406178093092430.855622867555
Winsorized Mean ( 4 / 20 )116.07050.268291773986272432.627874777627
Winsorized Mean ( 5 / 20 )116.0663333333330.267538789274524433.829926673685
Winsorized Mean ( 6 / 20 )116.0673333333330.267338405350818434.158845157406
Winsorized Mean ( 7 / 20 )116.0766666666670.26548459760048437.225615782604
Winsorized Mean ( 8 / 20 )116.0753333333330.264742222632591438.446622450634
Winsorized Mean ( 9 / 20 )116.0753333333330.264177913286053439.383186465125
Winsorized Mean ( 10 / 20 )115.9553333333330.240666032833258481.810133188472
Winsorized Mean ( 11 / 20 )115.9040.233247789000124496.913606327639
Winsorized Mean ( 12 / 20 )115.9320.227525350918825509.534430039672
Winsorized Mean ( 13 / 20 )116.1291666666670.188909641459971614.733931890256
Winsorized Mean ( 14 / 20 )116.2318333333330.169730675937053684.801569849633
Winsorized Mean ( 15 / 20 )116.3043333333330.158242709718040734.97435389325
Winsorized Mean ( 16 / 20 )116.4110.141324385443221823.714885685952
Winsorized Mean ( 17 / 20 )116.41950.140198290768694830.391721337562
Winsorized Mean ( 18 / 20 )116.42550.138532752251327840.418587719818
Winsorized Mean ( 19 / 20 )116.4413333333330.136486680434282853.133309146597
Winsorized Mean ( 20 / 20 )116.4480.135635728506384858.534851269067
Trimmed Mean ( 1 / 20 )116.0365517241380.286279464411521405.326145075282
Trimmed Mean ( 2 / 20 )116.0848214285710.269009968321968431.526096050217
Trimmed Mean ( 3 / 20 )116.0879629629630.264544937078234438.821336915747
Trimmed Mean ( 4 / 20 )116.0928846153850.261543789039432443.875517142875
Trimmed Mean ( 5 / 20 )116.09960.257975312851475450.041512564586
Trimmed Mean ( 6 / 20 )116.1079166666670.253492966863795458.03210283563
Trimmed Mean ( 7 / 20 )116.1167391304350.247637738835264468.897590797658
Trimmed Mean ( 8 / 20 )116.1245454545450.240480371649264482.885753453138
Trimmed Mean ( 9 / 20 )116.1333333333330.231213198513537502.278131525151
Trimmed Mean ( 10 / 20 )116.1430.218985188587066530.369203275238
Trimmed Mean ( 11 / 20 )116.1726315789470.209214368752569555.280367556117
Trimmed Mean ( 12 / 20 )116.2133333333330.197553689708546588.26202388214
Trimmed Mean ( 13 / 20 )116.2547058823530.18293275080757635.505153501153
Trimmed Mean ( 14 / 20 )116.27281250.175730752155177661.653188608257
Trimmed Mean ( 15 / 20 )116.2786666666670.171302470497268678.791533648786
Trimmed Mean ( 16 / 20 )116.2750.167928162393530692.409172724206
Trimmed Mean ( 17 / 20 )116.2553846153850.167116938117945695.652911815173
Trimmed Mean ( 18 / 20 )116.231250.164949830427227704.646071468859
Trimmed Mean ( 19 / 20 )116.2018181818180.160722982842204722.994410176571
Trimmed Mean ( 20 / 20 )116.1640.15288351258737759.820323552643
Median116.07
Midrange113.265
Midmean - Weighted Average at Xnp116.2728125
Midmean - Weighted Average at X(n+1)p116.327096774194
Midmean - Empirical Distribution Function116.2728125
Midmean - Empirical Distribution Function - Averaging116.327096774194
Midmean - Empirical Distribution Function - Interpolation116.327096774194
Midmean - Closest Observation116.2728125
Midmean - True Basic - Statistics Graphics Toolkit116.327096774194
Midmean - MS Excel (old versions)116.2728125
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')