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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 06 Dec 2009 11:00:44 -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/2009/Dec/06/t1260122523s9iehnbo8uo9fqh.htm/, Retrieved Mon, 06 May 2024 05:26:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64462, Retrieved Mon, 06 May 2024 05:26:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [invoer] [2008-12-18 17:20:12] [5e74953d94072114d25d7276793b561e]
-  M D    [Central Tendency] [central tendency ...] [2009-12-06 18:00:44] [a5c6be3c0aa55fdb2a703a08e16947ef] [Current]
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Dataseries X:
0,5270
0,4720
0,0000
0,0520
0,3130
0,3640
0,3630
-0,1550
0,0520
0,5680
0,6680
1,3780
0,2520
-0,4020
-0,0500
0,5550
0,0500
0,1500
0,4500
0,2990
0,1990
0,4960
0,4440
-0,3930
-0,4440
0,1980
0,4940
0,1330
0,3880
0,4840
0,2780
0,3690
0,1650
0,1550
0,0870
0,4140
0,3600
0,9750
0,2700
0,3590
0,1690
0,3810
0,1540
0,4860
0,9250
0,7280
-0,0140
0,0460
-0,8190
-1,6740
-0,7880
0,2790
0,3960
-0,1410
-0,0190
0,0990
0,7420
0,0050
0,4480




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64462&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64462&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64462&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' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.2159322033898310.0588183161098493.67117281947610
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean0.497275764984257
Winsorized Mean ( 1 / 19 )0.2235932203389830.05001546294295454.47048187065676
Winsorized Mean ( 2 / 19 )0.2229491525423730.04921246191555624.53033934626014
Winsorized Mean ( 3 / 19 )0.2311355932203390.04145828360816835.57513657354594
Winsorized Mean ( 4 / 19 )0.2330338983050850.04047230631041415.75786061011112
Winsorized Mean ( 5 / 19 )0.2287118644067800.03923744239062935.82891876921623
Winsorized Mean ( 6 / 19 )0.2427457627118640.03130663744872957.75381141169843
Winsorized Mean ( 7 / 19 )0.2428644067796610.03067200264295177.91811377974925
Winsorized Mean ( 8 / 19 )0.2514067796610170.02750480664272299.14046708005245
Winsorized Mean ( 9 / 19 )0.2514067796610170.02583567772498149.73099224789924
Winsorized Mean ( 10 / 19 )0.2519152542372880.02562813793859499.82963549052523
Winsorized Mean ( 11 / 19 )0.2530338983050850.024924502790120310.1520138811108
Winsorized Mean ( 12 / 19 )0.253644067796610.024681676059113310.2766144077544
Winsorized Mean ( 13 / 19 )0.2600338983050850.022736656784129111.4367693005155
Winsorized Mean ( 14 / 19 )0.2557627118644070.021760630445718311.7534605673491
Winsorized Mean ( 15 / 19 )0.2557627118644070.021599691251866311.8410355445385
Winsorized Mean ( 16 / 19 )0.2546779661016950.021433864419138911.882036814336
Winsorized Mean ( 17 / 19 )0.2561186440677970.018520765428111013.8287288968661
Winsorized Mean ( 18 / 19 )0.2542881355932200.017151558245019514.8259494537216
Winsorized Mean ( 19 / 19 )0.2626610169491530.015116933854779517.3752838685675
Trimmed Mean ( 1 / 19 )0.2287017543859650.04651781643828144.91643357098243
Trimmed Mean ( 2 / 19 )0.2341818181818180.04204735258251165.56947830953856
Trimmed Mean ( 3 / 19 )0.2404339622641510.03677266596064786.53838812017195
Trimmed Mean ( 4 / 19 )0.2440196078431370.03433439355145137.10714774901921
Trimmed Mean ( 5 / 19 )0.2473265306122450.03163591490753277.81790352310484
Trimmed Mean ( 6 / 19 )0.2520.02857989434509968.81738738978958
Trimmed Mean ( 7 / 19 )0.2540222222222220.02752643337287279.22830134878865
Trimmed Mean ( 8 / 19 )0.2562093023255810.02634445897009379.72535828564296
Trimmed Mean ( 9 / 19 )0.2570731707317070.02573666811503189.98859563260873
Trimmed Mean ( 10 / 19 )0.2580256410256410.025357883387712810.1753619212031
Trimmed Mean ( 11 / 19 )0.2590.024860602356933110.4180902892632
Trimmed Mean ( 12 / 19 )0.2599142857142860.024333169650871710.6814808528232
Trimmed Mean ( 13 / 19 )0.2608484848484850.023624634084552911.0413767220650
Trimmed Mean ( 14 / 19 )0.2609677419354840.023155225791232111.2703604917686
Trimmed Mean ( 15 / 19 )0.2617241379310340.022698923421863811.5302445436218
Trimmed Mean ( 16 / 19 )0.2625925925925930.021996908566742211.9377044185934
Trimmed Mean ( 17 / 19 )0.263760.020911741518422912.6130097661943
Trimmed Mean ( 18 / 19 )0.2649130434782610.020300792741728113.0493940236006
Trimmed Mean ( 19 / 19 )0.2665714285714290.019746316284378713.4998054691503
Median0.278
Midrange-0.148
Midmean - Weighted Average at Xnp0.254666666666667
Midmean - Weighted Average at X(n+1)p0.260967741935484
Midmean - Empirical Distribution Function0.260967741935484
Midmean - Empirical Distribution Function - Averaging0.260967741935484
Midmean - Empirical Distribution Function - Interpolation0.261724137931034
Midmean - Closest Observation0.254666666666667
Midmean - True Basic - Statistics Graphics Toolkit0.260967741935484
Midmean - MS Excel (old versions)0.260967741935484
Number of observations59

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.215932203389831 & 0.058818316109849 & 3.67117281947610 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 0.497275764984257 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 0.223593220338983 & 0.0500154629429545 & 4.47048187065676 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 0.222949152542373 & 0.0492124619155562 & 4.53033934626014 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 0.231135593220339 & 0.0414582836081683 & 5.57513657354594 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 0.233033898305085 & 0.0404723063104141 & 5.75786061011112 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 0.228711864406780 & 0.0392374423906293 & 5.82891876921623 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 0.242745762711864 & 0.0313066374487295 & 7.75381141169843 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 0.242864406779661 & 0.0306720026429517 & 7.91811377974925 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 0.251406779661017 & 0.0275048066427229 & 9.14046708005245 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 0.251406779661017 & 0.0258356777249814 & 9.73099224789924 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 0.251915254237288 & 0.0256281379385949 & 9.82963549052523 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 0.253033898305085 & 0.0249245027901203 & 10.1520138811108 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 0.25364406779661 & 0.0246816760591133 & 10.2766144077544 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 0.260033898305085 & 0.0227366567841291 & 11.4367693005155 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 0.255762711864407 & 0.0217606304457183 & 11.7534605673491 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 0.255762711864407 & 0.0215996912518663 & 11.8410355445385 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 0.254677966101695 & 0.0214338644191389 & 11.882036814336 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 0.256118644067797 & 0.0185207654281110 & 13.8287288968661 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 0.254288135593220 & 0.0171515582450195 & 14.8259494537216 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 0.262661016949153 & 0.0151169338547795 & 17.3752838685675 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 0.228701754385965 & 0.0465178164382814 & 4.91643357098243 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 0.234181818181818 & 0.0420473525825116 & 5.56947830953856 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 0.240433962264151 & 0.0367726659606478 & 6.53838812017195 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 0.244019607843137 & 0.0343343935514513 & 7.10714774901921 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 0.247326530612245 & 0.0316359149075327 & 7.81790352310484 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 0.252 & 0.0285798943450996 & 8.81738738978958 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 0.254022222222222 & 0.0275264333728727 & 9.22830134878865 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 0.256209302325581 & 0.0263444589700937 & 9.72535828564296 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 0.257073170731707 & 0.0257366681150318 & 9.98859563260873 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 0.258025641025641 & 0.0253578833877128 & 10.1753619212031 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 0.259 & 0.0248606023569331 & 10.4180902892632 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 0.259914285714286 & 0.0243331696508717 & 10.6814808528232 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 0.260848484848485 & 0.0236246340845529 & 11.0413767220650 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 0.260967741935484 & 0.0231552257912321 & 11.2703604917686 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 0.261724137931034 & 0.0226989234218638 & 11.5302445436218 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 0.262592592592593 & 0.0219969085667422 & 11.9377044185934 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 0.26376 & 0.0209117415184229 & 12.6130097661943 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 0.264913043478261 & 0.0203007927417281 & 13.0493940236006 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 0.266571428571429 & 0.0197463162843787 & 13.4998054691503 \tabularnewline
Median & 0.278 &  &  \tabularnewline
Midrange & -0.148 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.254666666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.260967741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.260967741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.260967741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.261724137931034 &  &  \tabularnewline
Midmean - Closest Observation & 0.254666666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.260967741935484 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.260967741935484 &  &  \tabularnewline
Number of observations & 59 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64462&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]0.215932203389831[/C][C]0.058818316109849[/C][C]3.67117281947610[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.497275764984257[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]0.223593220338983[/C][C]0.0500154629429545[/C][C]4.47048187065676[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]0.222949152542373[/C][C]0.0492124619155562[/C][C]4.53033934626014[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]0.231135593220339[/C][C]0.0414582836081683[/C][C]5.57513657354594[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]0.233033898305085[/C][C]0.0404723063104141[/C][C]5.75786061011112[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]0.228711864406780[/C][C]0.0392374423906293[/C][C]5.82891876921623[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]0.242745762711864[/C][C]0.0313066374487295[/C][C]7.75381141169843[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]0.242864406779661[/C][C]0.0306720026429517[/C][C]7.91811377974925[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]0.251406779661017[/C][C]0.0275048066427229[/C][C]9.14046708005245[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]0.251406779661017[/C][C]0.0258356777249814[/C][C]9.73099224789924[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]0.251915254237288[/C][C]0.0256281379385949[/C][C]9.82963549052523[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]0.253033898305085[/C][C]0.0249245027901203[/C][C]10.1520138811108[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]0.25364406779661[/C][C]0.0246816760591133[/C][C]10.2766144077544[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]0.260033898305085[/C][C]0.0227366567841291[/C][C]11.4367693005155[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]0.255762711864407[/C][C]0.0217606304457183[/C][C]11.7534605673491[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]0.255762711864407[/C][C]0.0215996912518663[/C][C]11.8410355445385[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]0.254677966101695[/C][C]0.0214338644191389[/C][C]11.882036814336[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]0.256118644067797[/C][C]0.0185207654281110[/C][C]13.8287288968661[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]0.254288135593220[/C][C]0.0171515582450195[/C][C]14.8259494537216[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]0.262661016949153[/C][C]0.0151169338547795[/C][C]17.3752838685675[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]0.228701754385965[/C][C]0.0465178164382814[/C][C]4.91643357098243[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]0.234181818181818[/C][C]0.0420473525825116[/C][C]5.56947830953856[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]0.240433962264151[/C][C]0.0367726659606478[/C][C]6.53838812017195[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]0.244019607843137[/C][C]0.0343343935514513[/C][C]7.10714774901921[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]0.247326530612245[/C][C]0.0316359149075327[/C][C]7.81790352310484[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]0.252[/C][C]0.0285798943450996[/C][C]8.81738738978958[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]0.254022222222222[/C][C]0.0275264333728727[/C][C]9.22830134878865[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]0.256209302325581[/C][C]0.0263444589700937[/C][C]9.72535828564296[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]0.257073170731707[/C][C]0.0257366681150318[/C][C]9.98859563260873[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]0.258025641025641[/C][C]0.0253578833877128[/C][C]10.1753619212031[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]0.259[/C][C]0.0248606023569331[/C][C]10.4180902892632[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]0.259914285714286[/C][C]0.0243331696508717[/C][C]10.6814808528232[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]0.260848484848485[/C][C]0.0236246340845529[/C][C]11.0413767220650[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]0.260967741935484[/C][C]0.0231552257912321[/C][C]11.2703604917686[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]0.261724137931034[/C][C]0.0226989234218638[/C][C]11.5302445436218[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]0.262592592592593[/C][C]0.0219969085667422[/C][C]11.9377044185934[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]0.26376[/C][C]0.0209117415184229[/C][C]12.6130097661943[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]0.264913043478261[/C][C]0.0203007927417281[/C][C]13.0493940236006[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]0.266571428571429[/C][C]0.0197463162843787[/C][C]13.4998054691503[/C][/ROW]
[ROW][C]Median[/C][C]0.278[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]-0.148[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.254666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.260967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.260967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.260967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.261724137931034[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.254666666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.260967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.260967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]59[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64462&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64462&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 Mean0.2159322033898310.0588183161098493.67117281947610
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean0.497275764984257
Winsorized Mean ( 1 / 19 )0.2235932203389830.05001546294295454.47048187065676
Winsorized Mean ( 2 / 19 )0.2229491525423730.04921246191555624.53033934626014
Winsorized Mean ( 3 / 19 )0.2311355932203390.04145828360816835.57513657354594
Winsorized Mean ( 4 / 19 )0.2330338983050850.04047230631041415.75786061011112
Winsorized Mean ( 5 / 19 )0.2287118644067800.03923744239062935.82891876921623
Winsorized Mean ( 6 / 19 )0.2427457627118640.03130663744872957.75381141169843
Winsorized Mean ( 7 / 19 )0.2428644067796610.03067200264295177.91811377974925
Winsorized Mean ( 8 / 19 )0.2514067796610170.02750480664272299.14046708005245
Winsorized Mean ( 9 / 19 )0.2514067796610170.02583567772498149.73099224789924
Winsorized Mean ( 10 / 19 )0.2519152542372880.02562813793859499.82963549052523
Winsorized Mean ( 11 / 19 )0.2530338983050850.024924502790120310.1520138811108
Winsorized Mean ( 12 / 19 )0.253644067796610.024681676059113310.2766144077544
Winsorized Mean ( 13 / 19 )0.2600338983050850.022736656784129111.4367693005155
Winsorized Mean ( 14 / 19 )0.2557627118644070.021760630445718311.7534605673491
Winsorized Mean ( 15 / 19 )0.2557627118644070.021599691251866311.8410355445385
Winsorized Mean ( 16 / 19 )0.2546779661016950.021433864419138911.882036814336
Winsorized Mean ( 17 / 19 )0.2561186440677970.018520765428111013.8287288968661
Winsorized Mean ( 18 / 19 )0.2542881355932200.017151558245019514.8259494537216
Winsorized Mean ( 19 / 19 )0.2626610169491530.015116933854779517.3752838685675
Trimmed Mean ( 1 / 19 )0.2287017543859650.04651781643828144.91643357098243
Trimmed Mean ( 2 / 19 )0.2341818181818180.04204735258251165.56947830953856
Trimmed Mean ( 3 / 19 )0.2404339622641510.03677266596064786.53838812017195
Trimmed Mean ( 4 / 19 )0.2440196078431370.03433439355145137.10714774901921
Trimmed Mean ( 5 / 19 )0.2473265306122450.03163591490753277.81790352310484
Trimmed Mean ( 6 / 19 )0.2520.02857989434509968.81738738978958
Trimmed Mean ( 7 / 19 )0.2540222222222220.02752643337287279.22830134878865
Trimmed Mean ( 8 / 19 )0.2562093023255810.02634445897009379.72535828564296
Trimmed Mean ( 9 / 19 )0.2570731707317070.02573666811503189.98859563260873
Trimmed Mean ( 10 / 19 )0.2580256410256410.025357883387712810.1753619212031
Trimmed Mean ( 11 / 19 )0.2590.024860602356933110.4180902892632
Trimmed Mean ( 12 / 19 )0.2599142857142860.024333169650871710.6814808528232
Trimmed Mean ( 13 / 19 )0.2608484848484850.023624634084552911.0413767220650
Trimmed Mean ( 14 / 19 )0.2609677419354840.023155225791232111.2703604917686
Trimmed Mean ( 15 / 19 )0.2617241379310340.022698923421863811.5302445436218
Trimmed Mean ( 16 / 19 )0.2625925925925930.021996908566742211.9377044185934
Trimmed Mean ( 17 / 19 )0.263760.020911741518422912.6130097661943
Trimmed Mean ( 18 / 19 )0.2649130434782610.020300792741728113.0493940236006
Trimmed Mean ( 19 / 19 )0.2665714285714290.019746316284378713.4998054691503
Median0.278
Midrange-0.148
Midmean - Weighted Average at Xnp0.254666666666667
Midmean - Weighted Average at X(n+1)p0.260967741935484
Midmean - Empirical Distribution Function0.260967741935484
Midmean - Empirical Distribution Function - Averaging0.260967741935484
Midmean - Empirical Distribution Function - Interpolation0.261724137931034
Midmean - Closest Observation0.254666666666667
Midmean - True Basic - Statistics Graphics Toolkit0.260967741935484
Midmean - MS Excel (old versions)0.260967741935484
Number of observations59



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')