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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 computationTue, 02 Dec 2008 11:19:55 -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/2008/Dec/02/t1228242036edh1t7aolvcfncx.htm/, Retrieved Sun, 19 May 2024 11:30:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28208, Retrieved Sun, 19 May 2024 11:30:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact155
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendency-...] [2008-12-02 18:19:55] [541f63fa3157af9df10fc4d202b2a90b] [Current]
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Dataseries X:
91,2
99,2
108,2
101,5
106,9
104,4
77,9
60
99,5
95
105,6
102,5
93,3
97,3
127
111,7
96,4
133
72,2
95,8
124,1
127,6
110,7
104,6
112,7
115,3
139,4
119
97,4
154
81,5
88,8
127,7
105,1
114,9
106,4
104,5
121,6
141,4
99
126,7
134,1
81,3
88,6
132,7
132,9
134,4
103,7
119,7
115
132,9
108,5
113,9
142
97,7
92,2
128,8
134,9
128,2
114,8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28208&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28208&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28208&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean110.6216666666672.4586697653540044.9924866793728
Geometric Mean108.922826877161
Harmonic Mean107.111893929402
Quadratic Mean112.222152447723
Winsorized Mean ( 1 / 20 )110.6252.3419589861172647.2360962150775
Winsorized Mean ( 2 / 20 )110.7952.2878127429692948.4283516386933
Winsorized Mean ( 3 / 20 )110.8652.2257314229779949.810592084675
Winsorized Mean ( 4 / 20 )110.5783333333332.1614497275371551.1593362198301
Winsorized Mean ( 5 / 20 )111.1283333333332.0299579629761054.7441549826032
Winsorized Mean ( 6 / 20 )111.1183333333332.0203980863917154.9982372690636
Winsorized Mean ( 7 / 20 )111.271.9451450499992957.2039601879772
Winsorized Mean ( 8 / 20 )111.391.9196599569409458.0259017214199
Winsorized Mean ( 9 / 20 )111.5551.8921879617220658.9555595198244
Winsorized Mean ( 10 / 20 )111.8051.8406910778476160.7407735852873
Winsorized Mean ( 11 / 20 )111.2366666666671.6858030771907865.9843775181803
Winsorized Mean ( 12 / 20 )111.2366666666671.6462488891101567.5697747785836
Winsorized Mean ( 13 / 20 )111.3233333333331.5979778299492869.6651300455568
Winsorized Mean ( 14 / 20 )111.3233333333331.5904612674675569.9943693131177
Winsorized Mean ( 15 / 20 )111.2483333333331.5534534003449671.6135632447228
Winsorized Mean ( 16 / 20 )111.5151.4893384285656074.8755271878677
Winsorized Mean ( 17 / 20 )110.8351.3563594198095981.7150663616574
Winsorized Mean ( 18 / 20 )110.1751.2214019568156190.2037199017137
Winsorized Mean ( 19 / 20 )110.2066666666671.03462612769322106.518348722143
Winsorized Mean ( 20 / 20 )110.3066666666670.951436222309415115.937005634408
Trimmed Mean ( 1 / 20 )110.7465517241382.2645886735472348.9036057707848
Trimmed Mean ( 2 / 20 )110.8767857142862.1690562779299851.1175237094816
Trimmed Mean ( 3 / 20 )110.9222222222222.0874950744853253.1365192560134
Trimmed Mean ( 4 / 20 )110.9442307692312.0164358844705555.0199644946118
Trimmed Mean ( 5 / 20 )111.0541.9526668524699056.8729887843027
Trimmed Mean ( 6 / 20 )111.0354166666671.917212741165657.9150212611048
Trimmed Mean ( 7 / 20 )111.0173913043481.8735362836783259.2555331175048
Trimmed Mean ( 8 / 20 )110.9681818181821.8377523635571160.382554265034
Trimmed Mean ( 9 / 20 )110.8928571428571.7963099124251061.7336999455436
Trimmed Mean ( 10 / 20 )110.78251.7471804667330063.4064437585827
Trimmed Mean ( 11 / 20 )110.6210526315791.6933606350460165.3263400259528
Trimmed Mean ( 12 / 20 )110.5277777777781.6621873670057566.4953783019549
Trimmed Mean ( 13 / 20 )110.4235294117651.6266883938063267.8824105662808
Trimmed Mean ( 14 / 20 )110.293751.5867707716790269.5083070400232
Trimmed Mean ( 15 / 20 )110.1466666666671.5280122564752972.0849366226586
Trimmed Mean ( 16 / 20 )109.9892857142861.4509834220818975.8032683491807
Trimmed Mean ( 17 / 20 )109.7692307692311.3532726057827981.113908831204
Trimmed Mean ( 18 / 20 )109.61251.2573740824962787.175727196783
Trimmed Mean ( 19 / 20 )109.5272727272731.1645778793840894.0489036123535
Trimmed Mean ( 20 / 20 )109.421.0983624174196899.6210342457404
Median108.35
Midrange107
Midmean - Weighted Average at Xnp109.735483870968
Midmean - Weighted Average at X(n+1)p110.146666666667
Midmean - Empirical Distribution Function109.735483870968
Midmean - Empirical Distribution Function - Averaging110.146666666667
Midmean - Empirical Distribution Function - Interpolation110.146666666667
Midmean - Closest Observation109.735483870968
Midmean - True Basic - Statistics Graphics Toolkit110.146666666667
Midmean - MS Excel (old versions)110.29375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 110.621666666667 & 2.45866976535400 & 44.9924866793728 \tabularnewline
Geometric Mean & 108.922826877161 &  &  \tabularnewline
Harmonic Mean & 107.111893929402 &  &  \tabularnewline
Quadratic Mean & 112.222152447723 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 110.625 & 2.34195898611726 & 47.2360962150775 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 110.795 & 2.28781274296929 & 48.4283516386933 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 110.865 & 2.22573142297799 & 49.810592084675 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 110.578333333333 & 2.16144972753715 & 51.1593362198301 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 111.128333333333 & 2.02995796297610 & 54.7441549826032 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 111.118333333333 & 2.02039808639171 & 54.9982372690636 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 111.27 & 1.94514504999929 & 57.2039601879772 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 111.39 & 1.91965995694094 & 58.0259017214199 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 111.555 & 1.89218796172206 & 58.9555595198244 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 111.805 & 1.84069107784761 & 60.7407735852873 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 111.236666666667 & 1.68580307719078 & 65.9843775181803 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 111.236666666667 & 1.64624888911015 & 67.5697747785836 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 111.323333333333 & 1.59797782994928 & 69.6651300455568 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 111.323333333333 & 1.59046126746755 & 69.9943693131177 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 111.248333333333 & 1.55345340034496 & 71.6135632447228 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 111.515 & 1.48933842856560 & 74.8755271878677 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 110.835 & 1.35635941980959 & 81.7150663616574 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 110.175 & 1.22140195681561 & 90.2037199017137 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 110.206666666667 & 1.03462612769322 & 106.518348722143 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 110.306666666667 & 0.951436222309415 & 115.937005634408 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 110.746551724138 & 2.26458867354723 & 48.9036057707848 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 110.876785714286 & 2.16905627792998 & 51.1175237094816 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 110.922222222222 & 2.08749507448532 & 53.1365192560134 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 110.944230769231 & 2.01643588447055 & 55.0199644946118 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 111.054 & 1.95266685246990 & 56.8729887843027 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 111.035416666667 & 1.9172127411656 & 57.9150212611048 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 111.017391304348 & 1.87353628367832 & 59.2555331175048 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 110.968181818182 & 1.83775236355711 & 60.382554265034 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 110.892857142857 & 1.79630991242510 & 61.7336999455436 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 110.7825 & 1.74718046673300 & 63.4064437585827 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 110.621052631579 & 1.69336063504601 & 65.3263400259528 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 110.527777777778 & 1.66218736700575 & 66.4953783019549 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 110.423529411765 & 1.62668839380632 & 67.8824105662808 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 110.29375 & 1.58677077167902 & 69.5083070400232 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 110.146666666667 & 1.52801225647529 & 72.0849366226586 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 109.989285714286 & 1.45098342208189 & 75.8032683491807 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 109.769230769231 & 1.35327260578279 & 81.113908831204 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 109.6125 & 1.25737408249627 & 87.175727196783 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 109.527272727273 & 1.16457787938408 & 94.0489036123535 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 109.42 & 1.09836241741968 & 99.6210342457404 \tabularnewline
Median & 108.35 &  &  \tabularnewline
Midrange & 107 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 109.735483870968 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 110.146666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 109.735483870968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 110.146666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 110.146666666667 &  &  \tabularnewline
Midmean - Closest Observation & 109.735483870968 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 110.146666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 110.29375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28208&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]110.621666666667[/C][C]2.45866976535400[/C][C]44.9924866793728[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]108.922826877161[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]107.111893929402[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]112.222152447723[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]110.625[/C][C]2.34195898611726[/C][C]47.2360962150775[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]110.795[/C][C]2.28781274296929[/C][C]48.4283516386933[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]110.865[/C][C]2.22573142297799[/C][C]49.810592084675[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]110.578333333333[/C][C]2.16144972753715[/C][C]51.1593362198301[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]111.128333333333[/C][C]2.02995796297610[/C][C]54.7441549826032[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]111.118333333333[/C][C]2.02039808639171[/C][C]54.9982372690636[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]111.27[/C][C]1.94514504999929[/C][C]57.2039601879772[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]111.39[/C][C]1.91965995694094[/C][C]58.0259017214199[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]111.555[/C][C]1.89218796172206[/C][C]58.9555595198244[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]111.805[/C][C]1.84069107784761[/C][C]60.7407735852873[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]111.236666666667[/C][C]1.68580307719078[/C][C]65.9843775181803[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]111.236666666667[/C][C]1.64624888911015[/C][C]67.5697747785836[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]111.323333333333[/C][C]1.59797782994928[/C][C]69.6651300455568[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]111.323333333333[/C][C]1.59046126746755[/C][C]69.9943693131177[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]111.248333333333[/C][C]1.55345340034496[/C][C]71.6135632447228[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]111.515[/C][C]1.48933842856560[/C][C]74.8755271878677[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]110.835[/C][C]1.35635941980959[/C][C]81.7150663616574[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]110.175[/C][C]1.22140195681561[/C][C]90.2037199017137[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]110.206666666667[/C][C]1.03462612769322[/C][C]106.518348722143[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]110.306666666667[/C][C]0.951436222309415[/C][C]115.937005634408[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]110.746551724138[/C][C]2.26458867354723[/C][C]48.9036057707848[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]110.876785714286[/C][C]2.16905627792998[/C][C]51.1175237094816[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]110.922222222222[/C][C]2.08749507448532[/C][C]53.1365192560134[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]110.944230769231[/C][C]2.01643588447055[/C][C]55.0199644946118[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]111.054[/C][C]1.95266685246990[/C][C]56.8729887843027[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]111.035416666667[/C][C]1.9172127411656[/C][C]57.9150212611048[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]111.017391304348[/C][C]1.87353628367832[/C][C]59.2555331175048[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]110.968181818182[/C][C]1.83775236355711[/C][C]60.382554265034[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]110.892857142857[/C][C]1.79630991242510[/C][C]61.7336999455436[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]110.7825[/C][C]1.74718046673300[/C][C]63.4064437585827[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]110.621052631579[/C][C]1.69336063504601[/C][C]65.3263400259528[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]110.527777777778[/C][C]1.66218736700575[/C][C]66.4953783019549[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]110.423529411765[/C][C]1.62668839380632[/C][C]67.8824105662808[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]110.29375[/C][C]1.58677077167902[/C][C]69.5083070400232[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]110.146666666667[/C][C]1.52801225647529[/C][C]72.0849366226586[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]109.989285714286[/C][C]1.45098342208189[/C][C]75.8032683491807[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]109.769230769231[/C][C]1.35327260578279[/C][C]81.113908831204[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]109.6125[/C][C]1.25737408249627[/C][C]87.175727196783[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]109.527272727273[/C][C]1.16457787938408[/C][C]94.0489036123535[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]109.42[/C][C]1.09836241741968[/C][C]99.6210342457404[/C][/ROW]
[ROW][C]Median[/C][C]108.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]107[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]109.735483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]110.146666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]109.735483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]110.146666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]110.146666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]109.735483870968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]110.146666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]110.29375[/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=28208&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28208&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 Mean110.6216666666672.4586697653540044.9924866793728
Geometric Mean108.922826877161
Harmonic Mean107.111893929402
Quadratic Mean112.222152447723
Winsorized Mean ( 1 / 20 )110.6252.3419589861172647.2360962150775
Winsorized Mean ( 2 / 20 )110.7952.2878127429692948.4283516386933
Winsorized Mean ( 3 / 20 )110.8652.2257314229779949.810592084675
Winsorized Mean ( 4 / 20 )110.5783333333332.1614497275371551.1593362198301
Winsorized Mean ( 5 / 20 )111.1283333333332.0299579629761054.7441549826032
Winsorized Mean ( 6 / 20 )111.1183333333332.0203980863917154.9982372690636
Winsorized Mean ( 7 / 20 )111.271.9451450499992957.2039601879772
Winsorized Mean ( 8 / 20 )111.391.9196599569409458.0259017214199
Winsorized Mean ( 9 / 20 )111.5551.8921879617220658.9555595198244
Winsorized Mean ( 10 / 20 )111.8051.8406910778476160.7407735852873
Winsorized Mean ( 11 / 20 )111.2366666666671.6858030771907865.9843775181803
Winsorized Mean ( 12 / 20 )111.2366666666671.6462488891101567.5697747785836
Winsorized Mean ( 13 / 20 )111.3233333333331.5979778299492869.6651300455568
Winsorized Mean ( 14 / 20 )111.3233333333331.5904612674675569.9943693131177
Winsorized Mean ( 15 / 20 )111.2483333333331.5534534003449671.6135632447228
Winsorized Mean ( 16 / 20 )111.5151.4893384285656074.8755271878677
Winsorized Mean ( 17 / 20 )110.8351.3563594198095981.7150663616574
Winsorized Mean ( 18 / 20 )110.1751.2214019568156190.2037199017137
Winsorized Mean ( 19 / 20 )110.2066666666671.03462612769322106.518348722143
Winsorized Mean ( 20 / 20 )110.3066666666670.951436222309415115.937005634408
Trimmed Mean ( 1 / 20 )110.7465517241382.2645886735472348.9036057707848
Trimmed Mean ( 2 / 20 )110.8767857142862.1690562779299851.1175237094816
Trimmed Mean ( 3 / 20 )110.9222222222222.0874950744853253.1365192560134
Trimmed Mean ( 4 / 20 )110.9442307692312.0164358844705555.0199644946118
Trimmed Mean ( 5 / 20 )111.0541.9526668524699056.8729887843027
Trimmed Mean ( 6 / 20 )111.0354166666671.917212741165657.9150212611048
Trimmed Mean ( 7 / 20 )111.0173913043481.8735362836783259.2555331175048
Trimmed Mean ( 8 / 20 )110.9681818181821.8377523635571160.382554265034
Trimmed Mean ( 9 / 20 )110.8928571428571.7963099124251061.7336999455436
Trimmed Mean ( 10 / 20 )110.78251.7471804667330063.4064437585827
Trimmed Mean ( 11 / 20 )110.6210526315791.6933606350460165.3263400259528
Trimmed Mean ( 12 / 20 )110.5277777777781.6621873670057566.4953783019549
Trimmed Mean ( 13 / 20 )110.4235294117651.6266883938063267.8824105662808
Trimmed Mean ( 14 / 20 )110.293751.5867707716790269.5083070400232
Trimmed Mean ( 15 / 20 )110.1466666666671.5280122564752972.0849366226586
Trimmed Mean ( 16 / 20 )109.9892857142861.4509834220818975.8032683491807
Trimmed Mean ( 17 / 20 )109.7692307692311.3532726057827981.113908831204
Trimmed Mean ( 18 / 20 )109.61251.2573740824962787.175727196783
Trimmed Mean ( 19 / 20 )109.5272727272731.1645778793840894.0489036123535
Trimmed Mean ( 20 / 20 )109.421.0983624174196899.6210342457404
Median108.35
Midrange107
Midmean - Weighted Average at Xnp109.735483870968
Midmean - Weighted Average at X(n+1)p110.146666666667
Midmean - Empirical Distribution Function109.735483870968
Midmean - Empirical Distribution Function - Averaging110.146666666667
Midmean - Empirical Distribution Function - Interpolation110.146666666667
Midmean - Closest Observation109.735483870968
Midmean - True Basic - Statistics Graphics Toolkit110.146666666667
Midmean - MS Excel (old versions)110.29375
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')