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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, 20 Oct 2009 09:05:40 -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/2009/Oct/20/t1256051404x9qzcjr43o213e5.htm/, Retrieved Thu, 02 May 2024 22:04:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48710, Retrieved Thu, 02 May 2024 22:04:47 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Invoer elektricit...] [2009-10-12 16:33:46] [34b80aeb109c116fd63bf2eb7493a276]
- RMP     [Central Tendency] [workshop3 part2] [2009-10-20 15:05:40] [307139c5e328127f586f26d5bcc435d8] [Current]
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Dataseries X:
1985
1963
2017
1975
1589
1679
1392
1511
1449
1767
1899
2179
2217
2049
2343
2175
1607
1702
1764
1766
1615
1953
2091
2411
2550
2351
2786
2525
2474
2332
1978
1789
1904
1997
2207
2453
1948
1384
1989
2140
2100
2045
2083
2022
1950
1422
1859
2147
2273
1881
2454
2081
2376
2265
2131
2333
1881
1563
1738
1990




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=48710&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=48710&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48710&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 Mean2008.3166666666740.57808606548949.4926415066853
Geometric Mean1983.4362528477
Harmonic Mean1957.81672868516
Quadratic Mean2032.35924891902
Winsorized Mean ( 1 / 20 )2004.5166666666739.440776539629250.8234584238618
Winsorized Mean ( 2 / 20 )2004.6833333333338.990557249338451.4145853446952
Winsorized Mean ( 3 / 20 )2003.4833333333338.097499744961352.5883154208383
Winsorized Mean ( 4 / 20 )2006.2833333333336.839183969218054.4605802074698
Winsorized Mean ( 5 / 20 )2010.5333333333335.869509790071556.0513189363362
Winsorized Mean ( 6 / 20 )2008.9333333333334.471365884069258.2783212040273
Winsorized Mean ( 7 / 20 )2006.9533.252436510702660.3549757731
Winsorized Mean ( 8 / 20 )2004.6833333333332.419631107827461.8354763712695
Winsorized Mean ( 9 / 20 )2013.0833333333330.323475380201966.3869595451341
Winsorized Mean ( 10 / 20 )2015.2529.31141603828668.7530755036781
Winsorized Mean ( 11 / 20 )2021.6666666666728.114652940791771.9079360831597
Winsorized Mean ( 12 / 20 )2015.0666666666725.092854303562480.304402292751
Winsorized Mean ( 13 / 20 )2013.7666666666724.719001207889381.466344442103
Winsorized Mean ( 14 / 20 )2002.822.820235841064687.7642112881235
Winsorized Mean ( 15 / 20 )2005.821.470210606857793.4224650483557
Winsorized Mean ( 16 / 20 )201717.2169933134988117.151697934307
Winsorized Mean ( 17 / 20 )2022.116.0865192535525125.701524868622
Winsorized Mean ( 18 / 20 )2013.714.7658045175618136.375908106124
Winsorized Mean ( 19 / 20 )2017.1833333333313.5708746718735148.640627970286
Winsorized Mean ( 20 / 20 )2015.8512.8674209769818156.663095394649
Trimmed Mean ( 1 / 20 )2005.6724137931038.238310811951252.451909386286
Trimmed Mean ( 2 / 20 )2006.9107142857136.755406676987354.60178231526
Trimmed Mean ( 3 / 20 )2008.1481481481535.220860577950657.0158739791075
Trimmed Mean ( 4 / 20 )2009.9423076923133.748385956171559.5566943646606
Trimmed Mean ( 5 / 20 )2011.0432.415125721030462.0401727671003
Trimmed Mean ( 6 / 20 )2011.1666666666731.073042713122564.7238407012303
Trimmed Mean ( 7 / 20 )2011.6521739130429.815393640913367.4702537266727
Trimmed Mean ( 8 / 20 )2012.5681818181828.563315628822070.4598936612033
Trimmed Mean ( 9 / 20 )2013.9761904761927.167191905354274.1326596246139
Trimmed Mean ( 10 / 20 )2014.12525.949487112662977.6171409960987
Trimmed Mean ( 11 / 20 )2013.9473684210524.607327181592481.8434019086638
Trimmed Mean ( 12 / 20 )2012.7777777777823.128492395610887.0258961695121
Trimmed Mean ( 13 / 20 )2012.4411764705922.027336410337391.3610769355736
Trimmed Mean ( 14 / 20 )2012.2520.573383603657197.8084129847415
Trimmed Mean ( 15 / 20 )2013.619.1110848257861105.362935613320
Trimmed Mean ( 16 / 20 )2014.7142857142917.4373297448863115.540298611668
Trimmed Mean ( 17 / 20 )2014.3846153846216.5775637927222121.512704796163
Trimmed Mean ( 18 / 20 )2013.2515.6391892094966128.731098078761
Trimmed Mean ( 19 / 20 )2013.1818181818214.6850980749291137.090117335940
Trimmed Mean ( 20 / 20 )2012.5513.6210894919374147.752498153049
Median1993.5
Midrange2085
Midmean - Weighted Average at Xnp2005.64516129032
Midmean - Weighted Average at X(n+1)p2013.6
Midmean - Empirical Distribution Function2005.64516129032
Midmean - Empirical Distribution Function - Averaging2013.6
Midmean - Empirical Distribution Function - Interpolation2013.6
Midmean - Closest Observation2005.64516129032
Midmean - True Basic - Statistics Graphics Toolkit2013.6
Midmean - MS Excel (old versions)2012.25
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 2008.31666666667 & 40.578086065489 & 49.4926415066853 \tabularnewline
Geometric Mean & 1983.4362528477 &  &  \tabularnewline
Harmonic Mean & 1957.81672868516 &  &  \tabularnewline
Quadratic Mean & 2032.35924891902 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 2004.51666666667 & 39.4407765396292 & 50.8234584238618 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 2004.68333333333 & 38.9905572493384 & 51.4145853446952 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 2003.48333333333 & 38.0974997449613 & 52.5883154208383 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 2006.28333333333 & 36.8391839692180 & 54.4605802074698 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 2010.53333333333 & 35.8695097900715 & 56.0513189363362 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 2008.93333333333 & 34.4713658840692 & 58.2783212040273 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 2006.95 & 33.2524365107026 & 60.3549757731 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 2004.68333333333 & 32.4196311078274 & 61.8354763712695 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 2013.08333333333 & 30.3234753802019 & 66.3869595451341 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 2015.25 & 29.311416038286 & 68.7530755036781 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 2021.66666666667 & 28.1146529407917 & 71.9079360831597 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 2015.06666666667 & 25.0928543035624 & 80.304402292751 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 2013.76666666667 & 24.7190012078893 & 81.466344442103 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 2002.8 & 22.8202358410646 & 87.7642112881235 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 2005.8 & 21.4702106068577 & 93.4224650483557 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 2017 & 17.2169933134988 & 117.151697934307 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 2022.1 & 16.0865192535525 & 125.701524868622 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 2013.7 & 14.7658045175618 & 136.375908106124 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 2017.18333333333 & 13.5708746718735 & 148.640627970286 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 2015.85 & 12.8674209769818 & 156.663095394649 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 2005.67241379310 & 38.2383108119512 & 52.451909386286 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 2006.91071428571 & 36.7554066769873 & 54.60178231526 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 2008.14814814815 & 35.2208605779506 & 57.0158739791075 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 2009.94230769231 & 33.7483859561715 & 59.5566943646606 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 2011.04 & 32.4151257210304 & 62.0401727671003 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 2011.16666666667 & 31.0730427131225 & 64.7238407012303 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 2011.65217391304 & 29.8153936409133 & 67.4702537266727 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 2012.56818181818 & 28.5633156288220 & 70.4598936612033 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 2013.97619047619 & 27.1671919053542 & 74.1326596246139 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 2014.125 & 25.9494871126629 & 77.6171409960987 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 2013.94736842105 & 24.6073271815924 & 81.8434019086638 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 2012.77777777778 & 23.1284923956108 & 87.0258961695121 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 2012.44117647059 & 22.0273364103373 & 91.3610769355736 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 2012.25 & 20.5733836036571 & 97.8084129847415 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 2013.6 & 19.1110848257861 & 105.362935613320 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 2014.71428571429 & 17.4373297448863 & 115.540298611668 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 2014.38461538462 & 16.5775637927222 & 121.512704796163 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 2013.25 & 15.6391892094966 & 128.731098078761 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 2013.18181818182 & 14.6850980749291 & 137.090117335940 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 2012.55 & 13.6210894919374 & 147.752498153049 \tabularnewline
Median & 1993.5 &  &  \tabularnewline
Midrange & 2085 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 2005.64516129032 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 2013.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 2005.64516129032 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 2013.6 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 2013.6 &  &  \tabularnewline
Midmean - Closest Observation & 2005.64516129032 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 2013.6 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 2012.25 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48710&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]2008.31666666667[/C][C]40.578086065489[/C][C]49.4926415066853[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1983.4362528477[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1957.81672868516[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]2032.35924891902[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]2004.51666666667[/C][C]39.4407765396292[/C][C]50.8234584238618[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]2004.68333333333[/C][C]38.9905572493384[/C][C]51.4145853446952[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]2003.48333333333[/C][C]38.0974997449613[/C][C]52.5883154208383[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]2006.28333333333[/C][C]36.8391839692180[/C][C]54.4605802074698[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]2010.53333333333[/C][C]35.8695097900715[/C][C]56.0513189363362[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]2008.93333333333[/C][C]34.4713658840692[/C][C]58.2783212040273[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]2006.95[/C][C]33.2524365107026[/C][C]60.3549757731[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]2004.68333333333[/C][C]32.4196311078274[/C][C]61.8354763712695[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]2013.08333333333[/C][C]30.3234753802019[/C][C]66.3869595451341[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]2015.25[/C][C]29.311416038286[/C][C]68.7530755036781[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]2021.66666666667[/C][C]28.1146529407917[/C][C]71.9079360831597[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]2015.06666666667[/C][C]25.0928543035624[/C][C]80.304402292751[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]2013.76666666667[/C][C]24.7190012078893[/C][C]81.466344442103[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]2002.8[/C][C]22.8202358410646[/C][C]87.7642112881235[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]2005.8[/C][C]21.4702106068577[/C][C]93.4224650483557[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]2017[/C][C]17.2169933134988[/C][C]117.151697934307[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]2022.1[/C][C]16.0865192535525[/C][C]125.701524868622[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]2013.7[/C][C]14.7658045175618[/C][C]136.375908106124[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]2017.18333333333[/C][C]13.5708746718735[/C][C]148.640627970286[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]2015.85[/C][C]12.8674209769818[/C][C]156.663095394649[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]2005.67241379310[/C][C]38.2383108119512[/C][C]52.451909386286[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]2006.91071428571[/C][C]36.7554066769873[/C][C]54.60178231526[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]2008.14814814815[/C][C]35.2208605779506[/C][C]57.0158739791075[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]2009.94230769231[/C][C]33.7483859561715[/C][C]59.5566943646606[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]2011.04[/C][C]32.4151257210304[/C][C]62.0401727671003[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]2011.16666666667[/C][C]31.0730427131225[/C][C]64.7238407012303[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]2011.65217391304[/C][C]29.8153936409133[/C][C]67.4702537266727[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]2012.56818181818[/C][C]28.5633156288220[/C][C]70.4598936612033[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]2013.97619047619[/C][C]27.1671919053542[/C][C]74.1326596246139[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]2014.125[/C][C]25.9494871126629[/C][C]77.6171409960987[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]2013.94736842105[/C][C]24.6073271815924[/C][C]81.8434019086638[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]2012.77777777778[/C][C]23.1284923956108[/C][C]87.0258961695121[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]2012.44117647059[/C][C]22.0273364103373[/C][C]91.3610769355736[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]2012.25[/C][C]20.5733836036571[/C][C]97.8084129847415[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]2013.6[/C][C]19.1110848257861[/C][C]105.362935613320[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]2014.71428571429[/C][C]17.4373297448863[/C][C]115.540298611668[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]2014.38461538462[/C][C]16.5775637927222[/C][C]121.512704796163[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]2013.25[/C][C]15.6391892094966[/C][C]128.731098078761[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]2013.18181818182[/C][C]14.6850980749291[/C][C]137.090117335940[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]2012.55[/C][C]13.6210894919374[/C][C]147.752498153049[/C][/ROW]
[ROW][C]Median[/C][C]1993.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2085[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]2005.64516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]2013.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]2005.64516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]2013.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]2013.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]2005.64516129032[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]2013.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]2012.25[/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=48710&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48710&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 Mean2008.3166666666740.57808606548949.4926415066853
Geometric Mean1983.4362528477
Harmonic Mean1957.81672868516
Quadratic Mean2032.35924891902
Winsorized Mean ( 1 / 20 )2004.5166666666739.440776539629250.8234584238618
Winsorized Mean ( 2 / 20 )2004.6833333333338.990557249338451.4145853446952
Winsorized Mean ( 3 / 20 )2003.4833333333338.097499744961352.5883154208383
Winsorized Mean ( 4 / 20 )2006.2833333333336.839183969218054.4605802074698
Winsorized Mean ( 5 / 20 )2010.5333333333335.869509790071556.0513189363362
Winsorized Mean ( 6 / 20 )2008.9333333333334.471365884069258.2783212040273
Winsorized Mean ( 7 / 20 )2006.9533.252436510702660.3549757731
Winsorized Mean ( 8 / 20 )2004.6833333333332.419631107827461.8354763712695
Winsorized Mean ( 9 / 20 )2013.0833333333330.323475380201966.3869595451341
Winsorized Mean ( 10 / 20 )2015.2529.31141603828668.7530755036781
Winsorized Mean ( 11 / 20 )2021.6666666666728.114652940791771.9079360831597
Winsorized Mean ( 12 / 20 )2015.0666666666725.092854303562480.304402292751
Winsorized Mean ( 13 / 20 )2013.7666666666724.719001207889381.466344442103
Winsorized Mean ( 14 / 20 )2002.822.820235841064687.7642112881235
Winsorized Mean ( 15 / 20 )2005.821.470210606857793.4224650483557
Winsorized Mean ( 16 / 20 )201717.2169933134988117.151697934307
Winsorized Mean ( 17 / 20 )2022.116.0865192535525125.701524868622
Winsorized Mean ( 18 / 20 )2013.714.7658045175618136.375908106124
Winsorized Mean ( 19 / 20 )2017.1833333333313.5708746718735148.640627970286
Winsorized Mean ( 20 / 20 )2015.8512.8674209769818156.663095394649
Trimmed Mean ( 1 / 20 )2005.6724137931038.238310811951252.451909386286
Trimmed Mean ( 2 / 20 )2006.9107142857136.755406676987354.60178231526
Trimmed Mean ( 3 / 20 )2008.1481481481535.220860577950657.0158739791075
Trimmed Mean ( 4 / 20 )2009.9423076923133.748385956171559.5566943646606
Trimmed Mean ( 5 / 20 )2011.0432.415125721030462.0401727671003
Trimmed Mean ( 6 / 20 )2011.1666666666731.073042713122564.7238407012303
Trimmed Mean ( 7 / 20 )2011.6521739130429.815393640913367.4702537266727
Trimmed Mean ( 8 / 20 )2012.5681818181828.563315628822070.4598936612033
Trimmed Mean ( 9 / 20 )2013.9761904761927.167191905354274.1326596246139
Trimmed Mean ( 10 / 20 )2014.12525.949487112662977.6171409960987
Trimmed Mean ( 11 / 20 )2013.9473684210524.607327181592481.8434019086638
Trimmed Mean ( 12 / 20 )2012.7777777777823.128492395610887.0258961695121
Trimmed Mean ( 13 / 20 )2012.4411764705922.027336410337391.3610769355736
Trimmed Mean ( 14 / 20 )2012.2520.573383603657197.8084129847415
Trimmed Mean ( 15 / 20 )2013.619.1110848257861105.362935613320
Trimmed Mean ( 16 / 20 )2014.7142857142917.4373297448863115.540298611668
Trimmed Mean ( 17 / 20 )2014.3846153846216.5775637927222121.512704796163
Trimmed Mean ( 18 / 20 )2013.2515.6391892094966128.731098078761
Trimmed Mean ( 19 / 20 )2013.1818181818214.6850980749291137.090117335940
Trimmed Mean ( 20 / 20 )2012.5513.6210894919374147.752498153049
Median1993.5
Midrange2085
Midmean - Weighted Average at Xnp2005.64516129032
Midmean - Weighted Average at X(n+1)p2013.6
Midmean - Empirical Distribution Function2005.64516129032
Midmean - Empirical Distribution Function - Averaging2013.6
Midmean - Empirical Distribution Function - Interpolation2013.6
Midmean - Closest Observation2005.64516129032
Midmean - True Basic - Statistics Graphics Toolkit2013.6
Midmean - MS Excel (old versions)2012.25
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')