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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 computationMon, 15 Dec 2008 03:13:56 -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/15/t1229336107pp2mvqby23luwx1.htm/, Retrieved Wed, 15 May 2024 22:02:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33645, Retrieved Wed, 15 May 2024 22:02:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact144
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [central tendency:...] [2008-12-15 10:13:56] [e515c0250d6233b5d2604259ab52cebe] [Current]
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Dataseries X:
124,1
110,7
128,1
108,9
111,2
131,9
120,5
115,4
130,8
112,6
111,1
129,5
131,8
127,7
142,6
115,8
119,5
139,8
130,6
126,2
141,7
118,9
120,3
141,2
138,9
141,3
153,7
131
136,5
160,1
139,8
143,8
155,8
131
131,8
151,7
153,8
152,9
156,1
147,2
145,7
165,3
147,4
154,4
165,3
145,2
139,7
158,4
169,1
162,1
166,2
157,2
161,4
169
171,8
161,4
175,7
164,7
146,1
173




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33645&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33645&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33645&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean141.9233333333332.3738849498614959.7852618517228
Geometric Mean140.732065755565
Harmonic Mean139.525730771995
Quadratic Mean143.089891327096
Winsorized Mean ( 1 / 20 )141.9083333333332.3565215335807560.2194086967255
Winsorized Mean ( 2 / 20 )141.8816666666672.3447434799605160.5105282856171
Winsorized Mean ( 3 / 20 )141.7516666666672.3155108180268261.218313282363
Winsorized Mean ( 4 / 20 )141.8383333333332.2936538482338461.8394678179325
Winsorized Mean ( 5 / 20 )141.8383333333332.1992937896647664.492672147705
Winsorized Mean ( 6 / 20 )141.7883333333332.1744706371411665.2059084687143
Winsorized Mean ( 7 / 20 )142.152.1039235609409667.5642417048768
Winsorized Mean ( 8 / 20 )142.152.0741964613922168.5325631616342
Winsorized Mean ( 9 / 20 )141.881.9823255760004671.5725013679425
Winsorized Mean ( 10 / 20 )141.7966666666671.9561809424162972.4864779080805
Winsorized Mean ( 11 / 20 )142.4566666666671.8393107998529677.4511119480486
Winsorized Mean ( 12 / 20 )142.6166666666671.7248191040278982.6849994492874
Winsorized Mean ( 13 / 20 )142.5733333333331.6108036851960188.5106823653586
Winsorized Mean ( 14 / 20 )142.3866666666671.5502095113855491.8499503589064
Winsorized Mean ( 15 / 20 )142.4616666666671.4522028691811698.1003892018165
Winsorized Mean ( 16 / 20 )142.6751.39575349716874102.220771998361
Winsorized Mean ( 17 / 20 )142.3351.32517736793879107.408263560516
Winsorized Mean ( 18 / 20 )142.2151.28872298066883110.353429040423
Winsorized Mean ( 19 / 20 )142.1833333333331.28390331461547110.743022246903
Winsorized Mean ( 20 / 20 )142.1833333333331.20434281647116118.058854496217
Trimmed Mean ( 1 / 20 )141.9103448275862.3150036547895361.3002681589667
Trimmed Mean ( 2 / 20 )141.91252.2632726312238162.7023444026114
Trimmed Mean ( 3 / 20 )141.9296296296302.2065204649066664.3228249576345
Trimmed Mean ( 4 / 20 )141.9980769230772.1493562303657866.0653989864266
Trimmed Mean ( 5 / 20 )142.0462.0857205675052268.1040414583938
Trimmed Mean ( 6 / 20 )142.0979166666672.0373843995038469.745265891538
Trimmed Mean ( 7 / 20 )142.1652173913041.9823355604720771.7160203479623
Trimmed Mean ( 8 / 20 )142.1681818181821.9314214242488073.6080588282155
Trimmed Mean ( 9 / 20 )142.1714285714291.8722817251872775.9348481902254
Trimmed Mean ( 10 / 20 )142.221.8188408537533078.1926575414881
Trimmed Mean ( 11 / 20 )142.2868421052631.7530634477032781.1646847646481
Trimmed Mean ( 12 / 20 )142.2611111111111.6961360278716183.8736450222255
Trimmed Mean ( 13 / 20 )142.2088235294121.6483631358340986.2727517000993
Trimmed Mean ( 14 / 20 )142.156251.6114005222616688.2190666045448
Trimmed Mean ( 15 / 20 )142.1233333333331.5727250187729390.3675668898688
Trimmed Mean ( 16 / 20 )142.0751.5418125199131292.148038860137
Trimmed Mean ( 17 / 20 )141.9884615384621.5073698634792594.196165770974
Trimmed Mean ( 18 / 20 )141.93751.4729543970527796.3624537758955
Trimmed Mean ( 19 / 20 )141.8954545454551.4243017165515799.6245759564225
Trimmed Mean ( 20 / 20 )141.851.33685609192849106.107157573987
Median141.5
Midrange142.3
Midmean - Weighted Average at Xnp141.670967741935
Midmean - Weighted Average at X(n+1)p142.123333333333
Midmean - Empirical Distribution Function141.670967741935
Midmean - Empirical Distribution Function - Averaging142.123333333333
Midmean - Empirical Distribution Function - Interpolation142.123333333333
Midmean - Closest Observation141.670967741935
Midmean - True Basic - Statistics Graphics Toolkit142.123333333333
Midmean - MS Excel (old versions)142.15625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 141.923333333333 & 2.37388494986149 & 59.7852618517228 \tabularnewline
Geometric Mean & 140.732065755565 &  &  \tabularnewline
Harmonic Mean & 139.525730771995 &  &  \tabularnewline
Quadratic Mean & 143.089891327096 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 141.908333333333 & 2.35652153358075 & 60.2194086967255 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 141.881666666667 & 2.34474347996051 & 60.5105282856171 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 141.751666666667 & 2.31551081802682 & 61.218313282363 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 141.838333333333 & 2.29365384823384 & 61.8394678179325 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 141.838333333333 & 2.19929378966476 & 64.492672147705 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 141.788333333333 & 2.17447063714116 & 65.2059084687143 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 142.15 & 2.10392356094096 & 67.5642417048768 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 142.15 & 2.07419646139221 & 68.5325631616342 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 141.88 & 1.98232557600046 & 71.5725013679425 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 141.796666666667 & 1.95618094241629 & 72.4864779080805 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 142.456666666667 & 1.83931079985296 & 77.4511119480486 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 142.616666666667 & 1.72481910402789 & 82.6849994492874 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 142.573333333333 & 1.61080368519601 & 88.5106823653586 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 142.386666666667 & 1.55020951138554 & 91.8499503589064 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 142.461666666667 & 1.45220286918116 & 98.1003892018165 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 142.675 & 1.39575349716874 & 102.220771998361 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 142.335 & 1.32517736793879 & 107.408263560516 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 142.215 & 1.28872298066883 & 110.353429040423 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 142.183333333333 & 1.28390331461547 & 110.743022246903 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 142.183333333333 & 1.20434281647116 & 118.058854496217 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 141.910344827586 & 2.31500365478953 & 61.3002681589667 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 141.9125 & 2.26327263122381 & 62.7023444026114 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 141.929629629630 & 2.20652046490666 & 64.3228249576345 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 141.998076923077 & 2.14935623036578 & 66.0653989864266 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 142.046 & 2.08572056750522 & 68.1040414583938 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 142.097916666667 & 2.03738439950384 & 69.745265891538 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 142.165217391304 & 1.98233556047207 & 71.7160203479623 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 142.168181818182 & 1.93142142424880 & 73.6080588282155 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 142.171428571429 & 1.87228172518727 & 75.9348481902254 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 142.22 & 1.81884085375330 & 78.1926575414881 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 142.286842105263 & 1.75306344770327 & 81.1646847646481 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 142.261111111111 & 1.69613602787161 & 83.8736450222255 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 142.208823529412 & 1.64836313583409 & 86.2727517000993 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 142.15625 & 1.61140052226166 & 88.2190666045448 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 142.123333333333 & 1.57272501877293 & 90.3675668898688 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 142.075 & 1.54181251991312 & 92.148038860137 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 141.988461538462 & 1.50736986347925 & 94.196165770974 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 141.9375 & 1.47295439705277 & 96.3624537758955 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 141.895454545455 & 1.42430171655157 & 99.6245759564225 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 141.85 & 1.33685609192849 & 106.107157573987 \tabularnewline
Median & 141.5 &  &  \tabularnewline
Midrange & 142.3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 141.670967741935 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 142.123333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 141.670967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 142.123333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 142.123333333333 &  &  \tabularnewline
Midmean - Closest Observation & 141.670967741935 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 142.123333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 142.15625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33645&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]141.923333333333[/C][C]2.37388494986149[/C][C]59.7852618517228[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]140.732065755565[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]139.525730771995[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]143.089891327096[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]141.908333333333[/C][C]2.35652153358075[/C][C]60.2194086967255[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]141.881666666667[/C][C]2.34474347996051[/C][C]60.5105282856171[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]141.751666666667[/C][C]2.31551081802682[/C][C]61.218313282363[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]141.838333333333[/C][C]2.29365384823384[/C][C]61.8394678179325[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]141.838333333333[/C][C]2.19929378966476[/C][C]64.492672147705[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]141.788333333333[/C][C]2.17447063714116[/C][C]65.2059084687143[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]142.15[/C][C]2.10392356094096[/C][C]67.5642417048768[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]142.15[/C][C]2.07419646139221[/C][C]68.5325631616342[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]141.88[/C][C]1.98232557600046[/C][C]71.5725013679425[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]141.796666666667[/C][C]1.95618094241629[/C][C]72.4864779080805[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]142.456666666667[/C][C]1.83931079985296[/C][C]77.4511119480486[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]142.616666666667[/C][C]1.72481910402789[/C][C]82.6849994492874[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]142.573333333333[/C][C]1.61080368519601[/C][C]88.5106823653586[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]142.386666666667[/C][C]1.55020951138554[/C][C]91.8499503589064[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]142.461666666667[/C][C]1.45220286918116[/C][C]98.1003892018165[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]142.675[/C][C]1.39575349716874[/C][C]102.220771998361[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]142.335[/C][C]1.32517736793879[/C][C]107.408263560516[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]142.215[/C][C]1.28872298066883[/C][C]110.353429040423[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]142.183333333333[/C][C]1.28390331461547[/C][C]110.743022246903[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]142.183333333333[/C][C]1.20434281647116[/C][C]118.058854496217[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]141.910344827586[/C][C]2.31500365478953[/C][C]61.3002681589667[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]141.9125[/C][C]2.26327263122381[/C][C]62.7023444026114[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]141.929629629630[/C][C]2.20652046490666[/C][C]64.3228249576345[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]141.998076923077[/C][C]2.14935623036578[/C][C]66.0653989864266[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]142.046[/C][C]2.08572056750522[/C][C]68.1040414583938[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]142.097916666667[/C][C]2.03738439950384[/C][C]69.745265891538[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]142.165217391304[/C][C]1.98233556047207[/C][C]71.7160203479623[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]142.168181818182[/C][C]1.93142142424880[/C][C]73.6080588282155[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]142.171428571429[/C][C]1.87228172518727[/C][C]75.9348481902254[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]142.22[/C][C]1.81884085375330[/C][C]78.1926575414881[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]142.286842105263[/C][C]1.75306344770327[/C][C]81.1646847646481[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]142.261111111111[/C][C]1.69613602787161[/C][C]83.8736450222255[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]142.208823529412[/C][C]1.64836313583409[/C][C]86.2727517000993[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]142.15625[/C][C]1.61140052226166[/C][C]88.2190666045448[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]142.123333333333[/C][C]1.57272501877293[/C][C]90.3675668898688[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]142.075[/C][C]1.54181251991312[/C][C]92.148038860137[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]141.988461538462[/C][C]1.50736986347925[/C][C]94.196165770974[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]141.9375[/C][C]1.47295439705277[/C][C]96.3624537758955[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]141.895454545455[/C][C]1.42430171655157[/C][C]99.6245759564225[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]141.85[/C][C]1.33685609192849[/C][C]106.107157573987[/C][/ROW]
[ROW][C]Median[/C][C]141.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]142.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]141.670967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]142.123333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]141.670967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]142.123333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]142.123333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]141.670967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]142.123333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]142.15625[/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=33645&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33645&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 Mean141.9233333333332.3738849498614959.7852618517228
Geometric Mean140.732065755565
Harmonic Mean139.525730771995
Quadratic Mean143.089891327096
Winsorized Mean ( 1 / 20 )141.9083333333332.3565215335807560.2194086967255
Winsorized Mean ( 2 / 20 )141.8816666666672.3447434799605160.5105282856171
Winsorized Mean ( 3 / 20 )141.7516666666672.3155108180268261.218313282363
Winsorized Mean ( 4 / 20 )141.8383333333332.2936538482338461.8394678179325
Winsorized Mean ( 5 / 20 )141.8383333333332.1992937896647664.492672147705
Winsorized Mean ( 6 / 20 )141.7883333333332.1744706371411665.2059084687143
Winsorized Mean ( 7 / 20 )142.152.1039235609409667.5642417048768
Winsorized Mean ( 8 / 20 )142.152.0741964613922168.5325631616342
Winsorized Mean ( 9 / 20 )141.881.9823255760004671.5725013679425
Winsorized Mean ( 10 / 20 )141.7966666666671.9561809424162972.4864779080805
Winsorized Mean ( 11 / 20 )142.4566666666671.8393107998529677.4511119480486
Winsorized Mean ( 12 / 20 )142.6166666666671.7248191040278982.6849994492874
Winsorized Mean ( 13 / 20 )142.5733333333331.6108036851960188.5106823653586
Winsorized Mean ( 14 / 20 )142.3866666666671.5502095113855491.8499503589064
Winsorized Mean ( 15 / 20 )142.4616666666671.4522028691811698.1003892018165
Winsorized Mean ( 16 / 20 )142.6751.39575349716874102.220771998361
Winsorized Mean ( 17 / 20 )142.3351.32517736793879107.408263560516
Winsorized Mean ( 18 / 20 )142.2151.28872298066883110.353429040423
Winsorized Mean ( 19 / 20 )142.1833333333331.28390331461547110.743022246903
Winsorized Mean ( 20 / 20 )142.1833333333331.20434281647116118.058854496217
Trimmed Mean ( 1 / 20 )141.9103448275862.3150036547895361.3002681589667
Trimmed Mean ( 2 / 20 )141.91252.2632726312238162.7023444026114
Trimmed Mean ( 3 / 20 )141.9296296296302.2065204649066664.3228249576345
Trimmed Mean ( 4 / 20 )141.9980769230772.1493562303657866.0653989864266
Trimmed Mean ( 5 / 20 )142.0462.0857205675052268.1040414583938
Trimmed Mean ( 6 / 20 )142.0979166666672.0373843995038469.745265891538
Trimmed Mean ( 7 / 20 )142.1652173913041.9823355604720771.7160203479623
Trimmed Mean ( 8 / 20 )142.1681818181821.9314214242488073.6080588282155
Trimmed Mean ( 9 / 20 )142.1714285714291.8722817251872775.9348481902254
Trimmed Mean ( 10 / 20 )142.221.8188408537533078.1926575414881
Trimmed Mean ( 11 / 20 )142.2868421052631.7530634477032781.1646847646481
Trimmed Mean ( 12 / 20 )142.2611111111111.6961360278716183.8736450222255
Trimmed Mean ( 13 / 20 )142.2088235294121.6483631358340986.2727517000993
Trimmed Mean ( 14 / 20 )142.156251.6114005222616688.2190666045448
Trimmed Mean ( 15 / 20 )142.1233333333331.5727250187729390.3675668898688
Trimmed Mean ( 16 / 20 )142.0751.5418125199131292.148038860137
Trimmed Mean ( 17 / 20 )141.9884615384621.5073698634792594.196165770974
Trimmed Mean ( 18 / 20 )141.93751.4729543970527796.3624537758955
Trimmed Mean ( 19 / 20 )141.8954545454551.4243017165515799.6245759564225
Trimmed Mean ( 20 / 20 )141.851.33685609192849106.107157573987
Median141.5
Midrange142.3
Midmean - Weighted Average at Xnp141.670967741935
Midmean - Weighted Average at X(n+1)p142.123333333333
Midmean - Empirical Distribution Function141.670967741935
Midmean - Empirical Distribution Function - Averaging142.123333333333
Midmean - Empirical Distribution Function - Interpolation142.123333333333
Midmean - Closest Observation141.670967741935
Midmean - True Basic - Statistics Graphics Toolkit142.123333333333
Midmean - MS Excel (old versions)142.15625
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')