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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 computationFri, 14 Nov 2008 06:59:17 -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/Nov/14/t1226671209j4ht78y249b4ev7.htm/, Retrieved Sun, 19 May 2024 10:48:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=24935, Retrieved Sun, 19 May 2024 10:48:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact187
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [paper central ten...] [2008-11-14 13:59:17] [3817f5e632a8bfeb1be7b5e8c86bd450] [Current]
-         [Central Tendency] [paper central ten...] [2008-11-14 14:02:25] [077ffec662d24c06be4c491541a44245]
-    D      [Central Tendency] [paper centrale te...] [2008-12-05 10:30:52] [077ffec662d24c06be4c491541a44245]
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Dataseries X:
11947.20
11714.10
12192.50
11268.80
9097.40
12639.80
13040.10
11687.30
11191.70
11391.90
11793.10
13933.20
12778.10
11810.30
13698.40
11956.60
10723.80
13938.90
13979.80
13807.40
12973.90
12509.80
12934.10
14908.30
13772.10
13012.60
14049.90
11816.50
11593.20
14466.20
13615.90
14733.90
13880.70
13527.50
13584.00
16170.20
13260.60
14741.90
15486.50
13154.50
12621.20
15031.60
15452.40
15428.00
13105.90
14716.80
14180.00
16202.20
14392.40
15140.60
15960.10
14351.30
13230.20
15202.10
17157.30
16159.10
13405.70
17224.70
17338.40
17370.60




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=24935&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=24935&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24935&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 Mean13707.555227.74241212219860.1888549096644
Geometric Mean13594.6906900807
Harmonic Mean13480.0092841927
Quadratic Mean13818.7262020962
Winsorized Mean ( 1 / 20 )13734.125219.77121504870362.4928291767256
Winsorized Mean ( 2 / 20 )13745.9316666667215.34483820551863.8321855365207
Winsorized Mean ( 3 / 20 )13746.4166666667213.66117084649564.3374582859642
Winsorized Mean ( 4 / 20 )13690.95196.45727438349669.6891985443842
Winsorized Mean ( 5 / 20 )13705.0583333333192.65622380880771.1373765268766
Winsorized Mean ( 6 / 20 )13713.3583333333190.69364629192871.9130322377908
Winsorized Mean ( 7 / 20 )13693.2683333333185.19557616788973.9395001580368
Winsorized Mean ( 8 / 20 )13640.655170.91660715469279.8088332496224
Winsorized Mean ( 9 / 20 )13638.12169.51239655683280.4550007965204
Winsorized Mean ( 10 / 20 )13635.0866666667168.58812995569680.8780942658888
Winsorized Mean ( 11 / 20 )13617.6333333333156.95290069847386.762546424641
Winsorized Mean ( 12 / 20 )13607.2133333333154.52636248615288.0575528628832
Winsorized Mean ( 13 / 20 )13634.7083333333141.51377298747596.348984593465
Winsorized Mean ( 14 / 20 )13679.975124.369807443491109.994340919243
Winsorized Mean ( 15 / 20 )13666.225113.126850295446120.804432937970
Winsorized Mean ( 16 / 20 )13669.0516666667112.008512779079122.035828594804
Winsorized Mean ( 17 / 20 )13703.3916666667105.247937706533130.201046835486
Winsorized Mean ( 18 / 20 )13675.011666666786.348003195703158.37090796035
Winsorized Mean ( 19 / 20 )13664.24580.922333882836168.856289041093
Winsorized Mean ( 20 / 20 )13663.44576.982975791555177.486578811868
Trimmed Mean ( 1 / 20 )13723.8844827586212.23958643386364.6622277839539
Trimmed Mean ( 2 / 20 )13712.9125202.94017556301867.5712064501579
Trimmed Mean ( 3 / 20 )13694.5685185185194.38446522349570.4509411427147
Trimmed Mean ( 4 / 20 )13674.6269230769184.47067260311074.129002350948
Trimmed Mean ( 5 / 20 )13669.73179.16516036259776.2968088903836
Trimmed Mean ( 6 / 20 )13660.8979166667173.71272707229478.6407429490263
Trimmed Mean ( 7 / 20 )13649.4934782609167.29623476975581.5887667588352
Trimmed Mean ( 8 / 20 )13640.9659090909160.67933935181884.8955812497031
Trimmed Mean ( 9 / 20 )13641.0214285714156.22352087032587.3173344998048
Trimmed Mean ( 10 / 20 )13641.505150.62716137187490.5647087534319
Trimmed Mean ( 11 / 20 )13642.5184210526143.29956103995195.2027928211808
Trimmed Mean ( 12 / 20 )13646.2888888889136.75655410879199.7852642443237
Trimmed Mean ( 13 / 20 )13652.0352941176128.323310686870106.387804530938
Trimmed Mean ( 14 / 20 )13654.534375120.659263277649113.166067851579
Trimmed Mean ( 15 / 20 )13650.9115.268039753028118.427449874642
Trimmed Mean ( 16 / 20 )13648.7107142857110.964685065687123.000490707527
Trimmed Mean ( 17 / 20 )13645.7769230769104.609085986858130.445427319680
Trimmed Mean ( 18 / 20 )13637.304166666797.1636989899987140.353900771834
Trimmed Mean ( 19 / 20 )13631.590909090993.385465629667145.971226005863
Trimmed Mean ( 20 / 20 )13626.43589.1053634970834152.924969555239
Median13657.15
Midrange13234
Midmean - Weighted Average at Xnp13614.0903225806
Midmean - Weighted Average at X(n+1)p13650.9
Midmean - Empirical Distribution Function13614.0903225806
Midmean - Empirical Distribution Function - Averaging13650.9
Midmean - Empirical Distribution Function - Interpolation13650.9
Midmean - Closest Observation13614.0903225806
Midmean - True Basic - Statistics Graphics Toolkit13650.9
Midmean - MS Excel (old versions)13654.534375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 13707.555 & 227.742412122198 & 60.1888549096644 \tabularnewline
Geometric Mean & 13594.6906900807 &  &  \tabularnewline
Harmonic Mean & 13480.0092841927 &  &  \tabularnewline
Quadratic Mean & 13818.7262020962 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 13734.125 & 219.771215048703 & 62.4928291767256 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 13745.9316666667 & 215.344838205518 & 63.8321855365207 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 13746.4166666667 & 213.661170846495 & 64.3374582859642 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 13690.95 & 196.457274383496 & 69.6891985443842 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 13705.0583333333 & 192.656223808807 & 71.1373765268766 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 13713.3583333333 & 190.693646291928 & 71.9130322377908 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 13693.2683333333 & 185.195576167889 & 73.9395001580368 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 13640.655 & 170.916607154692 & 79.8088332496224 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 13638.12 & 169.512396556832 & 80.4550007965204 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 13635.0866666667 & 168.588129955696 & 80.8780942658888 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 13617.6333333333 & 156.952900698473 & 86.762546424641 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 13607.2133333333 & 154.526362486152 & 88.0575528628832 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 13634.7083333333 & 141.513772987475 & 96.348984593465 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 13679.975 & 124.369807443491 & 109.994340919243 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 13666.225 & 113.126850295446 & 120.804432937970 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 13669.0516666667 & 112.008512779079 & 122.035828594804 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 13703.3916666667 & 105.247937706533 & 130.201046835486 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 13675.0116666667 & 86.348003195703 & 158.37090796035 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 13664.245 & 80.922333882836 & 168.856289041093 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 13663.445 & 76.982975791555 & 177.486578811868 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 13723.8844827586 & 212.239586433863 & 64.6622277839539 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 13712.9125 & 202.940175563018 & 67.5712064501579 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 13694.5685185185 & 194.384465223495 & 70.4509411427147 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 13674.6269230769 & 184.470672603110 & 74.129002350948 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 13669.73 & 179.165160362597 & 76.2968088903836 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 13660.8979166667 & 173.712727072294 & 78.6407429490263 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 13649.4934782609 & 167.296234769755 & 81.5887667588352 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 13640.9659090909 & 160.679339351818 & 84.8955812497031 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 13641.0214285714 & 156.223520870325 & 87.3173344998048 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 13641.505 & 150.627161371874 & 90.5647087534319 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 13642.5184210526 & 143.299561039951 & 95.2027928211808 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 13646.2888888889 & 136.756554108791 & 99.7852642443237 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 13652.0352941176 & 128.323310686870 & 106.387804530938 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 13654.534375 & 120.659263277649 & 113.166067851579 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 13650.9 & 115.268039753028 & 118.427449874642 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 13648.7107142857 & 110.964685065687 & 123.000490707527 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 13645.7769230769 & 104.609085986858 & 130.445427319680 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 13637.3041666667 & 97.1636989899987 & 140.353900771834 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 13631.5909090909 & 93.385465629667 & 145.971226005863 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 13626.435 & 89.1053634970834 & 152.924969555239 \tabularnewline
Median & 13657.15 &  &  \tabularnewline
Midrange & 13234 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 13614.0903225806 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 13650.9 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 13614.0903225806 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 13650.9 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 13650.9 &  &  \tabularnewline
Midmean - Closest Observation & 13614.0903225806 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 13650.9 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 13654.534375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=24935&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]13707.555[/C][C]227.742412122198[/C][C]60.1888549096644[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]13594.6906900807[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]13480.0092841927[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]13818.7262020962[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]13734.125[/C][C]219.771215048703[/C][C]62.4928291767256[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]13745.9316666667[/C][C]215.344838205518[/C][C]63.8321855365207[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]13746.4166666667[/C][C]213.661170846495[/C][C]64.3374582859642[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]13690.95[/C][C]196.457274383496[/C][C]69.6891985443842[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]13705.0583333333[/C][C]192.656223808807[/C][C]71.1373765268766[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]13713.3583333333[/C][C]190.693646291928[/C][C]71.9130322377908[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]13693.2683333333[/C][C]185.195576167889[/C][C]73.9395001580368[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]13640.655[/C][C]170.916607154692[/C][C]79.8088332496224[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]13638.12[/C][C]169.512396556832[/C][C]80.4550007965204[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]13635.0866666667[/C][C]168.588129955696[/C][C]80.8780942658888[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]13617.6333333333[/C][C]156.952900698473[/C][C]86.762546424641[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]13607.2133333333[/C][C]154.526362486152[/C][C]88.0575528628832[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]13634.7083333333[/C][C]141.513772987475[/C][C]96.348984593465[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]13679.975[/C][C]124.369807443491[/C][C]109.994340919243[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]13666.225[/C][C]113.126850295446[/C][C]120.804432937970[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]13669.0516666667[/C][C]112.008512779079[/C][C]122.035828594804[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]13703.3916666667[/C][C]105.247937706533[/C][C]130.201046835486[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]13675.0116666667[/C][C]86.348003195703[/C][C]158.37090796035[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]13664.245[/C][C]80.922333882836[/C][C]168.856289041093[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]13663.445[/C][C]76.982975791555[/C][C]177.486578811868[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]13723.8844827586[/C][C]212.239586433863[/C][C]64.6622277839539[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]13712.9125[/C][C]202.940175563018[/C][C]67.5712064501579[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]13694.5685185185[/C][C]194.384465223495[/C][C]70.4509411427147[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]13674.6269230769[/C][C]184.470672603110[/C][C]74.129002350948[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]13669.73[/C][C]179.165160362597[/C][C]76.2968088903836[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]13660.8979166667[/C][C]173.712727072294[/C][C]78.6407429490263[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]13649.4934782609[/C][C]167.296234769755[/C][C]81.5887667588352[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]13640.9659090909[/C][C]160.679339351818[/C][C]84.8955812497031[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]13641.0214285714[/C][C]156.223520870325[/C][C]87.3173344998048[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]13641.505[/C][C]150.627161371874[/C][C]90.5647087534319[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]13642.5184210526[/C][C]143.299561039951[/C][C]95.2027928211808[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]13646.2888888889[/C][C]136.756554108791[/C][C]99.7852642443237[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]13652.0352941176[/C][C]128.323310686870[/C][C]106.387804530938[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]13654.534375[/C][C]120.659263277649[/C][C]113.166067851579[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]13650.9[/C][C]115.268039753028[/C][C]118.427449874642[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]13648.7107142857[/C][C]110.964685065687[/C][C]123.000490707527[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]13645.7769230769[/C][C]104.609085986858[/C][C]130.445427319680[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]13637.3041666667[/C][C]97.1636989899987[/C][C]140.353900771834[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]13631.5909090909[/C][C]93.385465629667[/C][C]145.971226005863[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]13626.435[/C][C]89.1053634970834[/C][C]152.924969555239[/C][/ROW]
[ROW][C]Median[/C][C]13657.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]13234[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]13614.0903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]13650.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]13614.0903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]13650.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]13650.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]13614.0903225806[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]13650.9[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]13654.534375[/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=24935&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=24935&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 Mean13707.555227.74241212219860.1888549096644
Geometric Mean13594.6906900807
Harmonic Mean13480.0092841927
Quadratic Mean13818.7262020962
Winsorized Mean ( 1 / 20 )13734.125219.77121504870362.4928291767256
Winsorized Mean ( 2 / 20 )13745.9316666667215.34483820551863.8321855365207
Winsorized Mean ( 3 / 20 )13746.4166666667213.66117084649564.3374582859642
Winsorized Mean ( 4 / 20 )13690.95196.45727438349669.6891985443842
Winsorized Mean ( 5 / 20 )13705.0583333333192.65622380880771.1373765268766
Winsorized Mean ( 6 / 20 )13713.3583333333190.69364629192871.9130322377908
Winsorized Mean ( 7 / 20 )13693.2683333333185.19557616788973.9395001580368
Winsorized Mean ( 8 / 20 )13640.655170.91660715469279.8088332496224
Winsorized Mean ( 9 / 20 )13638.12169.51239655683280.4550007965204
Winsorized Mean ( 10 / 20 )13635.0866666667168.58812995569680.8780942658888
Winsorized Mean ( 11 / 20 )13617.6333333333156.95290069847386.762546424641
Winsorized Mean ( 12 / 20 )13607.2133333333154.52636248615288.0575528628832
Winsorized Mean ( 13 / 20 )13634.7083333333141.51377298747596.348984593465
Winsorized Mean ( 14 / 20 )13679.975124.369807443491109.994340919243
Winsorized Mean ( 15 / 20 )13666.225113.126850295446120.804432937970
Winsorized Mean ( 16 / 20 )13669.0516666667112.008512779079122.035828594804
Winsorized Mean ( 17 / 20 )13703.3916666667105.247937706533130.201046835486
Winsorized Mean ( 18 / 20 )13675.011666666786.348003195703158.37090796035
Winsorized Mean ( 19 / 20 )13664.24580.922333882836168.856289041093
Winsorized Mean ( 20 / 20 )13663.44576.982975791555177.486578811868
Trimmed Mean ( 1 / 20 )13723.8844827586212.23958643386364.6622277839539
Trimmed Mean ( 2 / 20 )13712.9125202.94017556301867.5712064501579
Trimmed Mean ( 3 / 20 )13694.5685185185194.38446522349570.4509411427147
Trimmed Mean ( 4 / 20 )13674.6269230769184.47067260311074.129002350948
Trimmed Mean ( 5 / 20 )13669.73179.16516036259776.2968088903836
Trimmed Mean ( 6 / 20 )13660.8979166667173.71272707229478.6407429490263
Trimmed Mean ( 7 / 20 )13649.4934782609167.29623476975581.5887667588352
Trimmed Mean ( 8 / 20 )13640.9659090909160.67933935181884.8955812497031
Trimmed Mean ( 9 / 20 )13641.0214285714156.22352087032587.3173344998048
Trimmed Mean ( 10 / 20 )13641.505150.62716137187490.5647087534319
Trimmed Mean ( 11 / 20 )13642.5184210526143.29956103995195.2027928211808
Trimmed Mean ( 12 / 20 )13646.2888888889136.75655410879199.7852642443237
Trimmed Mean ( 13 / 20 )13652.0352941176128.323310686870106.387804530938
Trimmed Mean ( 14 / 20 )13654.534375120.659263277649113.166067851579
Trimmed Mean ( 15 / 20 )13650.9115.268039753028118.427449874642
Trimmed Mean ( 16 / 20 )13648.7107142857110.964685065687123.000490707527
Trimmed Mean ( 17 / 20 )13645.7769230769104.609085986858130.445427319680
Trimmed Mean ( 18 / 20 )13637.304166666797.1636989899987140.353900771834
Trimmed Mean ( 19 / 20 )13631.590909090993.385465629667145.971226005863
Trimmed Mean ( 20 / 20 )13626.43589.1053634970834152.924969555239
Median13657.15
Midrange13234
Midmean - Weighted Average at Xnp13614.0903225806
Midmean - Weighted Average at X(n+1)p13650.9
Midmean - Empirical Distribution Function13614.0903225806
Midmean - Empirical Distribution Function - Averaging13650.9
Midmean - Empirical Distribution Function - Interpolation13650.9
Midmean - Closest Observation13614.0903225806
Midmean - True Basic - Statistics Graphics Toolkit13650.9
Midmean - MS Excel (old versions)13654.534375
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')