Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 11 Dec 2008 16:02:29 -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/12/t1229036591pa274dfhrh6bru1.htm/, Retrieved Fri, 17 May 2024 00:45:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32471, Retrieved Fri, 17 May 2024 00:45:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact209
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Paper central ten...] [2007-11-09 08:56:17] [74be16979710d4c4e7c6647856088456]
-    D  [Central Tendency] [central tendency ...] [2008-12-11 22:56:40] [4ddbf81f78ea7c738951638c7e93f6ee]
-    D    [Central Tendency] [central tendency ...] [2008-12-11 22:59:27] [4ddbf81f78ea7c738951638c7e93f6ee]
-    D        [Central Tendency] [central tendency ...] [2008-12-11 23:02:29] [e8f764b122b426f433a1e1038b457077] [Current]
Feedback Forum

Post a new message
Dataseries X:
8,3
8,4
8,4
8,4
8,6
8,9
8,8
8,3
7,5
7,2
7,5
8,8
9,3
9,3
8,7
8,2
8,3
8,5
8,6
8,6
8,2
8,1
8
8,6
8,7
8,8
8,5
8,4
8,5
8,7
8,7
8,6
8,5
8,3
8,1
8,2
8,1
8,1
7,9
7,9
7,9
8
8
7,9
8
7,7
7,2
7,5
7,3
7
7
7
7,2
7,3
7,1
6,8
6,6
6,2
6,2
6,8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32471&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32471&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32471&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean8.003333333333330.09348756425553785.6085341089558
Geometric Mean7.96952421803644
Harmonic Mean7.93404841720217
Quadratic Mean8.03548380621852
Winsorized Mean ( 1 / 20 )8.003333333333330.09348756425553785.6085341089558
Winsorized Mean ( 2 / 20 )8.003333333333330.086715544669812892.2941020990834
Winsorized Mean ( 3 / 20 )8.008333333333330.083269749754070196.1733805732002
Winsorized Mean ( 4 / 20 )8.008333333333330.083269749754070196.1733805732002
Winsorized Mean ( 5 / 20 )8.0250.0793912218176223101.081704201946
Winsorized Mean ( 6 / 20 )8.0150.0778171476898008102.997864069111
Winsorized Mean ( 7 / 20 )8.0150.0778171476898008102.997864069111
Winsorized Mean ( 8 / 20 )8.028333333333330.0749422250791346107.126967805611
Winsorized Mean ( 9 / 20 )8.043333333333330.071874288664293111.908353916402
Winsorized Mean ( 10 / 20 )8.026666666666670.0694150973771518115.632866191277
Winsorized Mean ( 11 / 20 )8.026666666666670.0694150973771518115.632866191277
Winsorized Mean ( 12 / 20 )8.046666666666670.0654608463934445122.923352049302
Winsorized Mean ( 13 / 20 )8.046666666666670.0654608463934445122.923352049302
Winsorized Mean ( 14 / 20 )8.093333333333330.056791156044726142.510452278158
Winsorized Mean ( 15 / 20 )8.068333333333330.0531755257128684151.730203419142
Winsorized Mean ( 16 / 20 )8.068333333333330.0531755257128684151.730203419142
Winsorized Mean ( 17 / 20 )8.1250.0432849577869896187.709551202154
Winsorized Mean ( 18 / 20 )8.1850.0339345498322342241.199604546548
Winsorized Mean ( 19 / 20 )8.153333333333330.0291563742937727279.641537427881
Winsorized Mean ( 20 / 20 )8.153333333333330.0291563742937727279.641537427881
Trimmed Mean ( 1 / 20 )8.012068965517240.088684599419912890.3434081895199
Trimmed Mean ( 2 / 20 )8.021428571428570.082678939580117897.019006438219
Trimmed Mean ( 3 / 20 )8.031481481481480.0798681685474783100.559229384446
Trimmed Mean ( 4 / 20 )8.040384615384620.0780251929470472103.048570746135
Trimmed Mean ( 5 / 20 )8.050.0756603581535163106.396535734954
Trimmed Mean ( 6 / 20 )8.056250.074012784620186108.849437855129
Trimmed Mean ( 7 / 20 )8.065217391304350.07231288639774111.532228805576
Trimmed Mean ( 8 / 20 )8.0750.0700441570178892115.284419768770
Trimmed Mean ( 9 / 20 )8.083333333333330.0678966101578369119.053562682176
Trimmed Mean ( 10 / 20 )8.090.0659059158466806122.750740901926
Trimmed Mean ( 11 / 20 )8.10.0637830604872556126.992965500902
Trimmed Mean ( 12 / 20 )8.111111111111110.0607855686948146133.438105215968
Trimmed Mean ( 13 / 20 )8.120588235294120.0578552209499819140.360508558332
Trimmed Mean ( 14 / 20 )8.131250.0535884669525317151.735074026331
Trimmed Mean ( 15 / 20 )8.136666666666670.0506244530740051160.726016235121
Trimmed Mean ( 16 / 20 )8.146428571428570.0472755467896781172.318019031505
Trimmed Mean ( 17 / 20 )8.15769230769230.0419424796314326194.497139400856
Trimmed Mean ( 18 / 20 )8.16250.0384540474867854212.266342127055
Trimmed Mean ( 19 / 20 )8.159090909090910.0370205809783958220.393378317113
Trimmed Mean ( 20 / 20 )8.160.0365628514378072223.177342004631
Median8.15
Midrange7.75
Midmean - Weighted Average at Xnp8.11612903225807
Midmean - Weighted Average at X(n+1)p8.11612903225807
Midmean - Empirical Distribution Function8.11612903225807
Midmean - Empirical Distribution Function - Averaging8.11612903225807
Midmean - Empirical Distribution Function - Interpolation8.11612903225807
Midmean - Closest Observation8.11612903225807
Midmean - True Basic - Statistics Graphics Toolkit8.11612903225807
Midmean - MS Excel (old versions)8.18333333333334
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 8.00333333333333 & 0.093487564255537 & 85.6085341089558 \tabularnewline
Geometric Mean & 7.96952421803644 &  &  \tabularnewline
Harmonic Mean & 7.93404841720217 &  &  \tabularnewline
Quadratic Mean & 8.03548380621852 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 8.00333333333333 & 0.093487564255537 & 85.6085341089558 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 8.00333333333333 & 0.0867155446698128 & 92.2941020990834 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 8.00833333333333 & 0.0832697497540701 & 96.1733805732002 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 8.00833333333333 & 0.0832697497540701 & 96.1733805732002 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 8.025 & 0.0793912218176223 & 101.081704201946 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 8.015 & 0.0778171476898008 & 102.997864069111 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 8.015 & 0.0778171476898008 & 102.997864069111 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 8.02833333333333 & 0.0749422250791346 & 107.126967805611 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 8.04333333333333 & 0.071874288664293 & 111.908353916402 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 8.02666666666667 & 0.0694150973771518 & 115.632866191277 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 8.02666666666667 & 0.0694150973771518 & 115.632866191277 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 8.04666666666667 & 0.0654608463934445 & 122.923352049302 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 8.04666666666667 & 0.0654608463934445 & 122.923352049302 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 8.09333333333333 & 0.056791156044726 & 142.510452278158 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 8.06833333333333 & 0.0531755257128684 & 151.730203419142 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 8.06833333333333 & 0.0531755257128684 & 151.730203419142 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 8.125 & 0.0432849577869896 & 187.709551202154 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 8.185 & 0.0339345498322342 & 241.199604546548 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 8.15333333333333 & 0.0291563742937727 & 279.641537427881 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 8.15333333333333 & 0.0291563742937727 & 279.641537427881 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 8.01206896551724 & 0.0886845994199128 & 90.3434081895199 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 8.02142857142857 & 0.0826789395801178 & 97.019006438219 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 8.03148148148148 & 0.0798681685474783 & 100.559229384446 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 8.04038461538462 & 0.0780251929470472 & 103.048570746135 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 8.05 & 0.0756603581535163 & 106.396535734954 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 8.05625 & 0.074012784620186 & 108.849437855129 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 8.06521739130435 & 0.07231288639774 & 111.532228805576 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 8.075 & 0.0700441570178892 & 115.284419768770 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 8.08333333333333 & 0.0678966101578369 & 119.053562682176 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 8.09 & 0.0659059158466806 & 122.750740901926 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 8.1 & 0.0637830604872556 & 126.992965500902 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 8.11111111111111 & 0.0607855686948146 & 133.438105215968 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 8.12058823529412 & 0.0578552209499819 & 140.360508558332 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 8.13125 & 0.0535884669525317 & 151.735074026331 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 8.13666666666667 & 0.0506244530740051 & 160.726016235121 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 8.14642857142857 & 0.0472755467896781 & 172.318019031505 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 8.1576923076923 & 0.0419424796314326 & 194.497139400856 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 8.1625 & 0.0384540474867854 & 212.266342127055 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 8.15909090909091 & 0.0370205809783958 & 220.393378317113 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 8.16 & 0.0365628514378072 & 223.177342004631 \tabularnewline
Median & 8.15 &  &  \tabularnewline
Midrange & 7.75 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.11612903225807 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 8.11612903225807 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 8.11612903225807 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 8.11612903225807 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 8.11612903225807 &  &  \tabularnewline
Midmean - Closest Observation & 8.11612903225807 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 8.11612903225807 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 8.18333333333334 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32471&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]8.00333333333333[/C][C]0.093487564255537[/C][C]85.6085341089558[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.96952421803644[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.93404841720217[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]8.03548380621852[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]8.00333333333333[/C][C]0.093487564255537[/C][C]85.6085341089558[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]8.00333333333333[/C][C]0.0867155446698128[/C][C]92.2941020990834[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]8.00833333333333[/C][C]0.0832697497540701[/C][C]96.1733805732002[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]8.00833333333333[/C][C]0.0832697497540701[/C][C]96.1733805732002[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]8.025[/C][C]0.0793912218176223[/C][C]101.081704201946[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]8.015[/C][C]0.0778171476898008[/C][C]102.997864069111[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]8.015[/C][C]0.0778171476898008[/C][C]102.997864069111[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]8.02833333333333[/C][C]0.0749422250791346[/C][C]107.126967805611[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]8.04333333333333[/C][C]0.071874288664293[/C][C]111.908353916402[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]8.02666666666667[/C][C]0.0694150973771518[/C][C]115.632866191277[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]8.02666666666667[/C][C]0.0694150973771518[/C][C]115.632866191277[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]8.04666666666667[/C][C]0.0654608463934445[/C][C]122.923352049302[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]8.04666666666667[/C][C]0.0654608463934445[/C][C]122.923352049302[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]8.09333333333333[/C][C]0.056791156044726[/C][C]142.510452278158[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]8.06833333333333[/C][C]0.0531755257128684[/C][C]151.730203419142[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]8.06833333333333[/C][C]0.0531755257128684[/C][C]151.730203419142[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]8.125[/C][C]0.0432849577869896[/C][C]187.709551202154[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]8.185[/C][C]0.0339345498322342[/C][C]241.199604546548[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]8.15333333333333[/C][C]0.0291563742937727[/C][C]279.641537427881[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]8.15333333333333[/C][C]0.0291563742937727[/C][C]279.641537427881[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]8.01206896551724[/C][C]0.0886845994199128[/C][C]90.3434081895199[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]8.02142857142857[/C][C]0.0826789395801178[/C][C]97.019006438219[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]8.03148148148148[/C][C]0.0798681685474783[/C][C]100.559229384446[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]8.04038461538462[/C][C]0.0780251929470472[/C][C]103.048570746135[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]8.05[/C][C]0.0756603581535163[/C][C]106.396535734954[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]8.05625[/C][C]0.074012784620186[/C][C]108.849437855129[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]8.06521739130435[/C][C]0.07231288639774[/C][C]111.532228805576[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]8.075[/C][C]0.0700441570178892[/C][C]115.284419768770[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]8.08333333333333[/C][C]0.0678966101578369[/C][C]119.053562682176[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]8.09[/C][C]0.0659059158466806[/C][C]122.750740901926[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]8.1[/C][C]0.0637830604872556[/C][C]126.992965500902[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]8.11111111111111[/C][C]0.0607855686948146[/C][C]133.438105215968[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]8.12058823529412[/C][C]0.0578552209499819[/C][C]140.360508558332[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]8.13125[/C][C]0.0535884669525317[/C][C]151.735074026331[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]8.13666666666667[/C][C]0.0506244530740051[/C][C]160.726016235121[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]8.14642857142857[/C][C]0.0472755467896781[/C][C]172.318019031505[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]8.1576923076923[/C][C]0.0419424796314326[/C][C]194.497139400856[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]8.1625[/C][C]0.0384540474867854[/C][C]212.266342127055[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]8.15909090909091[/C][C]0.0370205809783958[/C][C]220.393378317113[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]8.16[/C][C]0.0365628514378072[/C][C]223.177342004631[/C][/ROW]
[ROW][C]Median[/C][C]8.15[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.11612903225807[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]8.11612903225807[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]8.11612903225807[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]8.11612903225807[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]8.11612903225807[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.11612903225807[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]8.11612903225807[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]8.18333333333334[/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=32471&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32471&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 Mean8.003333333333330.09348756425553785.6085341089558
Geometric Mean7.96952421803644
Harmonic Mean7.93404841720217
Quadratic Mean8.03548380621852
Winsorized Mean ( 1 / 20 )8.003333333333330.09348756425553785.6085341089558
Winsorized Mean ( 2 / 20 )8.003333333333330.086715544669812892.2941020990834
Winsorized Mean ( 3 / 20 )8.008333333333330.083269749754070196.1733805732002
Winsorized Mean ( 4 / 20 )8.008333333333330.083269749754070196.1733805732002
Winsorized Mean ( 5 / 20 )8.0250.0793912218176223101.081704201946
Winsorized Mean ( 6 / 20 )8.0150.0778171476898008102.997864069111
Winsorized Mean ( 7 / 20 )8.0150.0778171476898008102.997864069111
Winsorized Mean ( 8 / 20 )8.028333333333330.0749422250791346107.126967805611
Winsorized Mean ( 9 / 20 )8.043333333333330.071874288664293111.908353916402
Winsorized Mean ( 10 / 20 )8.026666666666670.0694150973771518115.632866191277
Winsorized Mean ( 11 / 20 )8.026666666666670.0694150973771518115.632866191277
Winsorized Mean ( 12 / 20 )8.046666666666670.0654608463934445122.923352049302
Winsorized Mean ( 13 / 20 )8.046666666666670.0654608463934445122.923352049302
Winsorized Mean ( 14 / 20 )8.093333333333330.056791156044726142.510452278158
Winsorized Mean ( 15 / 20 )8.068333333333330.0531755257128684151.730203419142
Winsorized Mean ( 16 / 20 )8.068333333333330.0531755257128684151.730203419142
Winsorized Mean ( 17 / 20 )8.1250.0432849577869896187.709551202154
Winsorized Mean ( 18 / 20 )8.1850.0339345498322342241.199604546548
Winsorized Mean ( 19 / 20 )8.153333333333330.0291563742937727279.641537427881
Winsorized Mean ( 20 / 20 )8.153333333333330.0291563742937727279.641537427881
Trimmed Mean ( 1 / 20 )8.012068965517240.088684599419912890.3434081895199
Trimmed Mean ( 2 / 20 )8.021428571428570.082678939580117897.019006438219
Trimmed Mean ( 3 / 20 )8.031481481481480.0798681685474783100.559229384446
Trimmed Mean ( 4 / 20 )8.040384615384620.0780251929470472103.048570746135
Trimmed Mean ( 5 / 20 )8.050.0756603581535163106.396535734954
Trimmed Mean ( 6 / 20 )8.056250.074012784620186108.849437855129
Trimmed Mean ( 7 / 20 )8.065217391304350.07231288639774111.532228805576
Trimmed Mean ( 8 / 20 )8.0750.0700441570178892115.284419768770
Trimmed Mean ( 9 / 20 )8.083333333333330.0678966101578369119.053562682176
Trimmed Mean ( 10 / 20 )8.090.0659059158466806122.750740901926
Trimmed Mean ( 11 / 20 )8.10.0637830604872556126.992965500902
Trimmed Mean ( 12 / 20 )8.111111111111110.0607855686948146133.438105215968
Trimmed Mean ( 13 / 20 )8.120588235294120.0578552209499819140.360508558332
Trimmed Mean ( 14 / 20 )8.131250.0535884669525317151.735074026331
Trimmed Mean ( 15 / 20 )8.136666666666670.0506244530740051160.726016235121
Trimmed Mean ( 16 / 20 )8.146428571428570.0472755467896781172.318019031505
Trimmed Mean ( 17 / 20 )8.15769230769230.0419424796314326194.497139400856
Trimmed Mean ( 18 / 20 )8.16250.0384540474867854212.266342127055
Trimmed Mean ( 19 / 20 )8.159090909090910.0370205809783958220.393378317113
Trimmed Mean ( 20 / 20 )8.160.0365628514378072223.177342004631
Median8.15
Midrange7.75
Midmean - Weighted Average at Xnp8.11612903225807
Midmean - Weighted Average at X(n+1)p8.11612903225807
Midmean - Empirical Distribution Function8.11612903225807
Midmean - Empirical Distribution Function - Averaging8.11612903225807
Midmean - Empirical Distribution Function - Interpolation8.11612903225807
Midmean - Closest Observation8.11612903225807
Midmean - True Basic - Statistics Graphics Toolkit8.11612903225807
Midmean - MS Excel (old versions)8.18333333333334
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')