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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, 23 Oct 2009 01:18:30 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/23/t1256282393vi3ppbboifbvsf2.htm/, Retrieved Thu, 02 May 2024 01:00:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49842, Retrieved Thu, 02 May 2024 01:00:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKVN WS3
Estimated Impact142
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [WS3 Q1.1 Central ...] [2009-10-22 07:58:17] [0f9a80199ae32669ca1a3c3995927a06]
-   PD  [Central Tendency] [WS3 Q2 Central Te...] [2009-10-22 18:39:51] [1b4c3bbe3f2ba180dd536c5a6a81a8e6]
-    D    [Central Tendency] [WS3 Q2 Central Te...] [2009-10-22 20:08:54] [1b4c3bbe3f2ba180dd536c5a6a81a8e6]
-   PD        [Central Tendency] [WS3 Q2 Central Te...] [2009-10-23 07:18:30] [f1100e00818182135823a11ccbd0f3b9] [Current]
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Dataseries X:
8,12
4,04
4,28
3,33
2,13
1,64
2,23
1,50
2,03
3,18
4,58
4,45
7,08
3,85
3,73
3,13
1,91
1,86
2,21
1,51
2,01
2,99
4,58
4,29
6,08
3,66
4,35
2,55
1,94
1,97
1,79
1,84
1,97
2,99
4,66
4,35
6,14
4,29
4,65
2,70
2,09
2,03
1,72
1,87
1,89
3,29
4,63
4,26
6,70
4,58
4,19
2,77
2,24
1,81
1,85
1,83
1,71
3,54
5,04
3,75




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49842&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49842&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49842&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean3.306333333333330.19816074720433416.6851073180704
Geometric Mean2.99290311926345
Harmonic Mean2.72647590549401
Quadratic Mean3.63986721369521
Winsorized Mean ( 1 / 20 )3.289166666666670.19164988258616817.1623724589960
Winsorized Mean ( 2 / 20 )3.280833333333330.1868972483748617.5542088600093
Winsorized Mean ( 3 / 20 )3.256333333333330.17818624273442618.2748863400564
Winsorized Mean ( 4 / 20 )3.2530.17699824442935418.3787133623146
Winsorized Mean ( 5 / 20 )3.172166666666670.15538272262269820.4151826736192
Winsorized Mean ( 6 / 20 )3.136166666666670.14787670304412921.2079834220457
Winsorized Mean ( 7 / 20 )3.137333333333330.14732048669610321.2959745361493
Winsorized Mean ( 8 / 20 )3.1360.14665810195845521.3830668617842
Winsorized Mean ( 9 / 20 )3.130.14515119722722621.5637215523628
Winsorized Mean ( 10 / 20 )3.131666666666670.14490268830222921.6122054280652
Winsorized Mean ( 11 / 20 )3.13350.14463060779746621.6655384895292
Winsorized Mean ( 12 / 20 )3.11150.13972204550463822.2692130562655
Winsorized Mean ( 13 / 20 )3.094166666666670.13562020991393522.8149378962784
Winsorized Mean ( 14 / 20 )3.101166666666670.13459042109338323.0415109892180
Winsorized Mean ( 15 / 20 )3.093666666666670.13115824027664823.5872840329459
Winsorized Mean ( 16 / 20 )3.093666666666670.13115824027664823.5872840329459
Winsorized Mean ( 17 / 20 )3.102166666666670.12908458481811424.0320458948508
Winsorized Mean ( 18 / 20 )3.102166666666670.12729965796898624.3690102248543
Winsorized Mean ( 19 / 20 )3.080.12390788450218924.8571752505836
Winsorized Mean ( 20 / 20 )3.050.11354359027552126.8619302296059
Trimmed Mean ( 1 / 20 )3.254482758620690.18440190798062817.6488562090289
Trimmed Mean ( 2 / 20 )3.217321428571430.17531261337175818.3519107193329
Trimmed Mean ( 3 / 20 )3.182037037037040.16716704334117119.0350739801195
Trimmed Mean ( 4 / 20 )3.153461538461540.16132368290121019.5474184679544
Trimmed Mean ( 5 / 20 )3.12360.15433220463582820.2394568740247
Trimmed Mean ( 6 / 20 )3.111458333333330.15312495175374420.3197342934494
Trimmed Mean ( 7 / 20 )3.106086956521740.15354726042696120.2288660044132
Trimmed Mean ( 8 / 20 )3.10.15386184462186820.1479451102291
Trimmed Mean ( 9 / 20 )3.093571428571430.15403961262127520.0829603238315
Trimmed Mean ( 10 / 20 )3.08750.15421960283127420.0201527128683
Trimmed Mean ( 11 / 20 )3.080526315789470.15405008670282119.9969138721235
Trimmed Mean ( 12 / 20 )3.07250.15340131774438720.0291630161856
Trimmed Mean ( 13 / 20 )3.066764705882350.15325739454218920.0105496706597
Trimmed Mean ( 14 / 20 )3.06281250.15348126552099919.9556114526626
Trimmed Mean ( 15 / 20 )3.057333333333330.15331429167123119.9416068783040
Trimmed Mean ( 16 / 20 )3.052142857142860.15321541112794519.9205995968260
Trimmed Mean ( 17 / 20 )3.046153846153850.15212755470133720.0236824428959
Trimmed Mean ( 18 / 20 )3.037916666666670.15015207166604120.2322660817056
Trimmed Mean ( 19 / 20 )3.028181818181820.14663415080871320.6512725820068
Trimmed Mean ( 20 / 20 )3.020.14129290219443521.3740389863613
Median3.06
Midrange4.81
Midmean - Weighted Average at Xnp3.02129032258065
Midmean - Weighted Average at X(n+1)p3.05733333333333
Midmean - Empirical Distribution Function3.02129032258065
Midmean - Empirical Distribution Function - Averaging3.05733333333333
Midmean - Empirical Distribution Function - Interpolation3.05733333333333
Midmean - Closest Observation3.02129032258065
Midmean - True Basic - Statistics Graphics Toolkit3.05733333333333
Midmean - MS Excel (old versions)3.10181818181818
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 3.30633333333333 & 0.198160747204334 & 16.6851073180704 \tabularnewline
Geometric Mean & 2.99290311926345 &  &  \tabularnewline
Harmonic Mean & 2.72647590549401 &  &  \tabularnewline
Quadratic Mean & 3.63986721369521 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 3.28916666666667 & 0.191649882586168 & 17.1623724589960 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 3.28083333333333 & 0.18689724837486 & 17.5542088600093 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 3.25633333333333 & 0.178186242734426 & 18.2748863400564 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 3.253 & 0.176998244429354 & 18.3787133623146 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 3.17216666666667 & 0.155382722622698 & 20.4151826736192 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 3.13616666666667 & 0.147876703044129 & 21.2079834220457 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 3.13733333333333 & 0.147320486696103 & 21.2959745361493 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 3.136 & 0.146658101958455 & 21.3830668617842 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 3.13 & 0.145151197227226 & 21.5637215523628 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 3.13166666666667 & 0.144902688302229 & 21.6122054280652 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 3.1335 & 0.144630607797466 & 21.6655384895292 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 3.1115 & 0.139722045504638 & 22.2692130562655 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 3.09416666666667 & 0.135620209913935 & 22.8149378962784 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 3.10116666666667 & 0.134590421093383 & 23.0415109892180 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 3.09366666666667 & 0.131158240276648 & 23.5872840329459 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 3.09366666666667 & 0.131158240276648 & 23.5872840329459 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 3.10216666666667 & 0.129084584818114 & 24.0320458948508 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 3.10216666666667 & 0.127299657968986 & 24.3690102248543 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 3.08 & 0.123907884502189 & 24.8571752505836 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 3.05 & 0.113543590275521 & 26.8619302296059 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 3.25448275862069 & 0.184401907980628 & 17.6488562090289 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 3.21732142857143 & 0.175312613371758 & 18.3519107193329 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 3.18203703703704 & 0.167167043341171 & 19.0350739801195 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 3.15346153846154 & 0.161323682901210 & 19.5474184679544 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 3.1236 & 0.154332204635828 & 20.2394568740247 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 3.11145833333333 & 0.153124951753744 & 20.3197342934494 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 3.10608695652174 & 0.153547260426961 & 20.2288660044132 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 3.1 & 0.153861844621868 & 20.1479451102291 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 3.09357142857143 & 0.154039612621275 & 20.0829603238315 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 3.0875 & 0.154219602831274 & 20.0201527128683 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 3.08052631578947 & 0.154050086702821 & 19.9969138721235 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 3.0725 & 0.153401317744387 & 20.0291630161856 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 3.06676470588235 & 0.153257394542189 & 20.0105496706597 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 3.0628125 & 0.153481265520999 & 19.9556114526626 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 3.05733333333333 & 0.153314291671231 & 19.9416068783040 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 3.05214285714286 & 0.153215411127945 & 19.9205995968260 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 3.04615384615385 & 0.152127554701337 & 20.0236824428959 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 3.03791666666667 & 0.150152071666041 & 20.2322660817056 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 3.02818181818182 & 0.146634150808713 & 20.6512725820068 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 3.02 & 0.141292902194435 & 21.3740389863613 \tabularnewline
Median & 3.06 &  &  \tabularnewline
Midrange & 4.81 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 3.02129032258065 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 3.05733333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 3.02129032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 3.05733333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 3.05733333333333 &  &  \tabularnewline
Midmean - Closest Observation & 3.02129032258065 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 3.05733333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 3.10181818181818 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49842&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]3.30633333333333[/C][C]0.198160747204334[/C][C]16.6851073180704[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]2.99290311926345[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]2.72647590549401[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]3.63986721369521[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]3.28916666666667[/C][C]0.191649882586168[/C][C]17.1623724589960[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]3.28083333333333[/C][C]0.18689724837486[/C][C]17.5542088600093[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]3.25633333333333[/C][C]0.178186242734426[/C][C]18.2748863400564[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]3.253[/C][C]0.176998244429354[/C][C]18.3787133623146[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]3.17216666666667[/C][C]0.155382722622698[/C][C]20.4151826736192[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]3.13616666666667[/C][C]0.147876703044129[/C][C]21.2079834220457[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]3.13733333333333[/C][C]0.147320486696103[/C][C]21.2959745361493[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]3.136[/C][C]0.146658101958455[/C][C]21.3830668617842[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]3.13[/C][C]0.145151197227226[/C][C]21.5637215523628[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]3.13166666666667[/C][C]0.144902688302229[/C][C]21.6122054280652[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]3.1335[/C][C]0.144630607797466[/C][C]21.6655384895292[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]3.1115[/C][C]0.139722045504638[/C][C]22.2692130562655[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]3.09416666666667[/C][C]0.135620209913935[/C][C]22.8149378962784[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]3.10116666666667[/C][C]0.134590421093383[/C][C]23.0415109892180[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]3.09366666666667[/C][C]0.131158240276648[/C][C]23.5872840329459[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]3.09366666666667[/C][C]0.131158240276648[/C][C]23.5872840329459[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]3.10216666666667[/C][C]0.129084584818114[/C][C]24.0320458948508[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]3.10216666666667[/C][C]0.127299657968986[/C][C]24.3690102248543[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]3.08[/C][C]0.123907884502189[/C][C]24.8571752505836[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]3.05[/C][C]0.113543590275521[/C][C]26.8619302296059[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]3.25448275862069[/C][C]0.184401907980628[/C][C]17.6488562090289[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]3.21732142857143[/C][C]0.175312613371758[/C][C]18.3519107193329[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]3.18203703703704[/C][C]0.167167043341171[/C][C]19.0350739801195[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]3.15346153846154[/C][C]0.161323682901210[/C][C]19.5474184679544[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]3.1236[/C][C]0.154332204635828[/C][C]20.2394568740247[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]3.11145833333333[/C][C]0.153124951753744[/C][C]20.3197342934494[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]3.10608695652174[/C][C]0.153547260426961[/C][C]20.2288660044132[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]3.1[/C][C]0.153861844621868[/C][C]20.1479451102291[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]3.09357142857143[/C][C]0.154039612621275[/C][C]20.0829603238315[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]3.0875[/C][C]0.154219602831274[/C][C]20.0201527128683[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]3.08052631578947[/C][C]0.154050086702821[/C][C]19.9969138721235[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]3.0725[/C][C]0.153401317744387[/C][C]20.0291630161856[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]3.06676470588235[/C][C]0.153257394542189[/C][C]20.0105496706597[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]3.0628125[/C][C]0.153481265520999[/C][C]19.9556114526626[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]3.05733333333333[/C][C]0.153314291671231[/C][C]19.9416068783040[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]3.05214285714286[/C][C]0.153215411127945[/C][C]19.9205995968260[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]3.04615384615385[/C][C]0.152127554701337[/C][C]20.0236824428959[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]3.03791666666667[/C][C]0.150152071666041[/C][C]20.2322660817056[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]3.02818181818182[/C][C]0.146634150808713[/C][C]20.6512725820068[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]3.02[/C][C]0.141292902194435[/C][C]21.3740389863613[/C][/ROW]
[ROW][C]Median[/C][C]3.06[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4.81[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]3.02129032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]3.05733333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]3.02129032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]3.05733333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]3.05733333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]3.02129032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]3.05733333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]3.10181818181818[/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=49842&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49842&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 Mean3.306333333333330.19816074720433416.6851073180704
Geometric Mean2.99290311926345
Harmonic Mean2.72647590549401
Quadratic Mean3.63986721369521
Winsorized Mean ( 1 / 20 )3.289166666666670.19164988258616817.1623724589960
Winsorized Mean ( 2 / 20 )3.280833333333330.1868972483748617.5542088600093
Winsorized Mean ( 3 / 20 )3.256333333333330.17818624273442618.2748863400564
Winsorized Mean ( 4 / 20 )3.2530.17699824442935418.3787133623146
Winsorized Mean ( 5 / 20 )3.172166666666670.15538272262269820.4151826736192
Winsorized Mean ( 6 / 20 )3.136166666666670.14787670304412921.2079834220457
Winsorized Mean ( 7 / 20 )3.137333333333330.14732048669610321.2959745361493
Winsorized Mean ( 8 / 20 )3.1360.14665810195845521.3830668617842
Winsorized Mean ( 9 / 20 )3.130.14515119722722621.5637215523628
Winsorized Mean ( 10 / 20 )3.131666666666670.14490268830222921.6122054280652
Winsorized Mean ( 11 / 20 )3.13350.14463060779746621.6655384895292
Winsorized Mean ( 12 / 20 )3.11150.13972204550463822.2692130562655
Winsorized Mean ( 13 / 20 )3.094166666666670.13562020991393522.8149378962784
Winsorized Mean ( 14 / 20 )3.101166666666670.13459042109338323.0415109892180
Winsorized Mean ( 15 / 20 )3.093666666666670.13115824027664823.5872840329459
Winsorized Mean ( 16 / 20 )3.093666666666670.13115824027664823.5872840329459
Winsorized Mean ( 17 / 20 )3.102166666666670.12908458481811424.0320458948508
Winsorized Mean ( 18 / 20 )3.102166666666670.12729965796898624.3690102248543
Winsorized Mean ( 19 / 20 )3.080.12390788450218924.8571752505836
Winsorized Mean ( 20 / 20 )3.050.11354359027552126.8619302296059
Trimmed Mean ( 1 / 20 )3.254482758620690.18440190798062817.6488562090289
Trimmed Mean ( 2 / 20 )3.217321428571430.17531261337175818.3519107193329
Trimmed Mean ( 3 / 20 )3.182037037037040.16716704334117119.0350739801195
Trimmed Mean ( 4 / 20 )3.153461538461540.16132368290121019.5474184679544
Trimmed Mean ( 5 / 20 )3.12360.15433220463582820.2394568740247
Trimmed Mean ( 6 / 20 )3.111458333333330.15312495175374420.3197342934494
Trimmed Mean ( 7 / 20 )3.106086956521740.15354726042696120.2288660044132
Trimmed Mean ( 8 / 20 )3.10.15386184462186820.1479451102291
Trimmed Mean ( 9 / 20 )3.093571428571430.15403961262127520.0829603238315
Trimmed Mean ( 10 / 20 )3.08750.15421960283127420.0201527128683
Trimmed Mean ( 11 / 20 )3.080526315789470.15405008670282119.9969138721235
Trimmed Mean ( 12 / 20 )3.07250.15340131774438720.0291630161856
Trimmed Mean ( 13 / 20 )3.066764705882350.15325739454218920.0105496706597
Trimmed Mean ( 14 / 20 )3.06281250.15348126552099919.9556114526626
Trimmed Mean ( 15 / 20 )3.057333333333330.15331429167123119.9416068783040
Trimmed Mean ( 16 / 20 )3.052142857142860.15321541112794519.9205995968260
Trimmed Mean ( 17 / 20 )3.046153846153850.15212755470133720.0236824428959
Trimmed Mean ( 18 / 20 )3.037916666666670.15015207166604120.2322660817056
Trimmed Mean ( 19 / 20 )3.028181818181820.14663415080871320.6512725820068
Trimmed Mean ( 20 / 20 )3.020.14129290219443521.3740389863613
Median3.06
Midrange4.81
Midmean - Weighted Average at Xnp3.02129032258065
Midmean - Weighted Average at X(n+1)p3.05733333333333
Midmean - Empirical Distribution Function3.02129032258065
Midmean - Empirical Distribution Function - Averaging3.05733333333333
Midmean - Empirical Distribution Function - Interpolation3.05733333333333
Midmean - Closest Observation3.02129032258065
Midmean - True Basic - Statistics Graphics Toolkit3.05733333333333
Midmean - MS Excel (old versions)3.10181818181818
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')