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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 09:25:16 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/20/t12560523740ulnvvlybw7rpni.htm/, Retrieved Thu, 02 May 2024 22:50:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48727, Retrieved Thu, 02 May 2024 22:50:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact155
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD      [Central Tendency] [] [2009-10-20 15:12:09] [90f6d58d515a4caed6fb4b8be4e11eaa]
-    D          [Central Tendency] [] [2009-10-20 15:25:16] [2b548c9d2e9bba6e1eaf65bd4d551f41] [Current]
-    D            [Central Tendency] [] [2009-10-20 17:39:50] [90f6d58d515a4caed6fb4b8be4e11eaa]
-   PD              [Central Tendency] [WS3 Q2 Yt-Xt Cent...] [2009-10-22 20:19:23] [1b4c3bbe3f2ba180dd536c5a6a81a8e6]
- RMPD            [Univariate Explorative Data Analysis] [] [2009-10-20 17:46:31] [90f6d58d515a4caed6fb4b8be4e11eaa]
-    D              [Univariate Explorative Data Analysis] [WS3 Q2 Yt-Xt] [2009-10-22 20:33:00] [1b4c3bbe3f2ba180dd536c5a6a81a8e6]
-    D                [Univariate Explorative Data Analysis] [WS3 Q2 Yt-Xt Assu...] [2009-10-23 07:32:53] [1b4c3bbe3f2ba180dd536c5a6a81a8e6]
-    D            [Central Tendency] [] [2009-10-20 17:51:36] [90f6d58d515a4caed6fb4b8be4e11eaa]
- RMPD            [Univariate Explorative Data Analysis] [] [2009-10-20 17:58:47] [90f6d58d515a4caed6fb4b8be4e11eaa]
-    D              [Univariate Explorative Data Analysis] [WS3 Q2 Yt/Xt] [2009-10-22 20:03:33] [1b4c3bbe3f2ba180dd536c5a6a81a8e6]
-    D              [Univariate Explorative Data Analysis] [] [2009-10-27 20:33:59] [90f6d58d515a4caed6fb4b8be4e11eaa]
-    D                [Univariate Explorative Data Analysis] [] [2009-10-27 20:39:34] [90f6d58d515a4caed6fb4b8be4e11eaa]
-    D                  [Univariate Explorative Data Analysis] [] [2009-10-27 20:42:51] [90f6d58d515a4caed6fb4b8be4e11eaa]
-    D            [Central Tendency] [WS3 Q2 Yt Central...] [2009-10-23 06:57:10] [1b4c3bbe3f2ba180dd536c5a6a81a8e6]
-    D              [Central Tendency] [WS3 Q2 Central Te...] [2009-10-23 07:40:09] [1b4c3bbe3f2ba180dd536c5a6a81a8e6]
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Dataseries X:
8
8.1
7.7
7.5
7.6
7.8
7.8
7.8
7.5
7.5
7.1
7.5
7.5
7.6
7.7
7.7
7.9
8.1
8.2
8.2
8.2
7.9
7.3
6.9
6.6
6.7
6.9
7
7.1
7.2
7.1
6.9
7
6.8
6.4
6.7
6.6
6.4
6.3
6.2
6.5
6.8
6.8
6.4
6.1
5.8
6.1
7.2
7.3
6.9
6.1
5.8
6.2
7.1
7.7
7.9
7.7
7.4
7.5
8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48727&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]3 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=48727&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48727&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.171666666666670.084909112813612284.4628618651276
Geometric Mean7.14127905049718
Harmonic Mean7.11020076115804
Quadratic Mean7.2012614635678
Winsorized Mean ( 1 / 20 )7.171666666666670.084909112813612284.4628618651276
Winsorized Mean ( 2 / 20 )7.181666666666670.082424136208729487.13062698625
Winsorized Mean ( 3 / 20 )7.176666666666670.081419839149658888.143955350675
Winsorized Mean ( 4 / 20 )7.176666666666670.081419839149658888.143955350675
Winsorized Mean ( 5 / 20 )7.176666666666670.078054257047995291.9445900593708
Winsorized Mean ( 6 / 20 )7.176666666666670.078054257047995291.9445900593708
Winsorized Mean ( 7 / 20 )7.176666666666670.073621672482589797.4803536059823
Winsorized Mean ( 8 / 20 )7.190.0710176233399764101.242475625803
Winsorized Mean ( 9 / 20 )7.190.0710176233399764101.242475625803
Winsorized Mean ( 10 / 20 )7.173333333333330.0683074913241448105.015324004408
Winsorized Mean ( 11 / 20 )7.191666666666670.0648898095412334110.828906996511
Winsorized Mean ( 12 / 20 )7.211666666666670.061391200287118117.470690146775
Winsorized Mean ( 13 / 20 )7.190.0580132461009022123.937212330688
Winsorized Mean ( 14 / 20 )7.213333333333330.0541219937470554133.279150192537
Winsorized Mean ( 15 / 20 )7.213333333333330.0541219937470554133.279150192537
Winsorized Mean ( 16 / 20 )7.240.0499830479737457144.849109718217
Winsorized Mean ( 17 / 20 )7.240.0499830479737457144.849109718217
Winsorized Mean ( 18 / 20 )7.210.0454543913710794158.620537697649
Winsorized Mean ( 19 / 20 )7.241666666666670.0407757867297186177.597227361127
Winsorized Mean ( 20 / 20 )7.208333333333330.0359921261529437200.275285286079
Trimmed Mean ( 1 / 20 )7.177586206896550.082645428237256586.8479522701644
Trimmed Mean ( 2 / 20 )7.183928571428570.079844686317936389.9737841391553
Trimmed Mean ( 3 / 20 )7.185185185185190.078035246538713892.0761515326356
Trimmed Mean ( 4 / 20 )7.188461538461540.07623561586521694.292693210096
Trimmed Mean ( 5 / 20 )7.1920.07394647816260897.2595339048443
Trimmed Mean ( 6 / 20 )7.195833333333330.07219692910438899.66952088681
Trimmed Mean ( 7 / 20 )7.20.0699205898780101102.973959638524
Trimmed Mean ( 8 / 20 )7.204545454545450.0682733705275941105.524971139862
Trimmed Mean ( 9 / 20 )7.207142857142860.0668168624998129107.864131710211
Trimmed Mean ( 10 / 20 )7.210.0648271864464601111.218770938866
Trimmed Mean ( 11 / 20 )7.21578947368420.0628310652194201114.844296344254
Trimmed Mean ( 12 / 20 )7.219444444444440.0610515582844487118.251599915074
Trimmed Mean ( 13 / 20 )7.220588235294120.0595256669222931121.302097206574
Trimmed Mean ( 14 / 20 )7.2250.0581987695247378124.143518136220
Trimmed Mean ( 15 / 20 )7.226666666666670.0573221052892274126.071201157100
Trimmed Mean ( 16 / 20 )7.228571428571430.0558382828550408129.455474971127
Trimmed Mean ( 17 / 20 )7.226923076923080.0547884581634581131.905940031420
Trimmed Mean ( 18 / 20 )7.2250.0529047544505998136.566175857529
Trimmed Mean ( 19 / 20 )7.227272727272730.0514641968523212140.433022748061
Trimmed Mean ( 20 / 20 )7.2250.0507185214793632142.452890763777
Median7.2
Midrange7
Midmean - Weighted Average at Xnp7.23939393939394
Midmean - Weighted Average at X(n+1)p7.23939393939394
Midmean - Empirical Distribution Function7.23939393939394
Midmean - Empirical Distribution Function - Averaging7.23939393939394
Midmean - Empirical Distribution Function - Interpolation7.23939393939394
Midmean - Closest Observation7.23939393939394
Midmean - True Basic - Statistics Graphics Toolkit7.23939393939394
Midmean - MS Excel (old versions)7.23939393939394
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.17166666666667 & 0.0849091128136122 & 84.4628618651276 \tabularnewline
Geometric Mean & 7.14127905049718 &  &  \tabularnewline
Harmonic Mean & 7.11020076115804 &  &  \tabularnewline
Quadratic Mean & 7.2012614635678 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.17166666666667 & 0.0849091128136122 & 84.4628618651276 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.18166666666667 & 0.0824241362087294 & 87.13062698625 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.17666666666667 & 0.0814198391496588 & 88.143955350675 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.17666666666667 & 0.0814198391496588 & 88.143955350675 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.17666666666667 & 0.0780542570479952 & 91.9445900593708 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.17666666666667 & 0.0780542570479952 & 91.9445900593708 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.17666666666667 & 0.0736216724825897 & 97.4803536059823 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.19 & 0.0710176233399764 & 101.242475625803 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.19 & 0.0710176233399764 & 101.242475625803 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.17333333333333 & 0.0683074913241448 & 105.015324004408 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.19166666666667 & 0.0648898095412334 & 110.828906996511 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7.21166666666667 & 0.061391200287118 & 117.470690146775 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7.19 & 0.0580132461009022 & 123.937212330688 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7.21333333333333 & 0.0541219937470554 & 133.279150192537 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7.21333333333333 & 0.0541219937470554 & 133.279150192537 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.24 & 0.0499830479737457 & 144.849109718217 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7.24 & 0.0499830479737457 & 144.849109718217 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7.21 & 0.0454543913710794 & 158.620537697649 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7.24166666666667 & 0.0407757867297186 & 177.597227361127 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7.20833333333333 & 0.0359921261529437 & 200.275285286079 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.17758620689655 & 0.0826454282372565 & 86.8479522701644 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.18392857142857 & 0.0798446863179363 & 89.9737841391553 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.18518518518519 & 0.0780352465387138 & 92.0761515326356 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.18846153846154 & 0.076235615865216 & 94.292693210096 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7.192 & 0.073946478162608 & 97.2595339048443 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7.19583333333333 & 0.072196929104388 & 99.66952088681 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7.2 & 0.0699205898780101 & 102.973959638524 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7.20454545454545 & 0.0682733705275941 & 105.524971139862 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7.20714285714286 & 0.0668168624998129 & 107.864131710211 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7.21 & 0.0648271864464601 & 111.218770938866 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7.2157894736842 & 0.0628310652194201 & 114.844296344254 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7.21944444444444 & 0.0610515582844487 & 118.251599915074 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7.22058823529412 & 0.0595256669222931 & 121.302097206574 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7.225 & 0.0581987695247378 & 124.143518136220 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7.22666666666667 & 0.0573221052892274 & 126.071201157100 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7.22857142857143 & 0.0558382828550408 & 129.455474971127 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7.22692307692308 & 0.0547884581634581 & 131.905940031420 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7.225 & 0.0529047544505998 & 136.566175857529 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7.22727272727273 & 0.0514641968523212 & 140.433022748061 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7.225 & 0.0507185214793632 & 142.452890763777 \tabularnewline
Median & 7.2 &  &  \tabularnewline
Midrange & 7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.23939393939394 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.23939393939394 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.23939393939394 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.23939393939394 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.23939393939394 &  &  \tabularnewline
Midmean - Closest Observation & 7.23939393939394 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.23939393939394 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.23939393939394 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48727&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]7.17166666666667[/C][C]0.0849091128136122[/C][C]84.4628618651276[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.14127905049718[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.11020076115804[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.2012614635678[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.17166666666667[/C][C]0.0849091128136122[/C][C]84.4628618651276[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.18166666666667[/C][C]0.0824241362087294[/C][C]87.13062698625[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.17666666666667[/C][C]0.0814198391496588[/C][C]88.143955350675[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.17666666666667[/C][C]0.0814198391496588[/C][C]88.143955350675[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.17666666666667[/C][C]0.0780542570479952[/C][C]91.9445900593708[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.17666666666667[/C][C]0.0780542570479952[/C][C]91.9445900593708[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.17666666666667[/C][C]0.0736216724825897[/C][C]97.4803536059823[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.19[/C][C]0.0710176233399764[/C][C]101.242475625803[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.19[/C][C]0.0710176233399764[/C][C]101.242475625803[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.17333333333333[/C][C]0.0683074913241448[/C][C]105.015324004408[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.19166666666667[/C][C]0.0648898095412334[/C][C]110.828906996511[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7.21166666666667[/C][C]0.061391200287118[/C][C]117.470690146775[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7.19[/C][C]0.0580132461009022[/C][C]123.937212330688[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7.21333333333333[/C][C]0.0541219937470554[/C][C]133.279150192537[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7.21333333333333[/C][C]0.0541219937470554[/C][C]133.279150192537[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.24[/C][C]0.0499830479737457[/C][C]144.849109718217[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7.24[/C][C]0.0499830479737457[/C][C]144.849109718217[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7.21[/C][C]0.0454543913710794[/C][C]158.620537697649[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7.24166666666667[/C][C]0.0407757867297186[/C][C]177.597227361127[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7.20833333333333[/C][C]0.0359921261529437[/C][C]200.275285286079[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.17758620689655[/C][C]0.0826454282372565[/C][C]86.8479522701644[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.18392857142857[/C][C]0.0798446863179363[/C][C]89.9737841391553[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.18518518518519[/C][C]0.0780352465387138[/C][C]92.0761515326356[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.18846153846154[/C][C]0.076235615865216[/C][C]94.292693210096[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7.192[/C][C]0.073946478162608[/C][C]97.2595339048443[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7.19583333333333[/C][C]0.072196929104388[/C][C]99.66952088681[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7.2[/C][C]0.0699205898780101[/C][C]102.973959638524[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7.20454545454545[/C][C]0.0682733705275941[/C][C]105.524971139862[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7.20714285714286[/C][C]0.0668168624998129[/C][C]107.864131710211[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7.21[/C][C]0.0648271864464601[/C][C]111.218770938866[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7.2157894736842[/C][C]0.0628310652194201[/C][C]114.844296344254[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7.21944444444444[/C][C]0.0610515582844487[/C][C]118.251599915074[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7.22058823529412[/C][C]0.0595256669222931[/C][C]121.302097206574[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7.225[/C][C]0.0581987695247378[/C][C]124.143518136220[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7.22666666666667[/C][C]0.0573221052892274[/C][C]126.071201157100[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7.22857142857143[/C][C]0.0558382828550408[/C][C]129.455474971127[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7.22692307692308[/C][C]0.0547884581634581[/C][C]131.905940031420[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7.225[/C][C]0.0529047544505998[/C][C]136.566175857529[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7.22727272727273[/C][C]0.0514641968523212[/C][C]140.433022748061[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7.225[/C][C]0.0507185214793632[/C][C]142.452890763777[/C][/ROW]
[ROW][C]Median[/C][C]7.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.23939393939394[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.23939393939394[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.23939393939394[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.23939393939394[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.23939393939394[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.23939393939394[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.23939393939394[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.23939393939394[/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=48727&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48727&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 Mean7.171666666666670.084909112813612284.4628618651276
Geometric Mean7.14127905049718
Harmonic Mean7.11020076115804
Quadratic Mean7.2012614635678
Winsorized Mean ( 1 / 20 )7.171666666666670.084909112813612284.4628618651276
Winsorized Mean ( 2 / 20 )7.181666666666670.082424136208729487.13062698625
Winsorized Mean ( 3 / 20 )7.176666666666670.081419839149658888.143955350675
Winsorized Mean ( 4 / 20 )7.176666666666670.081419839149658888.143955350675
Winsorized Mean ( 5 / 20 )7.176666666666670.078054257047995291.9445900593708
Winsorized Mean ( 6 / 20 )7.176666666666670.078054257047995291.9445900593708
Winsorized Mean ( 7 / 20 )7.176666666666670.073621672482589797.4803536059823
Winsorized Mean ( 8 / 20 )7.190.0710176233399764101.242475625803
Winsorized Mean ( 9 / 20 )7.190.0710176233399764101.242475625803
Winsorized Mean ( 10 / 20 )7.173333333333330.0683074913241448105.015324004408
Winsorized Mean ( 11 / 20 )7.191666666666670.0648898095412334110.828906996511
Winsorized Mean ( 12 / 20 )7.211666666666670.061391200287118117.470690146775
Winsorized Mean ( 13 / 20 )7.190.0580132461009022123.937212330688
Winsorized Mean ( 14 / 20 )7.213333333333330.0541219937470554133.279150192537
Winsorized Mean ( 15 / 20 )7.213333333333330.0541219937470554133.279150192537
Winsorized Mean ( 16 / 20 )7.240.0499830479737457144.849109718217
Winsorized Mean ( 17 / 20 )7.240.0499830479737457144.849109718217
Winsorized Mean ( 18 / 20 )7.210.0454543913710794158.620537697649
Winsorized Mean ( 19 / 20 )7.241666666666670.0407757867297186177.597227361127
Winsorized Mean ( 20 / 20 )7.208333333333330.0359921261529437200.275285286079
Trimmed Mean ( 1 / 20 )7.177586206896550.082645428237256586.8479522701644
Trimmed Mean ( 2 / 20 )7.183928571428570.079844686317936389.9737841391553
Trimmed Mean ( 3 / 20 )7.185185185185190.078035246538713892.0761515326356
Trimmed Mean ( 4 / 20 )7.188461538461540.07623561586521694.292693210096
Trimmed Mean ( 5 / 20 )7.1920.07394647816260897.2595339048443
Trimmed Mean ( 6 / 20 )7.195833333333330.07219692910438899.66952088681
Trimmed Mean ( 7 / 20 )7.20.0699205898780101102.973959638524
Trimmed Mean ( 8 / 20 )7.204545454545450.0682733705275941105.524971139862
Trimmed Mean ( 9 / 20 )7.207142857142860.0668168624998129107.864131710211
Trimmed Mean ( 10 / 20 )7.210.0648271864464601111.218770938866
Trimmed Mean ( 11 / 20 )7.21578947368420.0628310652194201114.844296344254
Trimmed Mean ( 12 / 20 )7.219444444444440.0610515582844487118.251599915074
Trimmed Mean ( 13 / 20 )7.220588235294120.0595256669222931121.302097206574
Trimmed Mean ( 14 / 20 )7.2250.0581987695247378124.143518136220
Trimmed Mean ( 15 / 20 )7.226666666666670.0573221052892274126.071201157100
Trimmed Mean ( 16 / 20 )7.228571428571430.0558382828550408129.455474971127
Trimmed Mean ( 17 / 20 )7.226923076923080.0547884581634581131.905940031420
Trimmed Mean ( 18 / 20 )7.2250.0529047544505998136.566175857529
Trimmed Mean ( 19 / 20 )7.227272727272730.0514641968523212140.433022748061
Trimmed Mean ( 20 / 20 )7.2250.0507185214793632142.452890763777
Median7.2
Midrange7
Midmean - Weighted Average at Xnp7.23939393939394
Midmean - Weighted Average at X(n+1)p7.23939393939394
Midmean - Empirical Distribution Function7.23939393939394
Midmean - Empirical Distribution Function - Averaging7.23939393939394
Midmean - Empirical Distribution Function - Interpolation7.23939393939394
Midmean - Closest Observation7.23939393939394
Midmean - True Basic - Statistics Graphics Toolkit7.23939393939394
Midmean - MS Excel (old versions)7.23939393939394
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')