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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 computationSun, 29 Nov 2009 06:31:29 -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/2009/Nov/29/t1259501566r9noqvy5zgx72ul.htm/, Retrieved Thu, 28 Mar 2024 09:25:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=61593, Retrieved Thu, 28 Mar 2024 09:25:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsJSSHWPapWS1
Estimated Impact145
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]
- RMP       [Central Tendency] [Constante part 1] [2009-10-17 13:50:10] [214e6e00abbde49700521a7ef1d30da2]
-  MPD          [Central Tendency] [Paper constante term] [2009-11-29 13:31:29] [c8fd62404619100d8e91184019148412] [Current]
- RMP             [Harrell-Davis Quantiles] [Harell Davis Quan...] [2009-12-10 13:34:07] [214e6e00abbde49700521a7ef1d30da2]
- RMP               [Univariate Explorative Data Analysis] [Assumpties] [2009-12-10 13:48:30] [214e6e00abbde49700521a7ef1d30da2]
- RM              [Percentiles] [Percentiles] [2009-12-10 13:36:13] [214e6e00abbde49700521a7ef1d30da2]
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Dataseries X:
6
5
7
10
10
5
8
2
11
7
11
9
2
3
12
9
7
4
6
9
10
2
6
2
6
6
9
2
10
16
4
4
11
3
5
3
5
11
8
3
1
7
5
6
9
7
8
4
6
4
5
5
13
4
8
4
5
9
4
8




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=61593&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=61593&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61593&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 Mean6.516666666666670.40927914214611115.9223033758711
Geometric Mean5.68812419796339
Harmonic Mean4.76479950812926
Quadratic Mean7.23532998556389
Winsorized Mean ( 1 / 20 )6.483333333333330.38874829312152216.6774580057299
Winsorized Mean ( 2 / 20 )6.450.37987880910169216.9790992428676
Winsorized Mean ( 3 / 20 )6.40.36838324431122717.3732114552772
Winsorized Mean ( 4 / 20 )6.40.36838324431122717.3732114552772
Winsorized Mean ( 5 / 20 )6.40.36838324431122717.3732114552772
Winsorized Mean ( 6 / 20 )6.50.34973759331932118.5853626380545
Winsorized Mean ( 7 / 20 )6.383333333333330.32598539590409519.5816543119352
Winsorized Mean ( 8 / 20 )6.383333333333330.32598539590409519.5816543119352
Winsorized Mean ( 9 / 20 )6.383333333333330.32598539590409519.5816543119352
Winsorized Mean ( 10 / 20 )6.550.29917494834546921.8935443499649
Winsorized Mean ( 11 / 20 )6.366666666666670.26571156643029323.960818688474
Winsorized Mean ( 12 / 20 )6.366666666666670.26571156643029323.960818688474
Winsorized Mean ( 13 / 20 )6.366666666666670.26571156643029323.960818688474
Winsorized Mean ( 14 / 20 )6.366666666666670.26571156643029323.960818688474
Winsorized Mean ( 15 / 20 )6.366666666666670.26571156643029323.960818688474
Winsorized Mean ( 16 / 20 )6.366666666666670.26571156643029323.960818688474
Winsorized Mean ( 17 / 20 )6.083333333333330.22079935246500227.5514093017894
Winsorized Mean ( 18 / 20 )6.383333333333330.17642345480376636.1818860220907
Winsorized Mean ( 19 / 20 )6.383333333333330.17642345480376636.1818860220907
Winsorized Mean ( 20 / 20 )6.383333333333330.17642345480376636.1818860220907
Trimmed Mean ( 1 / 20 )6.448275862068970.37798812609432917.0594667316607
Trimmed Mean ( 2 / 20 )6.410714285714290.36465317601182417.5803056367907
Trimmed Mean ( 3 / 20 )6.388888888888890.35408829856021118.0432081909154
Trimmed Mean ( 4 / 20 )6.384615384615390.34644700172306418.4288371752716
Trimmed Mean ( 5 / 20 )6.380.33671886171810318.9475575185962
Trimmed Mean ( 6 / 20 )6.3750.32429000461346119.6583302269791
Trimmed Mean ( 7 / 20 )6.347826086956520.31426225440746720.1991362243779
Trimmed Mean ( 8 / 20 )6.340909090909090.30834616783063320.5642545698573
Trimmed Mean ( 9 / 20 )6.333333333333330.30034178491539221.0870869503472
Trimmed Mean ( 10 / 20 )6.3250.28953432992501621.8454233100374
Trimmed Mean ( 11 / 20 )6.289473684210530.28200636257070322.3025949729545
Trimmed Mean ( 12 / 20 )6.277777777777780.28062037597876322.3710689428086
Trimmed Mean ( 13 / 20 )6.264705882352940.27784767216846122.5472678373011
Trimmed Mean ( 14 / 20 )6.250.27312410035284022.8833705701028
Trimmed Mean ( 15 / 20 )6.233333333333330.26558689438192023.4700335942393
Trimmed Mean ( 16 / 20 )6.214285714285710.25384421574157924.4807063896703
Trimmed Mean ( 17 / 20 )6.192307692307690.23546504407713826.2982036954882
Trimmed Mean ( 18 / 20 )6.208333333333330.22505367046411827.5860123522098
Trimmed Mean ( 19 / 20 )6.181818181818180.22444123630849727.5431479682334
Trimmed Mean ( 20 / 20 )6.150.22094295524792027.8352391598053
Median6
Midrange8.5
Midmean - Weighted Average at Xnp6.23076923076923
Midmean - Weighted Average at X(n+1)p6.23076923076923
Midmean - Empirical Distribution Function6.23076923076923
Midmean - Empirical Distribution Function - Averaging6.23076923076923
Midmean - Empirical Distribution Function - Interpolation6.23076923076923
Midmean - Closest Observation6.23076923076923
Midmean - True Basic - Statistics Graphics Toolkit6.23076923076923
Midmean - MS Excel (old versions)6.23076923076923
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.51666666666667 & 0.409279142146111 & 15.9223033758711 \tabularnewline
Geometric Mean & 5.68812419796339 &  &  \tabularnewline
Harmonic Mean & 4.76479950812926 &  &  \tabularnewline
Quadratic Mean & 7.23532998556389 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 6.48333333333333 & 0.388748293121522 & 16.6774580057299 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 6.45 & 0.379878809101692 & 16.9790992428676 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 6.4 & 0.368383244311227 & 17.3732114552772 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 6.4 & 0.368383244311227 & 17.3732114552772 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 6.4 & 0.368383244311227 & 17.3732114552772 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 6.5 & 0.349737593319321 & 18.5853626380545 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 6.38333333333333 & 0.325985395904095 & 19.5816543119352 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 6.38333333333333 & 0.325985395904095 & 19.5816543119352 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 6.38333333333333 & 0.325985395904095 & 19.5816543119352 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 6.55 & 0.299174948345469 & 21.8935443499649 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 6.36666666666667 & 0.265711566430293 & 23.960818688474 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 6.36666666666667 & 0.265711566430293 & 23.960818688474 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 6.36666666666667 & 0.265711566430293 & 23.960818688474 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 6.36666666666667 & 0.265711566430293 & 23.960818688474 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 6.36666666666667 & 0.265711566430293 & 23.960818688474 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 6.36666666666667 & 0.265711566430293 & 23.960818688474 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 6.08333333333333 & 0.220799352465002 & 27.5514093017894 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 6.38333333333333 & 0.176423454803766 & 36.1818860220907 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 6.38333333333333 & 0.176423454803766 & 36.1818860220907 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 6.38333333333333 & 0.176423454803766 & 36.1818860220907 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 6.44827586206897 & 0.377988126094329 & 17.0594667316607 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 6.41071428571429 & 0.364653176011824 & 17.5803056367907 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 6.38888888888889 & 0.354088298560211 & 18.0432081909154 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 6.38461538461539 & 0.346447001723064 & 18.4288371752716 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 6.38 & 0.336718861718103 & 18.9475575185962 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 6.375 & 0.324290004613461 & 19.6583302269791 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 6.34782608695652 & 0.314262254407467 & 20.1991362243779 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 6.34090909090909 & 0.308346167830633 & 20.5642545698573 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 6.33333333333333 & 0.300341784915392 & 21.0870869503472 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 6.325 & 0.289534329925016 & 21.8454233100374 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 6.28947368421053 & 0.282006362570703 & 22.3025949729545 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 6.27777777777778 & 0.280620375978763 & 22.3710689428086 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 6.26470588235294 & 0.277847672168461 & 22.5472678373011 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 6.25 & 0.273124100352840 & 22.8833705701028 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 6.23333333333333 & 0.265586894381920 & 23.4700335942393 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 6.21428571428571 & 0.253844215741579 & 24.4807063896703 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 6.19230769230769 & 0.235465044077138 & 26.2982036954882 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 6.20833333333333 & 0.225053670464118 & 27.5860123522098 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 6.18181818181818 & 0.224441236308497 & 27.5431479682334 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 6.15 & 0.220942955247920 & 27.8352391598053 \tabularnewline
Median & 6 &  &  \tabularnewline
Midrange & 8.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6.23076923076923 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6.23076923076923 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6.23076923076923 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6.23076923076923 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6.23076923076923 &  &  \tabularnewline
Midmean - Closest Observation & 6.23076923076923 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6.23076923076923 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6.23076923076923 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=61593&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]6.51666666666667[/C][C]0.409279142146111[/C][C]15.9223033758711[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]5.68812419796339[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4.76479950812926[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.23532998556389[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]6.48333333333333[/C][C]0.388748293121522[/C][C]16.6774580057299[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]6.45[/C][C]0.379878809101692[/C][C]16.9790992428676[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]6.4[/C][C]0.368383244311227[/C][C]17.3732114552772[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]6.4[/C][C]0.368383244311227[/C][C]17.3732114552772[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]6.4[/C][C]0.368383244311227[/C][C]17.3732114552772[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]6.5[/C][C]0.349737593319321[/C][C]18.5853626380545[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]6.38333333333333[/C][C]0.325985395904095[/C][C]19.5816543119352[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]6.38333333333333[/C][C]0.325985395904095[/C][C]19.5816543119352[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]6.38333333333333[/C][C]0.325985395904095[/C][C]19.5816543119352[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]6.55[/C][C]0.299174948345469[/C][C]21.8935443499649[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]6.36666666666667[/C][C]0.265711566430293[/C][C]23.960818688474[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]6.36666666666667[/C][C]0.265711566430293[/C][C]23.960818688474[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]6.36666666666667[/C][C]0.265711566430293[/C][C]23.960818688474[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]6.36666666666667[/C][C]0.265711566430293[/C][C]23.960818688474[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]6.36666666666667[/C][C]0.265711566430293[/C][C]23.960818688474[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]6.36666666666667[/C][C]0.265711566430293[/C][C]23.960818688474[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]6.08333333333333[/C][C]0.220799352465002[/C][C]27.5514093017894[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]6.38333333333333[/C][C]0.176423454803766[/C][C]36.1818860220907[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]6.38333333333333[/C][C]0.176423454803766[/C][C]36.1818860220907[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]6.38333333333333[/C][C]0.176423454803766[/C][C]36.1818860220907[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]6.44827586206897[/C][C]0.377988126094329[/C][C]17.0594667316607[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]6.41071428571429[/C][C]0.364653176011824[/C][C]17.5803056367907[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]6.38888888888889[/C][C]0.354088298560211[/C][C]18.0432081909154[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]6.38461538461539[/C][C]0.346447001723064[/C][C]18.4288371752716[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]6.38[/C][C]0.336718861718103[/C][C]18.9475575185962[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]6.375[/C][C]0.324290004613461[/C][C]19.6583302269791[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]6.34782608695652[/C][C]0.314262254407467[/C][C]20.1991362243779[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]6.34090909090909[/C][C]0.308346167830633[/C][C]20.5642545698573[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]6.33333333333333[/C][C]0.300341784915392[/C][C]21.0870869503472[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]6.325[/C][C]0.289534329925016[/C][C]21.8454233100374[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]6.28947368421053[/C][C]0.282006362570703[/C][C]22.3025949729545[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]6.27777777777778[/C][C]0.280620375978763[/C][C]22.3710689428086[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]6.26470588235294[/C][C]0.277847672168461[/C][C]22.5472678373011[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]6.25[/C][C]0.273124100352840[/C][C]22.8833705701028[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]6.23333333333333[/C][C]0.265586894381920[/C][C]23.4700335942393[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]6.21428571428571[/C][C]0.253844215741579[/C][C]24.4807063896703[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]6.19230769230769[/C][C]0.235465044077138[/C][C]26.2982036954882[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]6.20833333333333[/C][C]0.225053670464118[/C][C]27.5860123522098[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]6.18181818181818[/C][C]0.224441236308497[/C][C]27.5431479682334[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]6.15[/C][C]0.220942955247920[/C][C]27.8352391598053[/C][/ROW]
[ROW][C]Median[/C][C]6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]8.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6.23076923076923[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6.23076923076923[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6.23076923076923[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6.23076923076923[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6.23076923076923[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6.23076923076923[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6.23076923076923[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6.23076923076923[/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=61593&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=61593&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 Mean6.516666666666670.40927914214611115.9223033758711
Geometric Mean5.68812419796339
Harmonic Mean4.76479950812926
Quadratic Mean7.23532998556389
Winsorized Mean ( 1 / 20 )6.483333333333330.38874829312152216.6774580057299
Winsorized Mean ( 2 / 20 )6.450.37987880910169216.9790992428676
Winsorized Mean ( 3 / 20 )6.40.36838324431122717.3732114552772
Winsorized Mean ( 4 / 20 )6.40.36838324431122717.3732114552772
Winsorized Mean ( 5 / 20 )6.40.36838324431122717.3732114552772
Winsorized Mean ( 6 / 20 )6.50.34973759331932118.5853626380545
Winsorized Mean ( 7 / 20 )6.383333333333330.32598539590409519.5816543119352
Winsorized Mean ( 8 / 20 )6.383333333333330.32598539590409519.5816543119352
Winsorized Mean ( 9 / 20 )6.383333333333330.32598539590409519.5816543119352
Winsorized Mean ( 10 / 20 )6.550.29917494834546921.8935443499649
Winsorized Mean ( 11 / 20 )6.366666666666670.26571156643029323.960818688474
Winsorized Mean ( 12 / 20 )6.366666666666670.26571156643029323.960818688474
Winsorized Mean ( 13 / 20 )6.366666666666670.26571156643029323.960818688474
Winsorized Mean ( 14 / 20 )6.366666666666670.26571156643029323.960818688474
Winsorized Mean ( 15 / 20 )6.366666666666670.26571156643029323.960818688474
Winsorized Mean ( 16 / 20 )6.366666666666670.26571156643029323.960818688474
Winsorized Mean ( 17 / 20 )6.083333333333330.22079935246500227.5514093017894
Winsorized Mean ( 18 / 20 )6.383333333333330.17642345480376636.1818860220907
Winsorized Mean ( 19 / 20 )6.383333333333330.17642345480376636.1818860220907
Winsorized Mean ( 20 / 20 )6.383333333333330.17642345480376636.1818860220907
Trimmed Mean ( 1 / 20 )6.448275862068970.37798812609432917.0594667316607
Trimmed Mean ( 2 / 20 )6.410714285714290.36465317601182417.5803056367907
Trimmed Mean ( 3 / 20 )6.388888888888890.35408829856021118.0432081909154
Trimmed Mean ( 4 / 20 )6.384615384615390.34644700172306418.4288371752716
Trimmed Mean ( 5 / 20 )6.380.33671886171810318.9475575185962
Trimmed Mean ( 6 / 20 )6.3750.32429000461346119.6583302269791
Trimmed Mean ( 7 / 20 )6.347826086956520.31426225440746720.1991362243779
Trimmed Mean ( 8 / 20 )6.340909090909090.30834616783063320.5642545698573
Trimmed Mean ( 9 / 20 )6.333333333333330.30034178491539221.0870869503472
Trimmed Mean ( 10 / 20 )6.3250.28953432992501621.8454233100374
Trimmed Mean ( 11 / 20 )6.289473684210530.28200636257070322.3025949729545
Trimmed Mean ( 12 / 20 )6.277777777777780.28062037597876322.3710689428086
Trimmed Mean ( 13 / 20 )6.264705882352940.27784767216846122.5472678373011
Trimmed Mean ( 14 / 20 )6.250.27312410035284022.8833705701028
Trimmed Mean ( 15 / 20 )6.233333333333330.26558689438192023.4700335942393
Trimmed Mean ( 16 / 20 )6.214285714285710.25384421574157924.4807063896703
Trimmed Mean ( 17 / 20 )6.192307692307690.23546504407713826.2982036954882
Trimmed Mean ( 18 / 20 )6.208333333333330.22505367046411827.5860123522098
Trimmed Mean ( 19 / 20 )6.181818181818180.22444123630849727.5431479682334
Trimmed Mean ( 20 / 20 )6.150.22094295524792027.8352391598053
Median6
Midrange8.5
Midmean - Weighted Average at Xnp6.23076923076923
Midmean - Weighted Average at X(n+1)p6.23076923076923
Midmean - Empirical Distribution Function6.23076923076923
Midmean - Empirical Distribution Function - Averaging6.23076923076923
Midmean - Empirical Distribution Function - Interpolation6.23076923076923
Midmean - Closest Observation6.23076923076923
Midmean - True Basic - Statistics Graphics Toolkit6.23076923076923
Midmean - MS Excel (old versions)6.23076923076923
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')