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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, 04 Dec 2009 05:32:51 -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/Dec/04/t12599307722vttiyg5tyd0bs7.htm/, Retrieved Sun, 28 Apr 2024 15:35:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63431, Retrieved Sun, 28 Apr 2024 15:35:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Harrell-Davis Quantiles] [WS3, part 1-3] [2009-10-20 14:26:04] [ed603017d2bee8fbd82b6d5ec04e12c3]
-   P   [Harrell-Davis Quantiles] [WS3 part 1 -3] [2009-10-20 14:31:26] [ed603017d2bee8fbd82b6d5ec04e12c3]
- RMPD    [Central Tendency] [WS part 2 Mediaan] [2009-10-20 15:29:15] [ed603017d2bee8fbd82b6d5ec04e12c3]
-  M D        [Central Tendency] [Mediaan] [2009-12-04 12:32:51] [307139c5e328127f586f26d5bcc435d8] [Current]
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Dataseries X:
5.4
5.4
5.5
5.8
5.7
5.4
5.6
5.8
6.2
6.8
6.7
6.7
6.4
6.3
6.3
6.4
6.3
6
6.3
6.3
6.6
7.5
7.8
7.9
7.8
7.6
7.5
7.6
7.5
7.3
7.6
7.5
7.6
7.9
7.9
8.1
8.2
8
7.5
6.8
6.5
6.6
7.6
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




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63431&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]2 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=63431&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63431&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.091803278688520.10672202496131166.4511686435809
Geometric Mean7.0405571082839
Harmonic Mean6.9863396004243
Quadratic Mean7.13982136893689
Winsorized Mean ( 1 / 20 )7.090163934426230.10645055595706066.6052316089947
Winsorized Mean ( 2 / 20 )7.090163934426230.10645055595706066.6052316089947
Winsorized Mean ( 3 / 20 )7.095081967213120.1051781270636367.4577705963596
Winsorized Mean ( 4 / 20 )7.095081967213110.10254750277399069.1882471565434
Winsorized Mean ( 5 / 20 )7.103278688524590.10059840662718170.6102504669825
Winsorized Mean ( 6 / 20 )7.103278688524590.096947036780490573.26968336957
Winsorized Mean ( 7 / 20 )7.103278688524590.096947036780490573.2696833695699
Winsorized Mean ( 8 / 20 )7.129508196721310.091297396173497578.091035402288
Winsorized Mean ( 9 / 20 )7.159016393442620.085487258155799683.7436659904964
Winsorized Mean ( 10 / 20 )7.159016393442620.080210687362131689.2526498510282
Winsorized Mean ( 11 / 20 )7.159016393442620.080210687362131689.2526498510282
Winsorized Mean ( 12 / 20 )7.159016393442620.080210687362131689.2526498510282
Winsorized Mean ( 13 / 20 )7.159016393442620.080210687362131689.2526498510282
Winsorized Mean ( 14 / 20 )7.159016393442620.080210687362131689.2526498510282
Winsorized Mean ( 15 / 20 )7.159016393442620.07270635036569498.4648020074537
Winsorized Mean ( 16 / 20 )7.159016393442620.07270635036569498.4648020074537
Winsorized Mean ( 17 / 20 )7.186885245901640.0679309923810932105.796853453622
Winsorized Mean ( 18 / 20 )7.186885245901640.0594361212796174120.917803705442
Winsorized Mean ( 19 / 20 )7.186885245901640.0594361212796174120.917803705442
Winsorized Mean ( 20 / 20 )7.219672131147540.0541107785052426133.423919052431
Trimmed Mean ( 1 / 20 )7.101694915254240.10480818039687967.7589753811401
Trimmed Mean ( 2 / 20 )7.11403508771930.10273327866096469.247620444362
Trimmed Mean ( 3 / 20 )7.127272727272730.10011624709483471.1899709996271
Trimmed Mean ( 4 / 20 )7.139622641509430.097439632706983873.2722655367492
Trimmed Mean ( 5 / 20 )7.152941176470590.095068724003938575.23968846131
Trimmed Mean ( 6 / 20 )7.165306122448980.092699088031318477.2964036067774
Trimmed Mean ( 7 / 20 )7.178723404255320.090733274017827379.1189724162807
Trimmed Mean ( 8 / 20 )7.193333333333330.088100034969437881.649608150879
Trimmed Mean ( 9 / 20 )7.20465116279070.086263233107624983.519373239836
Trimmed Mean ( 10 / 20 )7.212195121951220.085339717253272784.5115891413929
Trimmed Mean ( 11 / 20 )7.220512820512820.085222538500968684.725390108284
Trimmed Mean ( 12 / 20 )7.229729729729730.084794829654343285.2614452933148
Trimmed Mean ( 13 / 20 )7.240.083936750897687886.255423548917
Trimmed Mean ( 14 / 20 )7.251515151515150.082471438136825887.9275942719028
Trimmed Mean ( 15 / 20 )7.264516129032260.080127369989511190.6621062189262
Trimmed Mean ( 16 / 20 )7.279310344827590.078686775440241292.5099586823947
Trimmed Mean ( 17 / 20 )7.29629629629630.076139301314108695.82825387635
Trimmed Mean ( 18 / 20 )7.3120.073783466982786999.1007918034786
Trimmed Mean ( 19 / 20 )7.33043478260870.0726230134282177100.938179739047
Trimmed Mean ( 20 / 20 )7.352380952380950.069904372647158105.177697388003
Median7.5
Midrange6.8
Midmean - Weighted Average at Xnp7.26451612903225
Midmean - Weighted Average at X(n+1)p7.26451612903225
Midmean - Empirical Distribution Function7.26451612903225
Midmean - Empirical Distribution Function - Averaging7.26451612903225
Midmean - Empirical Distribution Function - Interpolation7.26451612903225
Midmean - Closest Observation7.13055555555555
Midmean - True Basic - Statistics Graphics Toolkit7.26451612903225
Midmean - MS Excel (old versions)7.26451612903225
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.09180327868852 & 0.106722024961311 & 66.4511686435809 \tabularnewline
Geometric Mean & 7.0405571082839 &  &  \tabularnewline
Harmonic Mean & 6.9863396004243 &  &  \tabularnewline
Quadratic Mean & 7.13982136893689 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 7.09016393442623 & 0.106450555957060 & 66.6052316089947 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 7.09016393442623 & 0.106450555957060 & 66.6052316089947 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 7.09508196721312 & 0.10517812706363 & 67.4577705963596 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 7.09508196721311 & 0.102547502773990 & 69.1882471565434 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 7.10327868852459 & 0.100598406627181 & 70.6102504669825 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 7.10327868852459 & 0.0969470367804905 & 73.26968336957 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 7.10327868852459 & 0.0969470367804905 & 73.2696833695699 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 7.12950819672131 & 0.0912973961734975 & 78.091035402288 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 7.15901639344262 & 0.0854872581557996 & 83.7436659904964 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 7.15901639344262 & 0.0802106873621316 & 89.2526498510282 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 7.15901639344262 & 0.0802106873621316 & 89.2526498510282 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 7.15901639344262 & 0.0802106873621316 & 89.2526498510282 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 7.15901639344262 & 0.0802106873621316 & 89.2526498510282 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 7.15901639344262 & 0.0802106873621316 & 89.2526498510282 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 7.15901639344262 & 0.072706350365694 & 98.4648020074537 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 7.15901639344262 & 0.072706350365694 & 98.4648020074537 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 7.18688524590164 & 0.0679309923810932 & 105.796853453622 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 7.18688524590164 & 0.0594361212796174 & 120.917803705442 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 7.18688524590164 & 0.0594361212796174 & 120.917803705442 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 7.21967213114754 & 0.0541107785052426 & 133.423919052431 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 7.10169491525424 & 0.104808180396879 & 67.7589753811401 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 7.1140350877193 & 0.102733278660964 & 69.247620444362 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 7.12727272727273 & 0.100116247094834 & 71.1899709996271 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 7.13962264150943 & 0.0974396327069838 & 73.2722655367492 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 7.15294117647059 & 0.0950687240039385 & 75.23968846131 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 7.16530612244898 & 0.0926990880313184 & 77.2964036067774 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 7.17872340425532 & 0.0907332740178273 & 79.1189724162807 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 7.19333333333333 & 0.0881000349694378 & 81.649608150879 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 7.2046511627907 & 0.0862632331076249 & 83.519373239836 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 7.21219512195122 & 0.0853397172532727 & 84.5115891413929 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 7.22051282051282 & 0.0852225385009686 & 84.725390108284 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 7.22972972972973 & 0.0847948296543432 & 85.2614452933148 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 7.24 & 0.0839367508976878 & 86.255423548917 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 7.25151515151515 & 0.0824714381368258 & 87.9275942719028 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 7.26451612903226 & 0.0801273699895111 & 90.6621062189262 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 7.27931034482759 & 0.0786867754402412 & 92.5099586823947 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 7.2962962962963 & 0.0761393013141086 & 95.82825387635 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 7.312 & 0.0737834669827869 & 99.1007918034786 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 7.3304347826087 & 0.0726230134282177 & 100.938179739047 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 7.35238095238095 & 0.069904372647158 & 105.177697388003 \tabularnewline
Median & 7.5 &  &  \tabularnewline
Midrange & 6.8 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.26451612903225 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.26451612903225 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.26451612903225 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.26451612903225 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.26451612903225 &  &  \tabularnewline
Midmean - Closest Observation & 7.13055555555555 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.26451612903225 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.26451612903225 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63431&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]7.09180327868852[/C][C]0.106722024961311[/C][C]66.4511686435809[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.0405571082839[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]6.9863396004243[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.13982136893689[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]7.09016393442623[/C][C]0.106450555957060[/C][C]66.6052316089947[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]7.09016393442623[/C][C]0.106450555957060[/C][C]66.6052316089947[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]7.09508196721312[/C][C]0.10517812706363[/C][C]67.4577705963596[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]7.09508196721311[/C][C]0.102547502773990[/C][C]69.1882471565434[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]7.10327868852459[/C][C]0.100598406627181[/C][C]70.6102504669825[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]7.10327868852459[/C][C]0.0969470367804905[/C][C]73.26968336957[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]7.10327868852459[/C][C]0.0969470367804905[/C][C]73.2696833695699[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]7.12950819672131[/C][C]0.0912973961734975[/C][C]78.091035402288[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]7.15901639344262[/C][C]0.0854872581557996[/C][C]83.7436659904964[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]7.15901639344262[/C][C]0.0802106873621316[/C][C]89.2526498510282[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]7.15901639344262[/C][C]0.0802106873621316[/C][C]89.2526498510282[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]7.15901639344262[/C][C]0.0802106873621316[/C][C]89.2526498510282[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]7.15901639344262[/C][C]0.0802106873621316[/C][C]89.2526498510282[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]7.15901639344262[/C][C]0.0802106873621316[/C][C]89.2526498510282[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]7.15901639344262[/C][C]0.072706350365694[/C][C]98.4648020074537[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]7.15901639344262[/C][C]0.072706350365694[/C][C]98.4648020074537[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]7.18688524590164[/C][C]0.0679309923810932[/C][C]105.796853453622[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]7.18688524590164[/C][C]0.0594361212796174[/C][C]120.917803705442[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]7.18688524590164[/C][C]0.0594361212796174[/C][C]120.917803705442[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]7.21967213114754[/C][C]0.0541107785052426[/C][C]133.423919052431[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]7.10169491525424[/C][C]0.104808180396879[/C][C]67.7589753811401[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]7.1140350877193[/C][C]0.102733278660964[/C][C]69.247620444362[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]7.12727272727273[/C][C]0.100116247094834[/C][C]71.1899709996271[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]7.13962264150943[/C][C]0.0974396327069838[/C][C]73.2722655367492[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]7.15294117647059[/C][C]0.0950687240039385[/C][C]75.23968846131[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]7.16530612244898[/C][C]0.0926990880313184[/C][C]77.2964036067774[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]7.17872340425532[/C][C]0.0907332740178273[/C][C]79.1189724162807[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]7.19333333333333[/C][C]0.0881000349694378[/C][C]81.649608150879[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]7.2046511627907[/C][C]0.0862632331076249[/C][C]83.519373239836[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]7.21219512195122[/C][C]0.0853397172532727[/C][C]84.5115891413929[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]7.22051282051282[/C][C]0.0852225385009686[/C][C]84.725390108284[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]7.22972972972973[/C][C]0.0847948296543432[/C][C]85.2614452933148[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]7.24[/C][C]0.0839367508976878[/C][C]86.255423548917[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]7.25151515151515[/C][C]0.0824714381368258[/C][C]87.9275942719028[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]7.26451612903226[/C][C]0.0801273699895111[/C][C]90.6621062189262[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]7.27931034482759[/C][C]0.0786867754402412[/C][C]92.5099586823947[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]7.2962962962963[/C][C]0.0761393013141086[/C][C]95.82825387635[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]7.312[/C][C]0.0737834669827869[/C][C]99.1007918034786[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]7.3304347826087[/C][C]0.0726230134282177[/C][C]100.938179739047[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]7.35238095238095[/C][C]0.069904372647158[/C][C]105.177697388003[/C][/ROW]
[ROW][C]Median[/C][C]7.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.26451612903225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.26451612903225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.26451612903225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.26451612903225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.26451612903225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.13055555555555[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.26451612903225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.26451612903225[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63431&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63431&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 Mean7.091803278688520.10672202496131166.4511686435809
Geometric Mean7.0405571082839
Harmonic Mean6.9863396004243
Quadratic Mean7.13982136893689
Winsorized Mean ( 1 / 20 )7.090163934426230.10645055595706066.6052316089947
Winsorized Mean ( 2 / 20 )7.090163934426230.10645055595706066.6052316089947
Winsorized Mean ( 3 / 20 )7.095081967213120.1051781270636367.4577705963596
Winsorized Mean ( 4 / 20 )7.095081967213110.10254750277399069.1882471565434
Winsorized Mean ( 5 / 20 )7.103278688524590.10059840662718170.6102504669825
Winsorized Mean ( 6 / 20 )7.103278688524590.096947036780490573.26968336957
Winsorized Mean ( 7 / 20 )7.103278688524590.096947036780490573.2696833695699
Winsorized Mean ( 8 / 20 )7.129508196721310.091297396173497578.091035402288
Winsorized Mean ( 9 / 20 )7.159016393442620.085487258155799683.7436659904964
Winsorized Mean ( 10 / 20 )7.159016393442620.080210687362131689.2526498510282
Winsorized Mean ( 11 / 20 )7.159016393442620.080210687362131689.2526498510282
Winsorized Mean ( 12 / 20 )7.159016393442620.080210687362131689.2526498510282
Winsorized Mean ( 13 / 20 )7.159016393442620.080210687362131689.2526498510282
Winsorized Mean ( 14 / 20 )7.159016393442620.080210687362131689.2526498510282
Winsorized Mean ( 15 / 20 )7.159016393442620.07270635036569498.4648020074537
Winsorized Mean ( 16 / 20 )7.159016393442620.07270635036569498.4648020074537
Winsorized Mean ( 17 / 20 )7.186885245901640.0679309923810932105.796853453622
Winsorized Mean ( 18 / 20 )7.186885245901640.0594361212796174120.917803705442
Winsorized Mean ( 19 / 20 )7.186885245901640.0594361212796174120.917803705442
Winsorized Mean ( 20 / 20 )7.219672131147540.0541107785052426133.423919052431
Trimmed Mean ( 1 / 20 )7.101694915254240.10480818039687967.7589753811401
Trimmed Mean ( 2 / 20 )7.11403508771930.10273327866096469.247620444362
Trimmed Mean ( 3 / 20 )7.127272727272730.10011624709483471.1899709996271
Trimmed Mean ( 4 / 20 )7.139622641509430.097439632706983873.2722655367492
Trimmed Mean ( 5 / 20 )7.152941176470590.095068724003938575.23968846131
Trimmed Mean ( 6 / 20 )7.165306122448980.092699088031318477.2964036067774
Trimmed Mean ( 7 / 20 )7.178723404255320.090733274017827379.1189724162807
Trimmed Mean ( 8 / 20 )7.193333333333330.088100034969437881.649608150879
Trimmed Mean ( 9 / 20 )7.20465116279070.086263233107624983.519373239836
Trimmed Mean ( 10 / 20 )7.212195121951220.085339717253272784.5115891413929
Trimmed Mean ( 11 / 20 )7.220512820512820.085222538500968684.725390108284
Trimmed Mean ( 12 / 20 )7.229729729729730.084794829654343285.2614452933148
Trimmed Mean ( 13 / 20 )7.240.083936750897687886.255423548917
Trimmed Mean ( 14 / 20 )7.251515151515150.082471438136825887.9275942719028
Trimmed Mean ( 15 / 20 )7.264516129032260.080127369989511190.6621062189262
Trimmed Mean ( 16 / 20 )7.279310344827590.078686775440241292.5099586823947
Trimmed Mean ( 17 / 20 )7.29629629629630.076139301314108695.82825387635
Trimmed Mean ( 18 / 20 )7.3120.073783466982786999.1007918034786
Trimmed Mean ( 19 / 20 )7.33043478260870.0726230134282177100.938179739047
Trimmed Mean ( 20 / 20 )7.352380952380950.069904372647158105.177697388003
Median7.5
Midrange6.8
Midmean - Weighted Average at Xnp7.26451612903225
Midmean - Weighted Average at X(n+1)p7.26451612903225
Midmean - Empirical Distribution Function7.26451612903225
Midmean - Empirical Distribution Function - Averaging7.26451612903225
Midmean - Empirical Distribution Function - Interpolation7.26451612903225
Midmean - Closest Observation7.13055555555555
Midmean - True Basic - Statistics Graphics Toolkit7.26451612903225
Midmean - MS Excel (old versions)7.26451612903225
Number of observations61



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')