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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 28 Oct 2009 11:08:24 -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/28/t1256749819k3pdsxxi670jjwz.htm/, Retrieved Mon, 06 May 2024 07:32:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=51595, Retrieved Mon, 06 May 2024 07:32:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact104
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-10-28 17:08:24] [6f76491bc22dc2a03dd3886755cb7a25] [Current]
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Dataseries X:
3,81
3,95
3,99
4
4,06
4,16
4,19
4,2
4,2
4,2
4,2
4,2
4,23
4,38
4,43
4,44
4,44
4,44
4,44
4,44
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,45
4,46
4,46
4,46
4,48
4,58
4,67
4,68
4,68
4,69
4,69
4,69
4,69
4,69
4,69
4,69
4,73
4,78
4,79
4,79
4,8
4,8
4,81
5,16
5,26
5,29
5,29
5,29
5,3
5,3
5,3
5,3
5,3
5,3
5,3
5,3
5,35
5,44
5,47
5,47
5,48
5,48
5,48
5,48
5,48




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=51595&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=51595&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51595&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 Mean4.730833333333330.055359739018761285.4562072940783
Geometric Mean4.70803266551123
Harmonic Mean4.68548765144722
Quadratic Mean4.75377510803548
Winsorized Mean ( 1 / 24 )4.732777777777780.054936733502096586.149602935478
Winsorized Mean ( 2 / 24 )4.733888888888890.054718855897665186.5129361941007
Winsorized Mean ( 3 / 24 )4.734305555555560.054639530934327786.6461602909038
Winsorized Mean ( 4 / 24 )4.737638888888890.054029527752453987.6861058381861
Winsorized Mean ( 5 / 24 )4.743888888888890.052739340257351889.9497199953614
Winsorized Mean ( 6 / 24 )4.746388888888890.052357304980323890.653804481965
Winsorized Mean ( 7 / 24 )4.744444444444440.051651856460132491.854286943325
Winsorized Mean ( 8 / 24 )4.734444444444450.049832225908561595.0076854510132
Winsorized Mean ( 9 / 24 )4.728194444444440.048772220724837596.944415779628
Winsorized Mean ( 10 / 24 )4.728194444444440.048772220724837596.944415779628
Winsorized Mean ( 11 / 24 )4.728194444444440.048772220724837596.944415779628
Winsorized Mean ( 12 / 24 )4.733194444444440.048021833514433698.5633845701
Winsorized Mean ( 13 / 24 )4.760277777777780.0443744436021554107.275210489548
Winsorized Mean ( 14 / 24 )4.770.0432488341905529110.291990276166
Winsorized Mean ( 15 / 24 )4.772083333333330.0430202383042664110.926473711794
Winsorized Mean ( 16 / 24 )4.772083333333330.0430202383042664110.926473711794
Winsorized Mean ( 17 / 24 )4.769722222222220.0426131799715263111.930680259237
Winsorized Mean ( 18 / 24 )4.769722222222220.0426131799715263111.930680259237
Winsorized Mean ( 19 / 24 )4.769722222222220.0426131799715263111.930680259237
Winsorized Mean ( 20 / 24 )4.764166666666670.0408831257207799116.531370404616
Winsorized Mean ( 21 / 24 )4.7350.0359604416634757131.672465102375
Winsorized Mean ( 22 / 24 )4.628055555555560.0194663134342438237.746893945219
Winsorized Mean ( 23 / 24 )4.624861111111110.0190491837830263242.785263861650
Winsorized Mean ( 24 / 24 )4.624861111111110.0190491837830263242.785263861650
Trimmed Mean ( 1 / 24 )4.733285714285710.054330375548004687.1204306346738
Trimmed Mean ( 2 / 24 )4.733823529411770.053593447886424588.3284005060414
Trimmed Mean ( 3 / 24 )4.733787878787880.052835569865016989.594716038488
Trimmed Mean ( 4 / 24 )4.733593750.051947855794076691.1220237609836
Trimmed Mean ( 5 / 24 )4.732419354838710.051084839111912192.6384312275379
Trimmed Mean ( 6 / 24 )4.729666666666670.05041520635696293.8142875619417
Trimmed Mean ( 7 / 24 )4.726206896551720.049673968849476295.144539605306
Trimmed Mean ( 8 / 24 )4.722857142857140.04891864056958596.5451428712343
Trimmed Mean ( 9 / 24 )4.720925925925930.04839728186149197.5452699892697
Trimmed Mean ( 10 / 24 )4.719807692307690.047947692074909798.4365980521823
Trimmed Mean ( 11 / 24 )4.71860.047337270124682399.680441807726
Trimmed Mean ( 12 / 24 )4.717291666666670.0465234055935935101.396095287493
Trimmed Mean ( 13 / 24 )4.715217391304350.0456077999202831103.386205858339
Trimmed Mean ( 14 / 24 )4.709545454545450.0451096321865962104.402213590756
Trimmed Mean ( 15 / 24 )4.702142857142860.0445711735750173105.497398430147
Trimmed Mean ( 16 / 24 )4.693750.0437939339845846107.178085477596
Trimmed Mean ( 17 / 24 )4.684473684210530.0426432776390155109.852570992915
Trimmed Mean ( 18 / 24 )4.674444444444440.0410834312651097113.779309578123
Trimmed Mean ( 19 / 24 )4.663235294117650.0387935726806048120.206389148816
Trimmed Mean ( 20 / 24 )4.6506250.0353665640231908131.497789747131
Trimmed Mean ( 21 / 24 )4.6370.0307685090543121150.706034920796
Trimmed Mean ( 22 / 24 )4.6250.0260011192270295177.876958280784
Trimmed Mean ( 23 / 24 )4.624615384615380.0262017660545754176.500140295231
Trimmed Mean ( 24 / 24 )4.624583333333330.0264093964301868175.111284559585
Median4.685
Midrange4.645
Midmean - Weighted Average at Xnp4.67225
Midmean - Weighted Average at X(n+1)p4.67225
Midmean - Empirical Distribution Function4.67225
Midmean - Empirical Distribution Function - Averaging4.67225
Midmean - Empirical Distribution Function - Interpolation4.67225
Midmean - Closest Observation4.67225
Midmean - True Basic - Statistics Graphics Toolkit4.67225
Midmean - MS Excel (old versions)4.67225
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.73083333333333 & 0.0553597390187612 & 85.4562072940783 \tabularnewline
Geometric Mean & 4.70803266551123 &  &  \tabularnewline
Harmonic Mean & 4.68548765144722 &  &  \tabularnewline
Quadratic Mean & 4.75377510803548 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 4.73277777777778 & 0.0549367335020965 & 86.149602935478 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 4.73388888888889 & 0.0547188558976651 & 86.5129361941007 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 4.73430555555556 & 0.0546395309343277 & 86.6461602909038 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 4.73763888888889 & 0.0540295277524539 & 87.6861058381861 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 4.74388888888889 & 0.0527393402573518 & 89.9497199953614 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 4.74638888888889 & 0.0523573049803238 & 90.653804481965 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 4.74444444444444 & 0.0516518564601324 & 91.854286943325 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 4.73444444444445 & 0.0498322259085615 & 95.0076854510132 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 4.72819444444444 & 0.0487722207248375 & 96.944415779628 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 4.72819444444444 & 0.0487722207248375 & 96.944415779628 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 4.72819444444444 & 0.0487722207248375 & 96.944415779628 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 4.73319444444444 & 0.0480218335144336 & 98.5633845701 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 4.76027777777778 & 0.0443744436021554 & 107.275210489548 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 4.77 & 0.0432488341905529 & 110.291990276166 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 4.77208333333333 & 0.0430202383042664 & 110.926473711794 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 4.77208333333333 & 0.0430202383042664 & 110.926473711794 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 4.76972222222222 & 0.0426131799715263 & 111.930680259237 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 4.76972222222222 & 0.0426131799715263 & 111.930680259237 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 4.76972222222222 & 0.0426131799715263 & 111.930680259237 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 4.76416666666667 & 0.0408831257207799 & 116.531370404616 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 4.735 & 0.0359604416634757 & 131.672465102375 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 4.62805555555556 & 0.0194663134342438 & 237.746893945219 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 4.62486111111111 & 0.0190491837830263 & 242.785263861650 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 4.62486111111111 & 0.0190491837830263 & 242.785263861650 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 4.73328571428571 & 0.0543303755480046 & 87.1204306346738 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 4.73382352941177 & 0.0535934478864245 & 88.3284005060414 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 4.73378787878788 & 0.0528355698650169 & 89.594716038488 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 4.73359375 & 0.0519478557940766 & 91.1220237609836 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 4.73241935483871 & 0.0510848391119121 & 92.6384312275379 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 4.72966666666667 & 0.050415206356962 & 93.8142875619417 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 4.72620689655172 & 0.0496739688494762 & 95.144539605306 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 4.72285714285714 & 0.048918640569585 & 96.5451428712343 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 4.72092592592593 & 0.048397281861491 & 97.5452699892697 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 4.71980769230769 & 0.0479476920749097 & 98.4365980521823 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 4.7186 & 0.0473372701246823 & 99.680441807726 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 4.71729166666667 & 0.0465234055935935 & 101.396095287493 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 4.71521739130435 & 0.0456077999202831 & 103.386205858339 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 4.70954545454545 & 0.0451096321865962 & 104.402213590756 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 4.70214285714286 & 0.0445711735750173 & 105.497398430147 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 4.69375 & 0.0437939339845846 & 107.178085477596 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 4.68447368421053 & 0.0426432776390155 & 109.852570992915 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 4.67444444444444 & 0.0410834312651097 & 113.779309578123 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 4.66323529411765 & 0.0387935726806048 & 120.206389148816 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 4.650625 & 0.0353665640231908 & 131.497789747131 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 4.637 & 0.0307685090543121 & 150.706034920796 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 4.625 & 0.0260011192270295 & 177.876958280784 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 4.62461538461538 & 0.0262017660545754 & 176.500140295231 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 4.62458333333333 & 0.0264093964301868 & 175.111284559585 \tabularnewline
Median & 4.685 &  &  \tabularnewline
Midrange & 4.645 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4.67225 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4.67225 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4.67225 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4.67225 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4.67225 &  &  \tabularnewline
Midmean - Closest Observation & 4.67225 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4.67225 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4.67225 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=51595&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]4.73083333333333[/C][C]0.0553597390187612[/C][C]85.4562072940783[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4.70803266551123[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4.68548765144722[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.75377510803548[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]4.73277777777778[/C][C]0.0549367335020965[/C][C]86.149602935478[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]4.73388888888889[/C][C]0.0547188558976651[/C][C]86.5129361941007[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]4.73430555555556[/C][C]0.0546395309343277[/C][C]86.6461602909038[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]4.73763888888889[/C][C]0.0540295277524539[/C][C]87.6861058381861[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]4.74388888888889[/C][C]0.0527393402573518[/C][C]89.9497199953614[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]4.74638888888889[/C][C]0.0523573049803238[/C][C]90.653804481965[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]4.74444444444444[/C][C]0.0516518564601324[/C][C]91.854286943325[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]4.73444444444445[/C][C]0.0498322259085615[/C][C]95.0076854510132[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]4.72819444444444[/C][C]0.0487722207248375[/C][C]96.944415779628[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]4.72819444444444[/C][C]0.0487722207248375[/C][C]96.944415779628[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]4.72819444444444[/C][C]0.0487722207248375[/C][C]96.944415779628[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]4.73319444444444[/C][C]0.0480218335144336[/C][C]98.5633845701[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]4.76027777777778[/C][C]0.0443744436021554[/C][C]107.275210489548[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]4.77[/C][C]0.0432488341905529[/C][C]110.291990276166[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]4.77208333333333[/C][C]0.0430202383042664[/C][C]110.926473711794[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]4.77208333333333[/C][C]0.0430202383042664[/C][C]110.926473711794[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]4.76972222222222[/C][C]0.0426131799715263[/C][C]111.930680259237[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]4.76972222222222[/C][C]0.0426131799715263[/C][C]111.930680259237[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]4.76972222222222[/C][C]0.0426131799715263[/C][C]111.930680259237[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]4.76416666666667[/C][C]0.0408831257207799[/C][C]116.531370404616[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]4.735[/C][C]0.0359604416634757[/C][C]131.672465102375[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]4.62805555555556[/C][C]0.0194663134342438[/C][C]237.746893945219[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]4.62486111111111[/C][C]0.0190491837830263[/C][C]242.785263861650[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]4.62486111111111[/C][C]0.0190491837830263[/C][C]242.785263861650[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]4.73328571428571[/C][C]0.0543303755480046[/C][C]87.1204306346738[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]4.73382352941177[/C][C]0.0535934478864245[/C][C]88.3284005060414[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]4.73378787878788[/C][C]0.0528355698650169[/C][C]89.594716038488[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]4.73359375[/C][C]0.0519478557940766[/C][C]91.1220237609836[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]4.73241935483871[/C][C]0.0510848391119121[/C][C]92.6384312275379[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]4.72966666666667[/C][C]0.050415206356962[/C][C]93.8142875619417[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]4.72620689655172[/C][C]0.0496739688494762[/C][C]95.144539605306[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]4.72285714285714[/C][C]0.048918640569585[/C][C]96.5451428712343[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]4.72092592592593[/C][C]0.048397281861491[/C][C]97.5452699892697[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]4.71980769230769[/C][C]0.0479476920749097[/C][C]98.4365980521823[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]4.7186[/C][C]0.0473372701246823[/C][C]99.680441807726[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]4.71729166666667[/C][C]0.0465234055935935[/C][C]101.396095287493[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]4.71521739130435[/C][C]0.0456077999202831[/C][C]103.386205858339[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]4.70954545454545[/C][C]0.0451096321865962[/C][C]104.402213590756[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]4.70214285714286[/C][C]0.0445711735750173[/C][C]105.497398430147[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]4.69375[/C][C]0.0437939339845846[/C][C]107.178085477596[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]4.68447368421053[/C][C]0.0426432776390155[/C][C]109.852570992915[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]4.67444444444444[/C][C]0.0410834312651097[/C][C]113.779309578123[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]4.66323529411765[/C][C]0.0387935726806048[/C][C]120.206389148816[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]4.650625[/C][C]0.0353665640231908[/C][C]131.497789747131[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]4.637[/C][C]0.0307685090543121[/C][C]150.706034920796[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]4.625[/C][C]0.0260011192270295[/C][C]177.876958280784[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]4.62461538461538[/C][C]0.0262017660545754[/C][C]176.500140295231[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]4.62458333333333[/C][C]0.0264093964301868[/C][C]175.111284559585[/C][/ROW]
[ROW][C]Median[/C][C]4.685[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4.645[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4.67225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4.67225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4.67225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4.67225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4.67225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4.67225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4.67225[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4.67225[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=51595&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=51595&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 Mean4.730833333333330.055359739018761285.4562072940783
Geometric Mean4.70803266551123
Harmonic Mean4.68548765144722
Quadratic Mean4.75377510803548
Winsorized Mean ( 1 / 24 )4.732777777777780.054936733502096586.149602935478
Winsorized Mean ( 2 / 24 )4.733888888888890.054718855897665186.5129361941007
Winsorized Mean ( 3 / 24 )4.734305555555560.054639530934327786.6461602909038
Winsorized Mean ( 4 / 24 )4.737638888888890.054029527752453987.6861058381861
Winsorized Mean ( 5 / 24 )4.743888888888890.052739340257351889.9497199953614
Winsorized Mean ( 6 / 24 )4.746388888888890.052357304980323890.653804481965
Winsorized Mean ( 7 / 24 )4.744444444444440.051651856460132491.854286943325
Winsorized Mean ( 8 / 24 )4.734444444444450.049832225908561595.0076854510132
Winsorized Mean ( 9 / 24 )4.728194444444440.048772220724837596.944415779628
Winsorized Mean ( 10 / 24 )4.728194444444440.048772220724837596.944415779628
Winsorized Mean ( 11 / 24 )4.728194444444440.048772220724837596.944415779628
Winsorized Mean ( 12 / 24 )4.733194444444440.048021833514433698.5633845701
Winsorized Mean ( 13 / 24 )4.760277777777780.0443744436021554107.275210489548
Winsorized Mean ( 14 / 24 )4.770.0432488341905529110.291990276166
Winsorized Mean ( 15 / 24 )4.772083333333330.0430202383042664110.926473711794
Winsorized Mean ( 16 / 24 )4.772083333333330.0430202383042664110.926473711794
Winsorized Mean ( 17 / 24 )4.769722222222220.0426131799715263111.930680259237
Winsorized Mean ( 18 / 24 )4.769722222222220.0426131799715263111.930680259237
Winsorized Mean ( 19 / 24 )4.769722222222220.0426131799715263111.930680259237
Winsorized Mean ( 20 / 24 )4.764166666666670.0408831257207799116.531370404616
Winsorized Mean ( 21 / 24 )4.7350.0359604416634757131.672465102375
Winsorized Mean ( 22 / 24 )4.628055555555560.0194663134342438237.746893945219
Winsorized Mean ( 23 / 24 )4.624861111111110.0190491837830263242.785263861650
Winsorized Mean ( 24 / 24 )4.624861111111110.0190491837830263242.785263861650
Trimmed Mean ( 1 / 24 )4.733285714285710.054330375548004687.1204306346738
Trimmed Mean ( 2 / 24 )4.733823529411770.053593447886424588.3284005060414
Trimmed Mean ( 3 / 24 )4.733787878787880.052835569865016989.594716038488
Trimmed Mean ( 4 / 24 )4.733593750.051947855794076691.1220237609836
Trimmed Mean ( 5 / 24 )4.732419354838710.051084839111912192.6384312275379
Trimmed Mean ( 6 / 24 )4.729666666666670.05041520635696293.8142875619417
Trimmed Mean ( 7 / 24 )4.726206896551720.049673968849476295.144539605306
Trimmed Mean ( 8 / 24 )4.722857142857140.04891864056958596.5451428712343
Trimmed Mean ( 9 / 24 )4.720925925925930.04839728186149197.5452699892697
Trimmed Mean ( 10 / 24 )4.719807692307690.047947692074909798.4365980521823
Trimmed Mean ( 11 / 24 )4.71860.047337270124682399.680441807726
Trimmed Mean ( 12 / 24 )4.717291666666670.0465234055935935101.396095287493
Trimmed Mean ( 13 / 24 )4.715217391304350.0456077999202831103.386205858339
Trimmed Mean ( 14 / 24 )4.709545454545450.0451096321865962104.402213590756
Trimmed Mean ( 15 / 24 )4.702142857142860.0445711735750173105.497398430147
Trimmed Mean ( 16 / 24 )4.693750.0437939339845846107.178085477596
Trimmed Mean ( 17 / 24 )4.684473684210530.0426432776390155109.852570992915
Trimmed Mean ( 18 / 24 )4.674444444444440.0410834312651097113.779309578123
Trimmed Mean ( 19 / 24 )4.663235294117650.0387935726806048120.206389148816
Trimmed Mean ( 20 / 24 )4.6506250.0353665640231908131.497789747131
Trimmed Mean ( 21 / 24 )4.6370.0307685090543121150.706034920796
Trimmed Mean ( 22 / 24 )4.6250.0260011192270295177.876958280784
Trimmed Mean ( 23 / 24 )4.624615384615380.0262017660545754176.500140295231
Trimmed Mean ( 24 / 24 )4.624583333333330.0264093964301868175.111284559585
Median4.685
Midrange4.645
Midmean - Weighted Average at Xnp4.67225
Midmean - Weighted Average at X(n+1)p4.67225
Midmean - Empirical Distribution Function4.67225
Midmean - Empirical Distribution Function - Averaging4.67225
Midmean - Empirical Distribution Function - Interpolation4.67225
Midmean - Closest Observation4.67225
Midmean - True Basic - Statistics Graphics Toolkit4.67225
Midmean - MS Excel (old versions)4.67225
Number of observations72



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')