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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 22 Oct 2012 16:35:15 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/22/t1350938337dgelq4slfqm458u.htm/, Retrieved Fri, 03 May 2024 20:51:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=182313, Retrieved Fri, 03 May 2024 20:51:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact42
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [opgave 5] [2012-10-22 20:35:15] [2f2dfc06a630b81f17a3d9dd284f5d45] [Current]
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Dataseries X:
20,89
21,04
21,07
21,12
21,25
21,24
21,24
21,22
21,29
21,25
21,15
21,16
21,16
21,52
21,59
21,6
21,68
21,67
21,67
21,65
21,74
21,72
21,84
21,94
21,94
21,95
21,96
22,1
22,13
22,18
22,18
22,27
22,3
22,04
22,05
22,06
22,06
22,06
21,97
22,03
22,08
22,13
22,13
22,4
22,4
22,12
22,22
22,14
22,14
22,19
22,29
22,24
22,26
22,29
22,29
22,29
22,29
22,35
22,39
22,43
22,43
22,11
22,12
22,05
22,05
22,08
22,08
22,09
22,09
22,24
22,25
22,24




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=182313&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=182313&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=182313&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 time5 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean21.9150.0488145864446813448.943678439948
Geometric Mean21.9110932807437
Harmonic Mean21.9071397210827
Quadratic Mean21.9188596494739
Winsorized Mean ( 1 / 24 )21.91708333333330.048239522648793454.338727455914
Winsorized Mean ( 2 / 24 )21.91708333333330.0479074802379994457.487708066706
Winsorized Mean ( 3 / 24 )21.91916666666670.0474006456180485462.4233780124
Winsorized Mean ( 4 / 24 )21.92027777777780.046931247045292467.072135471345
Winsorized Mean ( 5 / 24 )21.91819444444440.0463931143999629472.444989475894
Winsorized Mean ( 6 / 24 )21.91402777777780.0458729703649392477.711114049129
Winsorized Mean ( 7 / 24 )21.91888888888890.0444363744629664493.264564307699
Winsorized Mean ( 8 / 24 )21.92111111111110.0439476835242776498.800149477763
Winsorized Mean ( 9 / 24 )21.92111111111110.0439476835242776498.800149477763
Winsorized Mean ( 10 / 24 )21.92250.0436453868874721502.286760718178
Winsorized Mean ( 11 / 24 )21.92250.0436453868874721502.286760718178
Winsorized Mean ( 12 / 24 )21.92583333333330.0418169823833506524.328444657525
Winsorized Mean ( 13 / 24 )21.96555555555560.0331650027237837662.311284533781
Winsorized Mean ( 14 / 24 )21.97722222222220.030409452950118722.710213112761
Winsorized Mean ( 15 / 24 )21.97722222222220.0297756492594088738.093803790951
Winsorized Mean ( 16 / 24 )21.98833333333330.0278317941156022790.043690392452
Winsorized Mean ( 17 / 24 )21.99305555555560.0270299773370077813.654235863678
Winsorized Mean ( 18 / 24 )21.98805555555560.0263987709031896832.919670244908
Winsorized Mean ( 19 / 24 )21.98277777777780.0249970438175689879.41509956979
Winsorized Mean ( 20 / 24 )21.99111111111110.022793517215563964.796740368616
Winsorized Mean ( 21 / 24 )21.99694444444440.02182108111305321008.05933172972
Winsorized Mean ( 22 / 24 )22.01527777777780.01540020656912631429.54431675696
Winsorized Mean ( 23 / 24 )22.04722222222220.0104911137265352101.51398573238
Winsorized Mean ( 24 / 24 )22.04388888888890.01008290274864512186.26415809188
Trimmed Mean ( 1 / 24 )21.92228571428570.0474213619205572462.287138674151
Trimmed Mean ( 2 / 24 )21.92779411764710.0464342434361438472.233259228226
Trimmed Mean ( 3 / 24 )21.93363636363640.0454511886872421482.575637670683
Trimmed Mean ( 4 / 24 )21.93906250.0444904566356295493.118393449584
Trimmed Mean ( 5 / 24 )21.94451612903230.0434898052809102504.589891522572
Trimmed Mean ( 6 / 24 )21.95083333333330.0424226059464986517.432459500877
Trimmed Mean ( 7 / 24 )21.95844827586210.0412309107962705532.572476615004
Trimmed Mean ( 8 / 24 )21.96571428571430.0401376342676186547.259814548545
Trimmed Mean ( 9 / 24 )21.97314814814810.0388836391252083565.100094602589
Trimmed Mean ( 10 / 24 )21.98115384615380.0372809376785185589.608395467465
Trimmed Mean ( 11 / 24 )21.98960.0352969444246139622.988770230938
Trimmed Mean ( 12 / 24 )21.998750.0326919115617347672.911094796584
Trimmed Mean ( 13 / 24 )22.00826086956520.0297417294115354739.97919102274
Trimmed Mean ( 14 / 24 )22.01363636363640.0284186664623444774.61890735813
Trimmed Mean ( 15 / 24 )22.01809523809520.027389813240795803.878983931916
Trimmed Mean ( 16 / 24 )22.0230.026150942523584842.149378751407
Trimmed Mean ( 17 / 24 )22.02710526315790.0250175127700032880.467433579932
Trimmed Mean ( 18 / 24 )22.03111111111110.0236803373587676930.354613506135
Trimmed Mean ( 19 / 24 )22.03617647058820.02193010573596121004.83676348414
Trimmed Mean ( 20 / 24 )22.04250.01977188456760861114.84061747514
Trimmed Mean ( 21 / 24 )22.04866666666670.01741140683927081266.33458572323
Trimmed Mean ( 22 / 24 )22.0550.01409059876460091565.22801965007
Trimmed Mean ( 23 / 24 )22.060.0121528724050041815.20872307659
Trimmed Mean ( 24 / 24 )22.06166666666670.01166666666666661891.00000000001
Median22.07
Midrange21.66
Midmean - Weighted Average at Xnp22.0213513513513
Midmean - Weighted Average at X(n+1)p22.0213513513513
Midmean - Empirical Distribution Function22.0213513513513
Midmean - Empirical Distribution Function - Averaging22.0213513513513
Midmean - Empirical Distribution Function - Interpolation22.0213513513513
Midmean - Closest Observation22.0213513513513
Midmean - True Basic - Statistics Graphics Toolkit22.0213513513513
Midmean - MS Excel (old versions)22.03775
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 21.915 & 0.0488145864446813 & 448.943678439948 \tabularnewline
Geometric Mean & 21.9110932807437 &  &  \tabularnewline
Harmonic Mean & 21.9071397210827 &  &  \tabularnewline
Quadratic Mean & 21.9188596494739 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 21.9170833333333 & 0.048239522648793 & 454.338727455914 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 21.9170833333333 & 0.0479074802379994 & 457.487708066706 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 21.9191666666667 & 0.0474006456180485 & 462.4233780124 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 21.9202777777778 & 0.046931247045292 & 467.072135471345 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 21.9181944444444 & 0.0463931143999629 & 472.444989475894 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 21.9140277777778 & 0.0458729703649392 & 477.711114049129 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 21.9188888888889 & 0.0444363744629664 & 493.264564307699 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 21.9211111111111 & 0.0439476835242776 & 498.800149477763 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 21.9211111111111 & 0.0439476835242776 & 498.800149477763 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 21.9225 & 0.0436453868874721 & 502.286760718178 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 21.9225 & 0.0436453868874721 & 502.286760718178 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 21.9258333333333 & 0.0418169823833506 & 524.328444657525 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 21.9655555555556 & 0.0331650027237837 & 662.311284533781 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 21.9772222222222 & 0.030409452950118 & 722.710213112761 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 21.9772222222222 & 0.0297756492594088 & 738.093803790951 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 21.9883333333333 & 0.0278317941156022 & 790.043690392452 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 21.9930555555556 & 0.0270299773370077 & 813.654235863678 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 21.9880555555556 & 0.0263987709031896 & 832.919670244908 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 21.9827777777778 & 0.0249970438175689 & 879.41509956979 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 21.9911111111111 & 0.022793517215563 & 964.796740368616 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 21.9969444444444 & 0.0218210811130532 & 1008.05933172972 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 22.0152777777778 & 0.0154002065691263 & 1429.54431675696 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 22.0472222222222 & 0.010491113726535 & 2101.51398573238 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 22.0438888888889 & 0.0100829027486451 & 2186.26415809188 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 21.9222857142857 & 0.0474213619205572 & 462.287138674151 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 21.9277941176471 & 0.0464342434361438 & 472.233259228226 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 21.9336363636364 & 0.0454511886872421 & 482.575637670683 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 21.9390625 & 0.0444904566356295 & 493.118393449584 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 21.9445161290323 & 0.0434898052809102 & 504.589891522572 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 21.9508333333333 & 0.0424226059464986 & 517.432459500877 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 21.9584482758621 & 0.0412309107962705 & 532.572476615004 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 21.9657142857143 & 0.0401376342676186 & 547.259814548545 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 21.9731481481481 & 0.0388836391252083 & 565.100094602589 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 21.9811538461538 & 0.0372809376785185 & 589.608395467465 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 21.9896 & 0.0352969444246139 & 622.988770230938 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 21.99875 & 0.0326919115617347 & 672.911094796584 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 22.0082608695652 & 0.0297417294115354 & 739.97919102274 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 22.0136363636364 & 0.0284186664623444 & 774.61890735813 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 22.0180952380952 & 0.027389813240795 & 803.878983931916 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 22.023 & 0.026150942523584 & 842.149378751407 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 22.0271052631579 & 0.0250175127700032 & 880.467433579932 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 22.0311111111111 & 0.0236803373587676 & 930.354613506135 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 22.0361764705882 & 0.0219301057359612 & 1004.83676348414 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 22.0425 & 0.0197718845676086 & 1114.84061747514 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 22.0486666666667 & 0.0174114068392708 & 1266.33458572323 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 22.055 & 0.0140905987646009 & 1565.22801965007 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 22.06 & 0.012152872405004 & 1815.20872307659 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 22.0616666666667 & 0.0116666666666666 & 1891.00000000001 \tabularnewline
Median & 22.07 &  &  \tabularnewline
Midrange & 21.66 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 22.0213513513513 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 22.0213513513513 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 22.0213513513513 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 22.0213513513513 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 22.0213513513513 &  &  \tabularnewline
Midmean - Closest Observation & 22.0213513513513 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 22.0213513513513 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 22.03775 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=182313&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]21.915[/C][C]0.0488145864446813[/C][C]448.943678439948[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]21.9110932807437[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]21.9071397210827[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]21.9188596494739[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]21.9170833333333[/C][C]0.048239522648793[/C][C]454.338727455914[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]21.9170833333333[/C][C]0.0479074802379994[/C][C]457.487708066706[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]21.9191666666667[/C][C]0.0474006456180485[/C][C]462.4233780124[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]21.9202777777778[/C][C]0.046931247045292[/C][C]467.072135471345[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]21.9181944444444[/C][C]0.0463931143999629[/C][C]472.444989475894[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]21.9140277777778[/C][C]0.0458729703649392[/C][C]477.711114049129[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]21.9188888888889[/C][C]0.0444363744629664[/C][C]493.264564307699[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]21.9211111111111[/C][C]0.0439476835242776[/C][C]498.800149477763[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]21.9211111111111[/C][C]0.0439476835242776[/C][C]498.800149477763[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]21.9225[/C][C]0.0436453868874721[/C][C]502.286760718178[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]21.9225[/C][C]0.0436453868874721[/C][C]502.286760718178[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]21.9258333333333[/C][C]0.0418169823833506[/C][C]524.328444657525[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]21.9655555555556[/C][C]0.0331650027237837[/C][C]662.311284533781[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]21.9772222222222[/C][C]0.030409452950118[/C][C]722.710213112761[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]21.9772222222222[/C][C]0.0297756492594088[/C][C]738.093803790951[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]21.9883333333333[/C][C]0.0278317941156022[/C][C]790.043690392452[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]21.9930555555556[/C][C]0.0270299773370077[/C][C]813.654235863678[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]21.9880555555556[/C][C]0.0263987709031896[/C][C]832.919670244908[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]21.9827777777778[/C][C]0.0249970438175689[/C][C]879.41509956979[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]21.9911111111111[/C][C]0.022793517215563[/C][C]964.796740368616[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]21.9969444444444[/C][C]0.0218210811130532[/C][C]1008.05933172972[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]22.0152777777778[/C][C]0.0154002065691263[/C][C]1429.54431675696[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]22.0472222222222[/C][C]0.010491113726535[/C][C]2101.51398573238[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]22.0438888888889[/C][C]0.0100829027486451[/C][C]2186.26415809188[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]21.9222857142857[/C][C]0.0474213619205572[/C][C]462.287138674151[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]21.9277941176471[/C][C]0.0464342434361438[/C][C]472.233259228226[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]21.9336363636364[/C][C]0.0454511886872421[/C][C]482.575637670683[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]21.9390625[/C][C]0.0444904566356295[/C][C]493.118393449584[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]21.9445161290323[/C][C]0.0434898052809102[/C][C]504.589891522572[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]21.9508333333333[/C][C]0.0424226059464986[/C][C]517.432459500877[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]21.9584482758621[/C][C]0.0412309107962705[/C][C]532.572476615004[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]21.9657142857143[/C][C]0.0401376342676186[/C][C]547.259814548545[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]21.9731481481481[/C][C]0.0388836391252083[/C][C]565.100094602589[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]21.9811538461538[/C][C]0.0372809376785185[/C][C]589.608395467465[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]21.9896[/C][C]0.0352969444246139[/C][C]622.988770230938[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]21.99875[/C][C]0.0326919115617347[/C][C]672.911094796584[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]22.0082608695652[/C][C]0.0297417294115354[/C][C]739.97919102274[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]22.0136363636364[/C][C]0.0284186664623444[/C][C]774.61890735813[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]22.0180952380952[/C][C]0.027389813240795[/C][C]803.878983931916[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]22.023[/C][C]0.026150942523584[/C][C]842.149378751407[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]22.0271052631579[/C][C]0.0250175127700032[/C][C]880.467433579932[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]22.0311111111111[/C][C]0.0236803373587676[/C][C]930.354613506135[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]22.0361764705882[/C][C]0.0219301057359612[/C][C]1004.83676348414[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]22.0425[/C][C]0.0197718845676086[/C][C]1114.84061747514[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]22.0486666666667[/C][C]0.0174114068392708[/C][C]1266.33458572323[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]22.055[/C][C]0.0140905987646009[/C][C]1565.22801965007[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]22.06[/C][C]0.012152872405004[/C][C]1815.20872307659[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]22.0616666666667[/C][C]0.0116666666666666[/C][C]1891.00000000001[/C][/ROW]
[ROW][C]Median[/C][C]22.07[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]21.66[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]22.0213513513513[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]22.0213513513513[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]22.0213513513513[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]22.0213513513513[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]22.0213513513513[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]22.0213513513513[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]22.0213513513513[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]22.03775[/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=182313&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=182313&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 Mean21.9150.0488145864446813448.943678439948
Geometric Mean21.9110932807437
Harmonic Mean21.9071397210827
Quadratic Mean21.9188596494739
Winsorized Mean ( 1 / 24 )21.91708333333330.048239522648793454.338727455914
Winsorized Mean ( 2 / 24 )21.91708333333330.0479074802379994457.487708066706
Winsorized Mean ( 3 / 24 )21.91916666666670.0474006456180485462.4233780124
Winsorized Mean ( 4 / 24 )21.92027777777780.046931247045292467.072135471345
Winsorized Mean ( 5 / 24 )21.91819444444440.0463931143999629472.444989475894
Winsorized Mean ( 6 / 24 )21.91402777777780.0458729703649392477.711114049129
Winsorized Mean ( 7 / 24 )21.91888888888890.0444363744629664493.264564307699
Winsorized Mean ( 8 / 24 )21.92111111111110.0439476835242776498.800149477763
Winsorized Mean ( 9 / 24 )21.92111111111110.0439476835242776498.800149477763
Winsorized Mean ( 10 / 24 )21.92250.0436453868874721502.286760718178
Winsorized Mean ( 11 / 24 )21.92250.0436453868874721502.286760718178
Winsorized Mean ( 12 / 24 )21.92583333333330.0418169823833506524.328444657525
Winsorized Mean ( 13 / 24 )21.96555555555560.0331650027237837662.311284533781
Winsorized Mean ( 14 / 24 )21.97722222222220.030409452950118722.710213112761
Winsorized Mean ( 15 / 24 )21.97722222222220.0297756492594088738.093803790951
Winsorized Mean ( 16 / 24 )21.98833333333330.0278317941156022790.043690392452
Winsorized Mean ( 17 / 24 )21.99305555555560.0270299773370077813.654235863678
Winsorized Mean ( 18 / 24 )21.98805555555560.0263987709031896832.919670244908
Winsorized Mean ( 19 / 24 )21.98277777777780.0249970438175689879.41509956979
Winsorized Mean ( 20 / 24 )21.99111111111110.022793517215563964.796740368616
Winsorized Mean ( 21 / 24 )21.99694444444440.02182108111305321008.05933172972
Winsorized Mean ( 22 / 24 )22.01527777777780.01540020656912631429.54431675696
Winsorized Mean ( 23 / 24 )22.04722222222220.0104911137265352101.51398573238
Winsorized Mean ( 24 / 24 )22.04388888888890.01008290274864512186.26415809188
Trimmed Mean ( 1 / 24 )21.92228571428570.0474213619205572462.287138674151
Trimmed Mean ( 2 / 24 )21.92779411764710.0464342434361438472.233259228226
Trimmed Mean ( 3 / 24 )21.93363636363640.0454511886872421482.575637670683
Trimmed Mean ( 4 / 24 )21.93906250.0444904566356295493.118393449584
Trimmed Mean ( 5 / 24 )21.94451612903230.0434898052809102504.589891522572
Trimmed Mean ( 6 / 24 )21.95083333333330.0424226059464986517.432459500877
Trimmed Mean ( 7 / 24 )21.95844827586210.0412309107962705532.572476615004
Trimmed Mean ( 8 / 24 )21.96571428571430.0401376342676186547.259814548545
Trimmed Mean ( 9 / 24 )21.97314814814810.0388836391252083565.100094602589
Trimmed Mean ( 10 / 24 )21.98115384615380.0372809376785185589.608395467465
Trimmed Mean ( 11 / 24 )21.98960.0352969444246139622.988770230938
Trimmed Mean ( 12 / 24 )21.998750.0326919115617347672.911094796584
Trimmed Mean ( 13 / 24 )22.00826086956520.0297417294115354739.97919102274
Trimmed Mean ( 14 / 24 )22.01363636363640.0284186664623444774.61890735813
Trimmed Mean ( 15 / 24 )22.01809523809520.027389813240795803.878983931916
Trimmed Mean ( 16 / 24 )22.0230.026150942523584842.149378751407
Trimmed Mean ( 17 / 24 )22.02710526315790.0250175127700032880.467433579932
Trimmed Mean ( 18 / 24 )22.03111111111110.0236803373587676930.354613506135
Trimmed Mean ( 19 / 24 )22.03617647058820.02193010573596121004.83676348414
Trimmed Mean ( 20 / 24 )22.04250.01977188456760861114.84061747514
Trimmed Mean ( 21 / 24 )22.04866666666670.01741140683927081266.33458572323
Trimmed Mean ( 22 / 24 )22.0550.01409059876460091565.22801965007
Trimmed Mean ( 23 / 24 )22.060.0121528724050041815.20872307659
Trimmed Mean ( 24 / 24 )22.06166666666670.01166666666666661891.00000000001
Median22.07
Midrange21.66
Midmean - Weighted Average at Xnp22.0213513513513
Midmean - Weighted Average at X(n+1)p22.0213513513513
Midmean - Empirical Distribution Function22.0213513513513
Midmean - Empirical Distribution Function - Averaging22.0213513513513
Midmean - Empirical Distribution Function - Interpolation22.0213513513513
Midmean - Closest Observation22.0213513513513
Midmean - True Basic - Statistics Graphics Toolkit22.0213513513513
Midmean - MS Excel (old versions)22.03775
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')