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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 21 Oct 2012 05:44:52 -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/21/t1350812774s1we5nmkhmoavqi.htm/, Retrieved Mon, 29 Apr 2024 01:37:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=180702, Retrieved Mon, 29 Apr 2024 01:37:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact97
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-21 09:44:52] [38590a47bc58a2a98fa414b70b201b41] [Current]
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Dataseries X:
1,65
1,66
1,66
1,67
1,68
1,68
1,68
1,68
1,69
1,7
1,7
1,71
1,72
1,73
1,74
1,74
1,75
1,75
1,75
1,76
1,79
1,83
1,84
1,85
1,87
1,87
1,87
1,88
1,88
1,88
1,88
1,89
1,89
1,89
1,9
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,89
1,9
1,9
1,92
1,93
1,92
1,95
1,96
1,96
1,96
1,96
1,96
1,97
1,97
1,97
1,97
1,97
1,97





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=180702&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=180702&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180702&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'Herman Ole Andreas Wold' @ wold.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.847916666666670.0114482189674808161.415209816982
Geometric Mean1.84533044111351
Harmonic Mean1.84267684384581
Quadratic Mean1.85043275719192
Winsorized Mean ( 1 / 24 )1.848055555555560.0114151953900831161.894342795134
Winsorized Mean ( 2 / 24 )1.848055555555560.0114151953900831161.894342795134
Winsorized Mean ( 3 / 24 )1.848472222222220.0113205874928116163.284124909239
Winsorized Mean ( 4 / 24 )1.849027777777780.0111998486083801165.093997466561
Winsorized Mean ( 5 / 24 )1.849027777777780.0111998486083801165.093997466561
Winsorized Mean ( 6 / 24 )1.848194444444440.0110772052119947166.84663767384
Winsorized Mean ( 7 / 24 )1.848194444444440.0110772052119947166.84663767384
Winsorized Mean ( 8 / 24 )1.849305555555560.0108433979771328170.54668282539
Winsorized Mean ( 9 / 24 )1.850555555555560.0105888610548317174.764362850067
Winsorized Mean ( 10 / 24 )1.850555555555560.0105888610548317174.764362850067
Winsorized Mean ( 11 / 24 )1.850555555555560.0100680176799347183.805354180463
Winsorized Mean ( 12 / 24 )1.848888888888890.00930393499541388198.72117440634
Winsorized Mean ( 13 / 24 )1.848888888888890.00874019807692745211.538556977287
Winsorized Mean ( 14 / 24 )1.850833333333330.00837256025706689221.059422268252
Winsorized Mean ( 15 / 24 )1.846666666666670.00793163275259676232.823016933314
Winsorized Mean ( 16 / 24 )1.848888888888890.00751512703893997246.022306650145
Winsorized Mean ( 17 / 24 )1.848888888888890.00751512703893997246.022306650145
Winsorized Mean ( 18 / 24 )1.846388888888890.00728984532733992253.282313407141
Winsorized Mean ( 19 / 24 )1.849027777777780.00680076321956819271.885333760404
Winsorized Mean ( 20 / 24 )1.857361111111110.00528156008939753351.669029542932
Winsorized Mean ( 21 / 24 )1.869027777777780.00322693890122371579.195279175882
Winsorized Mean ( 22 / 24 )1.872083333333330.00271160420039376690.396973519028
Winsorized Mean ( 23 / 24 )1.875277777777780.00218448991175933858.451104618505
Winsorized Mean ( 24 / 24 )1.881944444444440.001130022935370581665.40375910802
Trimmed Mean ( 1 / 24 )1.8490.011291635629823163.749527580974
Trimmed Mean ( 2 / 24 )1.850.0111400218938884166.067896241294
Trimmed Mean ( 3 / 24 )1.851060606060610.0109547251949519168.973714366985
Trimmed Mean ( 4 / 24 )1.852031250.010771756517266171.934006030622
Trimmed Mean ( 5 / 24 )1.852903225806450.0105916640460615174.939765625917
Trimmed Mean ( 6 / 24 )1.853833333333330.0103691515179163178.783512819751
Trimmed Mean ( 7 / 24 )1.8550.0101269915998125183.173846024947
Trimmed Mean ( 8 / 24 )1.856250.00982496984562968188.931877569649
Trimmed Mean ( 9 / 24 )1.857407407407410.00950995353801799195.311932911348
Trimmed Mean ( 10 / 24 )1.858461538461540.00917972311096654202.452897107684
Trimmed Mean ( 11 / 24 )1.85960.00875964774242826212.291641705275
Trimmed Mean ( 12 / 24 )1.860833333333330.00835192960532999222.802803815036
Trimmed Mean ( 13 / 24 )1.862391304347830.00800473762259808232.661130464805
Trimmed Mean ( 14 / 24 )1.864090909090910.00768237172280372242.645237219867
Trimmed Mean ( 15 / 24 )1.865714285714290.00735007215228324253.836186510729
Trimmed Mean ( 16 / 24 )1.8680.00697247334992286267.910669034062
Trimmed Mean ( 17 / 24 )1.870263157894740.00657040697446794284.649514887347
Trimmed Mean ( 18 / 24 )1.872777777777780.00598425329326509312.950954112433
Trimmed Mean ( 19 / 24 )1.875882352941180.00512095494135387366.314949931044
Trimmed Mean ( 20 / 24 )1.87906250.00394925919451785475.801259792827
Trimmed Mean ( 21 / 24 )1.881666666666670.00288010749054407653.332097098643
Trimmed Mean ( 22 / 24 )1.883214285714290.00241542504659256779.661653492803
Trimmed Mean ( 23 / 24 )1.884615384615380.00193992618660283971.488192504732
Trimmed Mean ( 24 / 24 )1.885833333333330.001464144735592511288.01018607643
Median1.89
Midrange1.81
Midmean - Weighted Average at Xnp1.86631578947368
Midmean - Weighted Average at X(n+1)p1.86631578947368
Midmean - Empirical Distribution Function1.86631578947368
Midmean - Empirical Distribution Function - Averaging1.86631578947368
Midmean - Empirical Distribution Function - Interpolation1.86631578947368
Midmean - Closest Observation1.86631578947368
Midmean - True Basic - Statistics Graphics Toolkit1.86631578947368
Midmean - MS Excel (old versions)1.86878048780488
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.84791666666667 & 0.0114482189674808 & 161.415209816982 \tabularnewline
Geometric Mean & 1.84533044111351 &  &  \tabularnewline
Harmonic Mean & 1.84267684384581 &  &  \tabularnewline
Quadratic Mean & 1.85043275719192 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 1.84805555555556 & 0.0114151953900831 & 161.894342795134 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 1.84805555555556 & 0.0114151953900831 & 161.894342795134 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 1.84847222222222 & 0.0113205874928116 & 163.284124909239 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 1.84902777777778 & 0.0111998486083801 & 165.093997466561 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 1.84902777777778 & 0.0111998486083801 & 165.093997466561 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 1.84819444444444 & 0.0110772052119947 & 166.84663767384 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 1.84819444444444 & 0.0110772052119947 & 166.84663767384 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 1.84930555555556 & 0.0108433979771328 & 170.54668282539 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 1.85055555555556 & 0.0105888610548317 & 174.764362850067 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 1.85055555555556 & 0.0105888610548317 & 174.764362850067 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 1.85055555555556 & 0.0100680176799347 & 183.805354180463 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 1.84888888888889 & 0.00930393499541388 & 198.72117440634 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 1.84888888888889 & 0.00874019807692745 & 211.538556977287 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 1.85083333333333 & 0.00837256025706689 & 221.059422268252 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 1.84666666666667 & 0.00793163275259676 & 232.823016933314 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 1.84888888888889 & 0.00751512703893997 & 246.022306650145 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 1.84888888888889 & 0.00751512703893997 & 246.022306650145 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 1.84638888888889 & 0.00728984532733992 & 253.282313407141 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 1.84902777777778 & 0.00680076321956819 & 271.885333760404 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 1.85736111111111 & 0.00528156008939753 & 351.669029542932 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 1.86902777777778 & 0.00322693890122371 & 579.195279175882 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 1.87208333333333 & 0.00271160420039376 & 690.396973519028 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 1.87527777777778 & 0.00218448991175933 & 858.451104618505 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 1.88194444444444 & 0.00113002293537058 & 1665.40375910802 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 1.849 & 0.011291635629823 & 163.749527580974 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 1.85 & 0.0111400218938884 & 166.067896241294 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 1.85106060606061 & 0.0109547251949519 & 168.973714366985 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 1.85203125 & 0.010771756517266 & 171.934006030622 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 1.85290322580645 & 0.0105916640460615 & 174.939765625917 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 1.85383333333333 & 0.0103691515179163 & 178.783512819751 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 1.855 & 0.0101269915998125 & 183.173846024947 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 1.85625 & 0.00982496984562968 & 188.931877569649 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 1.85740740740741 & 0.00950995353801799 & 195.311932911348 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 1.85846153846154 & 0.00917972311096654 & 202.452897107684 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 1.8596 & 0.00875964774242826 & 212.291641705275 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 1.86083333333333 & 0.00835192960532999 & 222.802803815036 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 1.86239130434783 & 0.00800473762259808 & 232.661130464805 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 1.86409090909091 & 0.00768237172280372 & 242.645237219867 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 1.86571428571429 & 0.00735007215228324 & 253.836186510729 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 1.868 & 0.00697247334992286 & 267.910669034062 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 1.87026315789474 & 0.00657040697446794 & 284.649514887347 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 1.87277777777778 & 0.00598425329326509 & 312.950954112433 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 1.87588235294118 & 0.00512095494135387 & 366.314949931044 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 1.8790625 & 0.00394925919451785 & 475.801259792827 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 1.88166666666667 & 0.00288010749054407 & 653.332097098643 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 1.88321428571429 & 0.00241542504659256 & 779.661653492803 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 1.88461538461538 & 0.00193992618660283 & 971.488192504732 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 1.88583333333333 & 0.00146414473559251 & 1288.01018607643 \tabularnewline
Median & 1.89 &  &  \tabularnewline
Midrange & 1.81 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.86631578947368 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.86631578947368 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.86631578947368 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.86631578947368 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.86631578947368 &  &  \tabularnewline
Midmean - Closest Observation & 1.86631578947368 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.86631578947368 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.86878048780488 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=180702&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]1.84791666666667[/C][C]0.0114482189674808[/C][C]161.415209816982[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.84533044111351[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.84267684384581[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.85043275719192[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]1.84805555555556[/C][C]0.0114151953900831[/C][C]161.894342795134[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]1.84805555555556[/C][C]0.0114151953900831[/C][C]161.894342795134[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]1.84847222222222[/C][C]0.0113205874928116[/C][C]163.284124909239[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]1.84902777777778[/C][C]0.0111998486083801[/C][C]165.093997466561[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]1.84902777777778[/C][C]0.0111998486083801[/C][C]165.093997466561[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]1.84819444444444[/C][C]0.0110772052119947[/C][C]166.84663767384[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]1.84819444444444[/C][C]0.0110772052119947[/C][C]166.84663767384[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]1.84930555555556[/C][C]0.0108433979771328[/C][C]170.54668282539[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]1.85055555555556[/C][C]0.0105888610548317[/C][C]174.764362850067[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]1.85055555555556[/C][C]0.0105888610548317[/C][C]174.764362850067[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]1.85055555555556[/C][C]0.0100680176799347[/C][C]183.805354180463[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]1.84888888888889[/C][C]0.00930393499541388[/C][C]198.72117440634[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]1.84888888888889[/C][C]0.00874019807692745[/C][C]211.538556977287[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]1.85083333333333[/C][C]0.00837256025706689[/C][C]221.059422268252[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]1.84666666666667[/C][C]0.00793163275259676[/C][C]232.823016933314[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]1.84888888888889[/C][C]0.00751512703893997[/C][C]246.022306650145[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]1.84888888888889[/C][C]0.00751512703893997[/C][C]246.022306650145[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]1.84638888888889[/C][C]0.00728984532733992[/C][C]253.282313407141[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]1.84902777777778[/C][C]0.00680076321956819[/C][C]271.885333760404[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]1.85736111111111[/C][C]0.00528156008939753[/C][C]351.669029542932[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]1.86902777777778[/C][C]0.00322693890122371[/C][C]579.195279175882[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]1.87208333333333[/C][C]0.00271160420039376[/C][C]690.396973519028[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]1.87527777777778[/C][C]0.00218448991175933[/C][C]858.451104618505[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]1.88194444444444[/C][C]0.00113002293537058[/C][C]1665.40375910802[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]1.849[/C][C]0.011291635629823[/C][C]163.749527580974[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]1.85[/C][C]0.0111400218938884[/C][C]166.067896241294[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]1.85106060606061[/C][C]0.0109547251949519[/C][C]168.973714366985[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]1.85203125[/C][C]0.010771756517266[/C][C]171.934006030622[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]1.85290322580645[/C][C]0.0105916640460615[/C][C]174.939765625917[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]1.85383333333333[/C][C]0.0103691515179163[/C][C]178.783512819751[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]1.855[/C][C]0.0101269915998125[/C][C]183.173846024947[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]1.85625[/C][C]0.00982496984562968[/C][C]188.931877569649[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]1.85740740740741[/C][C]0.00950995353801799[/C][C]195.311932911348[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]1.85846153846154[/C][C]0.00917972311096654[/C][C]202.452897107684[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]1.8596[/C][C]0.00875964774242826[/C][C]212.291641705275[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]1.86083333333333[/C][C]0.00835192960532999[/C][C]222.802803815036[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]1.86239130434783[/C][C]0.00800473762259808[/C][C]232.661130464805[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]1.86409090909091[/C][C]0.00768237172280372[/C][C]242.645237219867[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]1.86571428571429[/C][C]0.00735007215228324[/C][C]253.836186510729[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]1.868[/C][C]0.00697247334992286[/C][C]267.910669034062[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]1.87026315789474[/C][C]0.00657040697446794[/C][C]284.649514887347[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]1.87277777777778[/C][C]0.00598425329326509[/C][C]312.950954112433[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]1.87588235294118[/C][C]0.00512095494135387[/C][C]366.314949931044[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]1.8790625[/C][C]0.00394925919451785[/C][C]475.801259792827[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]1.88166666666667[/C][C]0.00288010749054407[/C][C]653.332097098643[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]1.88321428571429[/C][C]0.00241542504659256[/C][C]779.661653492803[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]1.88461538461538[/C][C]0.00193992618660283[/C][C]971.488192504732[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]1.88583333333333[/C][C]0.00146414473559251[/C][C]1288.01018607643[/C][/ROW]
[ROW][C]Median[/C][C]1.89[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.81[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.86631578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.86631578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.86631578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.86631578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.86631578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.86631578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.86631578947368[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.86878048780488[/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=180702&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=180702&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 Mean1.847916666666670.0114482189674808161.415209816982
Geometric Mean1.84533044111351
Harmonic Mean1.84267684384581
Quadratic Mean1.85043275719192
Winsorized Mean ( 1 / 24 )1.848055555555560.0114151953900831161.894342795134
Winsorized Mean ( 2 / 24 )1.848055555555560.0114151953900831161.894342795134
Winsorized Mean ( 3 / 24 )1.848472222222220.0113205874928116163.284124909239
Winsorized Mean ( 4 / 24 )1.849027777777780.0111998486083801165.093997466561
Winsorized Mean ( 5 / 24 )1.849027777777780.0111998486083801165.093997466561
Winsorized Mean ( 6 / 24 )1.848194444444440.0110772052119947166.84663767384
Winsorized Mean ( 7 / 24 )1.848194444444440.0110772052119947166.84663767384
Winsorized Mean ( 8 / 24 )1.849305555555560.0108433979771328170.54668282539
Winsorized Mean ( 9 / 24 )1.850555555555560.0105888610548317174.764362850067
Winsorized Mean ( 10 / 24 )1.850555555555560.0105888610548317174.764362850067
Winsorized Mean ( 11 / 24 )1.850555555555560.0100680176799347183.805354180463
Winsorized Mean ( 12 / 24 )1.848888888888890.00930393499541388198.72117440634
Winsorized Mean ( 13 / 24 )1.848888888888890.00874019807692745211.538556977287
Winsorized Mean ( 14 / 24 )1.850833333333330.00837256025706689221.059422268252
Winsorized Mean ( 15 / 24 )1.846666666666670.00793163275259676232.823016933314
Winsorized Mean ( 16 / 24 )1.848888888888890.00751512703893997246.022306650145
Winsorized Mean ( 17 / 24 )1.848888888888890.00751512703893997246.022306650145
Winsorized Mean ( 18 / 24 )1.846388888888890.00728984532733992253.282313407141
Winsorized Mean ( 19 / 24 )1.849027777777780.00680076321956819271.885333760404
Winsorized Mean ( 20 / 24 )1.857361111111110.00528156008939753351.669029542932
Winsorized Mean ( 21 / 24 )1.869027777777780.00322693890122371579.195279175882
Winsorized Mean ( 22 / 24 )1.872083333333330.00271160420039376690.396973519028
Winsorized Mean ( 23 / 24 )1.875277777777780.00218448991175933858.451104618505
Winsorized Mean ( 24 / 24 )1.881944444444440.001130022935370581665.40375910802
Trimmed Mean ( 1 / 24 )1.8490.011291635629823163.749527580974
Trimmed Mean ( 2 / 24 )1.850.0111400218938884166.067896241294
Trimmed Mean ( 3 / 24 )1.851060606060610.0109547251949519168.973714366985
Trimmed Mean ( 4 / 24 )1.852031250.010771756517266171.934006030622
Trimmed Mean ( 5 / 24 )1.852903225806450.0105916640460615174.939765625917
Trimmed Mean ( 6 / 24 )1.853833333333330.0103691515179163178.783512819751
Trimmed Mean ( 7 / 24 )1.8550.0101269915998125183.173846024947
Trimmed Mean ( 8 / 24 )1.856250.00982496984562968188.931877569649
Trimmed Mean ( 9 / 24 )1.857407407407410.00950995353801799195.311932911348
Trimmed Mean ( 10 / 24 )1.858461538461540.00917972311096654202.452897107684
Trimmed Mean ( 11 / 24 )1.85960.00875964774242826212.291641705275
Trimmed Mean ( 12 / 24 )1.860833333333330.00835192960532999222.802803815036
Trimmed Mean ( 13 / 24 )1.862391304347830.00800473762259808232.661130464805
Trimmed Mean ( 14 / 24 )1.864090909090910.00768237172280372242.645237219867
Trimmed Mean ( 15 / 24 )1.865714285714290.00735007215228324253.836186510729
Trimmed Mean ( 16 / 24 )1.8680.00697247334992286267.910669034062
Trimmed Mean ( 17 / 24 )1.870263157894740.00657040697446794284.649514887347
Trimmed Mean ( 18 / 24 )1.872777777777780.00598425329326509312.950954112433
Trimmed Mean ( 19 / 24 )1.875882352941180.00512095494135387366.314949931044
Trimmed Mean ( 20 / 24 )1.87906250.00394925919451785475.801259792827
Trimmed Mean ( 21 / 24 )1.881666666666670.00288010749054407653.332097098643
Trimmed Mean ( 22 / 24 )1.883214285714290.00241542504659256779.661653492803
Trimmed Mean ( 23 / 24 )1.884615384615380.00193992618660283971.488192504732
Trimmed Mean ( 24 / 24 )1.885833333333330.001464144735592511288.01018607643
Median1.89
Midrange1.81
Midmean - Weighted Average at Xnp1.86631578947368
Midmean - Weighted Average at X(n+1)p1.86631578947368
Midmean - Empirical Distribution Function1.86631578947368
Midmean - Empirical Distribution Function - Averaging1.86631578947368
Midmean - Empirical Distribution Function - Interpolation1.86631578947368
Midmean - Closest Observation1.86631578947368
Midmean - True Basic - Statistics Graphics Toolkit1.86631578947368
Midmean - MS Excel (old versions)1.86878048780488
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')