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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 01 Mar 2012 11:33:53 -0500
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/Mar/01/t1330619969jlkyfx3q0dp0qjc.htm/, Retrieved Sun, 28 Apr 2024 01:02:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163392, Retrieved Sun, 28 Apr 2024 01:02:18 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten maxi...] [2012-03-01 16:33:53] [91562a5fde803f4db5c5e8dd5d4cb92f] [Current]
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Dataseries X:
1,45
1,45
1,45
1,44
1,44
1,44
1,44
1,45
1,44
1,45
1,46
1,46
1,47
1,46
1,46
1,45
1,45
1,45
1,44
1,45
1,44
1,45
1,47
1,48
1,5
1,5
1,52
1,54
1,55
1,54
1,55
1,54
1,57
1,61
1,62
1,64
1,63
1,63
1,67
1,7
1,69
1,68
1,67
1,68
1,66
1,65
1,65
1,66
1,67
1,67
1,65
1,65
1,65
1,65
1,66
1,66
1,67
1,67
1,67
1,66




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163392&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163392&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163392&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.5570.012634139025931123.237523095505
Geometric Mean1.5539755052003
Harmonic Mean1.5509582047545
Quadratic Mean1.56002136737503
Winsorized Mean ( 1 / 20 )1.556833333333330.0126032272493918123.526562088172
Winsorized Mean ( 2 / 20 )1.55650.0125455666646769124.067731781495
Winsorized Mean ( 3 / 20 )1.55650.0125455666646769124.067731781495
Winsorized Mean ( 4 / 20 )1.555833333333330.0124380763737594125.086330601384
Winsorized Mean ( 5 / 20 )1.555833333333330.0124380763737594125.086330601384
Winsorized Mean ( 6 / 20 )1.555833333333330.0124380763737594125.086330601384
Winsorized Mean ( 7 / 20 )1.5570.012259667003155127.001818205935
Winsorized Mean ( 8 / 20 )1.5570.012259667003155127.001818205935
Winsorized Mean ( 9 / 20 )1.5570.012259667003155127.001818205935
Winsorized Mean ( 10 / 20 )1.5570.012259667003155127.001818205935
Winsorized Mean ( 11 / 20 )1.555166666666670.0119804258119874129.808964311652
Winsorized Mean ( 12 / 20 )1.555166666666670.0119804258119874129.808964311652
Winsorized Mean ( 13 / 20 )1.555166666666670.0119804258119874129.808964311652
Winsorized Mean ( 14 / 20 )1.555166666666670.0119804258119874129.808964311652
Winsorized Mean ( 15 / 20 )1.555166666666670.0119804258119874129.808964311652
Winsorized Mean ( 16 / 20 )1.55250.0115924800288954133.923025627841
Winsorized Mean ( 17 / 20 )1.555333333333330.0111752012246109139.177210510362
Winsorized Mean ( 18 / 20 )1.555333333333330.0111752012246109139.177210510362
Winsorized Mean ( 19 / 20 )1.555333333333330.0111752012246109139.177210510362
Winsorized Mean ( 20 / 20 )1.555333333333330.0111752012246109139.177210510362
Trimmed Mean ( 1 / 20 )1.556551724137930.012672408648879122.829981834245
Trimmed Mean ( 2 / 20 )1.556250.012734966946046122.202908464022
Trimmed Mean ( 3 / 20 )1.556111111111110.0128241797153477121.341960706367
Trimmed Mean ( 4 / 20 )1.555961538461540.0129077817894021120.544456347957
Trimmed Mean ( 5 / 20 )1.5560.0130211758458352119.497656618905
Trimmed Mean ( 6 / 20 )1.556041666666670.0131303462037473118.507284006159
Trimmed Mean ( 7 / 20 )1.556086956521740.0132332411958592117.589253720295
Trimmed Mean ( 8 / 20 )1.555909090909090.0133710985766989116.363594358693
Trimmed Mean ( 9 / 20 )1.555714285714290.0135041734725985115.202480838313
Trimmed Mean ( 10 / 20 )1.55550.0136294835013224114.127582299731
Trimmed Mean ( 11 / 20 )1.555263157894740.0137428985520673113.168495860052
Trimmed Mean ( 12 / 20 )1.555277777777780.0139015022090575111.878396621369
Trimmed Mean ( 13 / 20 )1.555294117647060.0140487773531724110.70672404783
Trimmed Mean ( 14 / 20 )1.55531250.0141776201922084109.701944255408
Trimmed Mean ( 15 / 20 )1.555333333333330.0142774907912777108.936041778679
Trimmed Mean ( 16 / 20 )1.555357142857140.0143324302304743108.520126583283
Trimmed Mean ( 17 / 20 )1.555769230769230.0144240512491418107.859380412406
Trimmed Mean ( 18 / 20 )1.555833333333330.014570128597339106.782402292419
Trimmed Mean ( 19 / 20 )1.555909090909090.0146482434109207106.218134643306
Trimmed Mean ( 20 / 20 )1.5560.0146071359633787106.523277656963
Median1.545
Midrange1.57
Midmean - Weighted Average at Xnp1.54523809523809
Midmean - Weighted Average at X(n+1)p1.54523809523809
Midmean - Empirical Distribution Function1.54523809523809
Midmean - Empirical Distribution Function - Averaging1.54523809523809
Midmean - Empirical Distribution Function - Interpolation1.54523809523809
Midmean - Closest Observation1.54523809523809
Midmean - True Basic - Statistics Graphics Toolkit1.54523809523809
Midmean - MS Excel (old versions)1.54523809523809
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.557 & 0.012634139025931 & 123.237523095505 \tabularnewline
Geometric Mean & 1.5539755052003 &  &  \tabularnewline
Harmonic Mean & 1.5509582047545 &  &  \tabularnewline
Quadratic Mean & 1.56002136737503 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1.55683333333333 & 0.0126032272493918 & 123.526562088172 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1.5565 & 0.0125455666646769 & 124.067731781495 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1.5565 & 0.0125455666646769 & 124.067731781495 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1.55583333333333 & 0.0124380763737594 & 125.086330601384 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1.55583333333333 & 0.0124380763737594 & 125.086330601384 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1.55583333333333 & 0.0124380763737594 & 125.086330601384 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1.557 & 0.012259667003155 & 127.001818205935 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1.557 & 0.012259667003155 & 127.001818205935 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1.557 & 0.012259667003155 & 127.001818205935 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1.557 & 0.012259667003155 & 127.001818205935 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1.55516666666667 & 0.0119804258119874 & 129.808964311652 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1.55516666666667 & 0.0119804258119874 & 129.808964311652 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1.55516666666667 & 0.0119804258119874 & 129.808964311652 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1.55516666666667 & 0.0119804258119874 & 129.808964311652 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1.55516666666667 & 0.0119804258119874 & 129.808964311652 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1.5525 & 0.0115924800288954 & 133.923025627841 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1.55533333333333 & 0.0111752012246109 & 139.177210510362 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1.55533333333333 & 0.0111752012246109 & 139.177210510362 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1.55533333333333 & 0.0111752012246109 & 139.177210510362 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1.55533333333333 & 0.0111752012246109 & 139.177210510362 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1.55655172413793 & 0.012672408648879 & 122.829981834245 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1.55625 & 0.012734966946046 & 122.202908464022 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1.55611111111111 & 0.0128241797153477 & 121.341960706367 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1.55596153846154 & 0.0129077817894021 & 120.544456347957 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1.556 & 0.0130211758458352 & 119.497656618905 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1.55604166666667 & 0.0131303462037473 & 118.507284006159 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1.55608695652174 & 0.0132332411958592 & 117.589253720295 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1.55590909090909 & 0.0133710985766989 & 116.363594358693 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1.55571428571429 & 0.0135041734725985 & 115.202480838313 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1.5555 & 0.0136294835013224 & 114.127582299731 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1.55526315789474 & 0.0137428985520673 & 113.168495860052 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1.55527777777778 & 0.0139015022090575 & 111.878396621369 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1.55529411764706 & 0.0140487773531724 & 110.70672404783 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1.5553125 & 0.0141776201922084 & 109.701944255408 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1.55533333333333 & 0.0142774907912777 & 108.936041778679 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1.55535714285714 & 0.0143324302304743 & 108.520126583283 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1.55576923076923 & 0.0144240512491418 & 107.859380412406 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1.55583333333333 & 0.014570128597339 & 106.782402292419 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1.55590909090909 & 0.0146482434109207 & 106.218134643306 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1.556 & 0.0146071359633787 & 106.523277656963 \tabularnewline
Median & 1.545 &  &  \tabularnewline
Midrange & 1.57 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.54523809523809 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.54523809523809 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.54523809523809 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.54523809523809 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.54523809523809 &  &  \tabularnewline
Midmean - Closest Observation & 1.54523809523809 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.54523809523809 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.54523809523809 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163392&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]1.557[/C][C]0.012634139025931[/C][C]123.237523095505[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.5539755052003[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.5509582047545[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.56002136737503[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1.55683333333333[/C][C]0.0126032272493918[/C][C]123.526562088172[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1.5565[/C][C]0.0125455666646769[/C][C]124.067731781495[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1.5565[/C][C]0.0125455666646769[/C][C]124.067731781495[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1.55583333333333[/C][C]0.0124380763737594[/C][C]125.086330601384[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1.55583333333333[/C][C]0.0124380763737594[/C][C]125.086330601384[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1.55583333333333[/C][C]0.0124380763737594[/C][C]125.086330601384[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1.557[/C][C]0.012259667003155[/C][C]127.001818205935[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1.557[/C][C]0.012259667003155[/C][C]127.001818205935[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1.557[/C][C]0.012259667003155[/C][C]127.001818205935[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1.557[/C][C]0.012259667003155[/C][C]127.001818205935[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1.55516666666667[/C][C]0.0119804258119874[/C][C]129.808964311652[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1.55516666666667[/C][C]0.0119804258119874[/C][C]129.808964311652[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1.55516666666667[/C][C]0.0119804258119874[/C][C]129.808964311652[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1.55516666666667[/C][C]0.0119804258119874[/C][C]129.808964311652[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1.55516666666667[/C][C]0.0119804258119874[/C][C]129.808964311652[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1.5525[/C][C]0.0115924800288954[/C][C]133.923025627841[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1.55533333333333[/C][C]0.0111752012246109[/C][C]139.177210510362[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1.55533333333333[/C][C]0.0111752012246109[/C][C]139.177210510362[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1.55533333333333[/C][C]0.0111752012246109[/C][C]139.177210510362[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1.55533333333333[/C][C]0.0111752012246109[/C][C]139.177210510362[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1.55655172413793[/C][C]0.012672408648879[/C][C]122.829981834245[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1.55625[/C][C]0.012734966946046[/C][C]122.202908464022[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1.55611111111111[/C][C]0.0128241797153477[/C][C]121.341960706367[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1.55596153846154[/C][C]0.0129077817894021[/C][C]120.544456347957[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1.556[/C][C]0.0130211758458352[/C][C]119.497656618905[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1.55604166666667[/C][C]0.0131303462037473[/C][C]118.507284006159[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1.55608695652174[/C][C]0.0132332411958592[/C][C]117.589253720295[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1.55590909090909[/C][C]0.0133710985766989[/C][C]116.363594358693[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1.55571428571429[/C][C]0.0135041734725985[/C][C]115.202480838313[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1.5555[/C][C]0.0136294835013224[/C][C]114.127582299731[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1.55526315789474[/C][C]0.0137428985520673[/C][C]113.168495860052[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1.55527777777778[/C][C]0.0139015022090575[/C][C]111.878396621369[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1.55529411764706[/C][C]0.0140487773531724[/C][C]110.70672404783[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1.5553125[/C][C]0.0141776201922084[/C][C]109.701944255408[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1.55533333333333[/C][C]0.0142774907912777[/C][C]108.936041778679[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1.55535714285714[/C][C]0.0143324302304743[/C][C]108.520126583283[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1.55576923076923[/C][C]0.0144240512491418[/C][C]107.859380412406[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1.55583333333333[/C][C]0.014570128597339[/C][C]106.782402292419[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1.55590909090909[/C][C]0.0146482434109207[/C][C]106.218134643306[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1.556[/C][C]0.0146071359633787[/C][C]106.523277656963[/C][/ROW]
[ROW][C]Median[/C][C]1.545[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.57[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.54523809523809[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.54523809523809[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.54523809523809[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.54523809523809[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.54523809523809[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.54523809523809[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.54523809523809[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.54523809523809[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163392&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163392&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 Mean1.5570.012634139025931123.237523095505
Geometric Mean1.5539755052003
Harmonic Mean1.5509582047545
Quadratic Mean1.56002136737503
Winsorized Mean ( 1 / 20 )1.556833333333330.0126032272493918123.526562088172
Winsorized Mean ( 2 / 20 )1.55650.0125455666646769124.067731781495
Winsorized Mean ( 3 / 20 )1.55650.0125455666646769124.067731781495
Winsorized Mean ( 4 / 20 )1.555833333333330.0124380763737594125.086330601384
Winsorized Mean ( 5 / 20 )1.555833333333330.0124380763737594125.086330601384
Winsorized Mean ( 6 / 20 )1.555833333333330.0124380763737594125.086330601384
Winsorized Mean ( 7 / 20 )1.5570.012259667003155127.001818205935
Winsorized Mean ( 8 / 20 )1.5570.012259667003155127.001818205935
Winsorized Mean ( 9 / 20 )1.5570.012259667003155127.001818205935
Winsorized Mean ( 10 / 20 )1.5570.012259667003155127.001818205935
Winsorized Mean ( 11 / 20 )1.555166666666670.0119804258119874129.808964311652
Winsorized Mean ( 12 / 20 )1.555166666666670.0119804258119874129.808964311652
Winsorized Mean ( 13 / 20 )1.555166666666670.0119804258119874129.808964311652
Winsorized Mean ( 14 / 20 )1.555166666666670.0119804258119874129.808964311652
Winsorized Mean ( 15 / 20 )1.555166666666670.0119804258119874129.808964311652
Winsorized Mean ( 16 / 20 )1.55250.0115924800288954133.923025627841
Winsorized Mean ( 17 / 20 )1.555333333333330.0111752012246109139.177210510362
Winsorized Mean ( 18 / 20 )1.555333333333330.0111752012246109139.177210510362
Winsorized Mean ( 19 / 20 )1.555333333333330.0111752012246109139.177210510362
Winsorized Mean ( 20 / 20 )1.555333333333330.0111752012246109139.177210510362
Trimmed Mean ( 1 / 20 )1.556551724137930.012672408648879122.829981834245
Trimmed Mean ( 2 / 20 )1.556250.012734966946046122.202908464022
Trimmed Mean ( 3 / 20 )1.556111111111110.0128241797153477121.341960706367
Trimmed Mean ( 4 / 20 )1.555961538461540.0129077817894021120.544456347957
Trimmed Mean ( 5 / 20 )1.5560.0130211758458352119.497656618905
Trimmed Mean ( 6 / 20 )1.556041666666670.0131303462037473118.507284006159
Trimmed Mean ( 7 / 20 )1.556086956521740.0132332411958592117.589253720295
Trimmed Mean ( 8 / 20 )1.555909090909090.0133710985766989116.363594358693
Trimmed Mean ( 9 / 20 )1.555714285714290.0135041734725985115.202480838313
Trimmed Mean ( 10 / 20 )1.55550.0136294835013224114.127582299731
Trimmed Mean ( 11 / 20 )1.555263157894740.0137428985520673113.168495860052
Trimmed Mean ( 12 / 20 )1.555277777777780.0139015022090575111.878396621369
Trimmed Mean ( 13 / 20 )1.555294117647060.0140487773531724110.70672404783
Trimmed Mean ( 14 / 20 )1.55531250.0141776201922084109.701944255408
Trimmed Mean ( 15 / 20 )1.555333333333330.0142774907912777108.936041778679
Trimmed Mean ( 16 / 20 )1.555357142857140.0143324302304743108.520126583283
Trimmed Mean ( 17 / 20 )1.555769230769230.0144240512491418107.859380412406
Trimmed Mean ( 18 / 20 )1.555833333333330.014570128597339106.782402292419
Trimmed Mean ( 19 / 20 )1.555909090909090.0146482434109207106.218134643306
Trimmed Mean ( 20 / 20 )1.5560.0146071359633787106.523277656963
Median1.545
Midrange1.57
Midmean - Weighted Average at Xnp1.54523809523809
Midmean - Weighted Average at X(n+1)p1.54523809523809
Midmean - Empirical Distribution Function1.54523809523809
Midmean - Empirical Distribution Function - Averaging1.54523809523809
Midmean - Empirical Distribution Function - Interpolation1.54523809523809
Midmean - Closest Observation1.54523809523809
Midmean - True Basic - Statistics Graphics Toolkit1.54523809523809
Midmean - MS Excel (old versions)1.54523809523809
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')