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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 18 Oct 2011 10:25:32 -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/2011/Oct/18/t1318948058rvt860c86fsdwyn.htm/, Retrieved Thu, 16 May 2024 13:14:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=132027, Retrieved Thu, 16 May 2024 13:14:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2011W52a
Estimated Impact50
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Seizoensabbonemen...] [2011-10-18 14:25:32] [9f264d4de2a9fd4816a4aa7cc978cf4e] [Current]
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Dataseries X:
98,19
98,19
98,19
98,19
98,19
98,19
98,19
100,48
102,78
102,78
102,78
102,78
102,78
102,78
102,78
102,78
102,78
102,78
102,78
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
101,67
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
105,79
104,47
104,47
104,47
104,47
104,47
104,47
104,47
104,47
105,5
105,5
105,5
105,5
106,61
106,61
106,61
106,61
106,61




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132027&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=132027&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132027&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean103.3120.329817001134399313.240371614139
Geometric Mean103.280606574845
Harmonic Mean103.248880634999
Quadratic Mean103.343056467283
Winsorized Mean ( 1 / 20 )103.3120.329817001134399313.240371614139
Winsorized Mean ( 2 / 20 )103.3120.329817001134399313.240371614139
Winsorized Mean ( 3 / 20 )103.3120.329817001134399313.240371614139
Winsorized Mean ( 4 / 20 )103.3120.329817001134399313.240371614139
Winsorized Mean ( 5 / 20 )103.2436666666670.319390659846194323.251990889104
Winsorized Mean ( 6 / 20 )103.2436666666670.319390659846194323.251990889104
Winsorized Mean ( 7 / 20 )103.5108333333330.255737693527513404.753917600329
Winsorized Mean ( 8 / 20 )103.66950.227758349614694455.173213958483
Winsorized Mean ( 9 / 20 )103.66950.227758349614694455.173213958483
Winsorized Mean ( 10 / 20 )103.66950.227758349614694455.173213958483
Winsorized Mean ( 11 / 20 )103.66950.227758349614694455.173213958483
Winsorized Mean ( 12 / 20 )103.66950.227758349614694455.173213958483
Winsorized Mean ( 13 / 20 )103.66950.227758349614694455.173213958483
Winsorized Mean ( 14 / 20 )103.66950.227758349614694455.173213958483
Winsorized Mean ( 15 / 20 )103.66950.227758349614694455.173213958483
Winsorized Mean ( 16 / 20 )103.66950.227758349614694455.173213958483
Winsorized Mean ( 17 / 20 )103.5873333333330.215074532694915481.634585161568
Winsorized Mean ( 18 / 20 )103.5873333333330.215074532694915481.634585161568
Winsorized Mean ( 19 / 20 )103.5873333333330.215074532694915481.634585161568
Winsorized Mean ( 20 / 20 )103.9573333333330.163859155909939634.431031674974
Trimmed Mean ( 1 / 20 )103.3434482758620.324400657448755318.567320697206
Trimmed Mean ( 2 / 20 )103.3771428571430.31756865647761325.526908114218
Trimmed Mean ( 3 / 20 )103.4133333333330.308956110809786334.718523813246
Trimmed Mean ( 4 / 20 )103.4523076923080.298063207002093347.081777495541
Trimmed Mean ( 5 / 20 )103.49440.28417918463461364.18712416629
Trimmed Mean ( 6 / 20 )103.5570833333330.269835114864519383.779121502878
Trimmed Mean ( 7 / 20 )103.6252173913040.250850291040329413.09586272174
Trimmed Mean ( 8 / 20 )103.64750.247242749686876419.21350628589
Trimmed Mean ( 9 / 20 )103.6435714285710.249453018679449415.483332201143
Trimmed Mean ( 10 / 20 )103.639250.251472175016824412.130089514143
Trimmed Mean ( 11 / 20 )103.6344736842110.253211435208043409.280384983651
Trimmed Mean ( 12 / 20 )103.6291666666670.254547022194204407.112076084724
Trimmed Mean ( 13 / 20 )103.6232352941180.255303712947159405.882210242532
Trimmed Mean ( 14 / 20 )103.61656250.25522863302523405.975463143892
Trimmed Mean ( 15 / 20 )103.6090.253947840603393407.993231026575
Trimmed Mean ( 16 / 20 )103.6003571428570.250890731787868412.930188391545
Trimmed Mean ( 17 / 20 )103.5903846153850.245149549816327422.559962655438
Trimmed Mean ( 18 / 20 )103.5908333333330.239751469042866432.075906549761
Trimmed Mean ( 19 / 20 )103.5913636363640.229788435968823450.81190965771
Trimmed Mean ( 20 / 20 )103.5920.211885768628684488.904944727732
Median102.78
Midrange102.4
Midmean - Weighted Average at Xnp103.784255319149
Midmean - Weighted Average at X(n+1)p103.784255319149
Midmean - Empirical Distribution Function103.784255319149
Midmean - Empirical Distribution Function - Averaging103.784255319149
Midmean - Empirical Distribution Function - Interpolation103.784255319149
Midmean - Closest Observation103.784255319149
Midmean - True Basic - Statistics Graphics Toolkit103.784255319149
Midmean - MS Excel (old versions)103.784255319149
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 103.312 & 0.329817001134399 & 313.240371614139 \tabularnewline
Geometric Mean & 103.280606574845 &  &  \tabularnewline
Harmonic Mean & 103.248880634999 &  &  \tabularnewline
Quadratic Mean & 103.343056467283 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 103.312 & 0.329817001134399 & 313.240371614139 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 103.312 & 0.329817001134399 & 313.240371614139 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 103.312 & 0.329817001134399 & 313.240371614139 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 103.312 & 0.329817001134399 & 313.240371614139 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 103.243666666667 & 0.319390659846194 & 323.251990889104 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 103.243666666667 & 0.319390659846194 & 323.251990889104 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 103.510833333333 & 0.255737693527513 & 404.753917600329 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 103.6695 & 0.227758349614694 & 455.173213958483 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 103.6695 & 0.227758349614694 & 455.173213958483 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 103.6695 & 0.227758349614694 & 455.173213958483 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 103.6695 & 0.227758349614694 & 455.173213958483 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 103.6695 & 0.227758349614694 & 455.173213958483 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 103.6695 & 0.227758349614694 & 455.173213958483 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 103.6695 & 0.227758349614694 & 455.173213958483 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 103.6695 & 0.227758349614694 & 455.173213958483 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 103.6695 & 0.227758349614694 & 455.173213958483 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 103.587333333333 & 0.215074532694915 & 481.634585161568 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 103.587333333333 & 0.215074532694915 & 481.634585161568 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 103.587333333333 & 0.215074532694915 & 481.634585161568 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 103.957333333333 & 0.163859155909939 & 634.431031674974 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 103.343448275862 & 0.324400657448755 & 318.567320697206 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 103.377142857143 & 0.31756865647761 & 325.526908114218 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 103.413333333333 & 0.308956110809786 & 334.718523813246 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 103.452307692308 & 0.298063207002093 & 347.081777495541 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 103.4944 & 0.28417918463461 & 364.18712416629 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 103.557083333333 & 0.269835114864519 & 383.779121502878 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 103.625217391304 & 0.250850291040329 & 413.09586272174 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 103.6475 & 0.247242749686876 & 419.21350628589 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 103.643571428571 & 0.249453018679449 & 415.483332201143 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 103.63925 & 0.251472175016824 & 412.130089514143 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 103.634473684211 & 0.253211435208043 & 409.280384983651 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 103.629166666667 & 0.254547022194204 & 407.112076084724 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 103.623235294118 & 0.255303712947159 & 405.882210242532 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 103.6165625 & 0.25522863302523 & 405.975463143892 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 103.609 & 0.253947840603393 & 407.993231026575 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 103.600357142857 & 0.250890731787868 & 412.930188391545 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 103.590384615385 & 0.245149549816327 & 422.559962655438 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 103.590833333333 & 0.239751469042866 & 432.075906549761 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 103.591363636364 & 0.229788435968823 & 450.81190965771 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 103.592 & 0.211885768628684 & 488.904944727732 \tabularnewline
Median & 102.78 &  &  \tabularnewline
Midrange & 102.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 103.784255319149 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 103.784255319149 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 103.784255319149 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 103.784255319149 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 103.784255319149 &  &  \tabularnewline
Midmean - Closest Observation & 103.784255319149 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 103.784255319149 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 103.784255319149 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=132027&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]103.312[/C][C]0.329817001134399[/C][C]313.240371614139[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]103.280606574845[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]103.248880634999[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]103.343056467283[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]103.312[/C][C]0.329817001134399[/C][C]313.240371614139[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]103.312[/C][C]0.329817001134399[/C][C]313.240371614139[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]103.312[/C][C]0.329817001134399[/C][C]313.240371614139[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]103.312[/C][C]0.329817001134399[/C][C]313.240371614139[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]103.243666666667[/C][C]0.319390659846194[/C][C]323.251990889104[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]103.243666666667[/C][C]0.319390659846194[/C][C]323.251990889104[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]103.510833333333[/C][C]0.255737693527513[/C][C]404.753917600329[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]103.6695[/C][C]0.227758349614694[/C][C]455.173213958483[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]103.6695[/C][C]0.227758349614694[/C][C]455.173213958483[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]103.6695[/C][C]0.227758349614694[/C][C]455.173213958483[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]103.6695[/C][C]0.227758349614694[/C][C]455.173213958483[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]103.6695[/C][C]0.227758349614694[/C][C]455.173213958483[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]103.6695[/C][C]0.227758349614694[/C][C]455.173213958483[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]103.6695[/C][C]0.227758349614694[/C][C]455.173213958483[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]103.6695[/C][C]0.227758349614694[/C][C]455.173213958483[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]103.6695[/C][C]0.227758349614694[/C][C]455.173213958483[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]103.587333333333[/C][C]0.215074532694915[/C][C]481.634585161568[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]103.587333333333[/C][C]0.215074532694915[/C][C]481.634585161568[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]103.587333333333[/C][C]0.215074532694915[/C][C]481.634585161568[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]103.957333333333[/C][C]0.163859155909939[/C][C]634.431031674974[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]103.343448275862[/C][C]0.324400657448755[/C][C]318.567320697206[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]103.377142857143[/C][C]0.31756865647761[/C][C]325.526908114218[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]103.413333333333[/C][C]0.308956110809786[/C][C]334.718523813246[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]103.452307692308[/C][C]0.298063207002093[/C][C]347.081777495541[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]103.4944[/C][C]0.28417918463461[/C][C]364.18712416629[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]103.557083333333[/C][C]0.269835114864519[/C][C]383.779121502878[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]103.625217391304[/C][C]0.250850291040329[/C][C]413.09586272174[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]103.6475[/C][C]0.247242749686876[/C][C]419.21350628589[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]103.643571428571[/C][C]0.249453018679449[/C][C]415.483332201143[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]103.63925[/C][C]0.251472175016824[/C][C]412.130089514143[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]103.634473684211[/C][C]0.253211435208043[/C][C]409.280384983651[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]103.629166666667[/C][C]0.254547022194204[/C][C]407.112076084724[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]103.623235294118[/C][C]0.255303712947159[/C][C]405.882210242532[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]103.6165625[/C][C]0.25522863302523[/C][C]405.975463143892[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]103.609[/C][C]0.253947840603393[/C][C]407.993231026575[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]103.600357142857[/C][C]0.250890731787868[/C][C]412.930188391545[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]103.590384615385[/C][C]0.245149549816327[/C][C]422.559962655438[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]103.590833333333[/C][C]0.239751469042866[/C][C]432.075906549761[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]103.591363636364[/C][C]0.229788435968823[/C][C]450.81190965771[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]103.592[/C][C]0.211885768628684[/C][C]488.904944727732[/C][/ROW]
[ROW][C]Median[/C][C]102.78[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]102.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]103.784255319149[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]103.784255319149[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]103.784255319149[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]103.784255319149[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]103.784255319149[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]103.784255319149[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]103.784255319149[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]103.784255319149[/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=132027&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=132027&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 Mean103.3120.329817001134399313.240371614139
Geometric Mean103.280606574845
Harmonic Mean103.248880634999
Quadratic Mean103.343056467283
Winsorized Mean ( 1 / 20 )103.3120.329817001134399313.240371614139
Winsorized Mean ( 2 / 20 )103.3120.329817001134399313.240371614139
Winsorized Mean ( 3 / 20 )103.3120.329817001134399313.240371614139
Winsorized Mean ( 4 / 20 )103.3120.329817001134399313.240371614139
Winsorized Mean ( 5 / 20 )103.2436666666670.319390659846194323.251990889104
Winsorized Mean ( 6 / 20 )103.2436666666670.319390659846194323.251990889104
Winsorized Mean ( 7 / 20 )103.5108333333330.255737693527513404.753917600329
Winsorized Mean ( 8 / 20 )103.66950.227758349614694455.173213958483
Winsorized Mean ( 9 / 20 )103.66950.227758349614694455.173213958483
Winsorized Mean ( 10 / 20 )103.66950.227758349614694455.173213958483
Winsorized Mean ( 11 / 20 )103.66950.227758349614694455.173213958483
Winsorized Mean ( 12 / 20 )103.66950.227758349614694455.173213958483
Winsorized Mean ( 13 / 20 )103.66950.227758349614694455.173213958483
Winsorized Mean ( 14 / 20 )103.66950.227758349614694455.173213958483
Winsorized Mean ( 15 / 20 )103.66950.227758349614694455.173213958483
Winsorized Mean ( 16 / 20 )103.66950.227758349614694455.173213958483
Winsorized Mean ( 17 / 20 )103.5873333333330.215074532694915481.634585161568
Winsorized Mean ( 18 / 20 )103.5873333333330.215074532694915481.634585161568
Winsorized Mean ( 19 / 20 )103.5873333333330.215074532694915481.634585161568
Winsorized Mean ( 20 / 20 )103.9573333333330.163859155909939634.431031674974
Trimmed Mean ( 1 / 20 )103.3434482758620.324400657448755318.567320697206
Trimmed Mean ( 2 / 20 )103.3771428571430.31756865647761325.526908114218
Trimmed Mean ( 3 / 20 )103.4133333333330.308956110809786334.718523813246
Trimmed Mean ( 4 / 20 )103.4523076923080.298063207002093347.081777495541
Trimmed Mean ( 5 / 20 )103.49440.28417918463461364.18712416629
Trimmed Mean ( 6 / 20 )103.5570833333330.269835114864519383.779121502878
Trimmed Mean ( 7 / 20 )103.6252173913040.250850291040329413.09586272174
Trimmed Mean ( 8 / 20 )103.64750.247242749686876419.21350628589
Trimmed Mean ( 9 / 20 )103.6435714285710.249453018679449415.483332201143
Trimmed Mean ( 10 / 20 )103.639250.251472175016824412.130089514143
Trimmed Mean ( 11 / 20 )103.6344736842110.253211435208043409.280384983651
Trimmed Mean ( 12 / 20 )103.6291666666670.254547022194204407.112076084724
Trimmed Mean ( 13 / 20 )103.6232352941180.255303712947159405.882210242532
Trimmed Mean ( 14 / 20 )103.61656250.25522863302523405.975463143892
Trimmed Mean ( 15 / 20 )103.6090.253947840603393407.993231026575
Trimmed Mean ( 16 / 20 )103.6003571428570.250890731787868412.930188391545
Trimmed Mean ( 17 / 20 )103.5903846153850.245149549816327422.559962655438
Trimmed Mean ( 18 / 20 )103.5908333333330.239751469042866432.075906549761
Trimmed Mean ( 19 / 20 )103.5913636363640.229788435968823450.81190965771
Trimmed Mean ( 20 / 20 )103.5920.211885768628684488.904944727732
Median102.78
Midrange102.4
Midmean - Weighted Average at Xnp103.784255319149
Midmean - Weighted Average at X(n+1)p103.784255319149
Midmean - Empirical Distribution Function103.784255319149
Midmean - Empirical Distribution Function - Averaging103.784255319149
Midmean - Empirical Distribution Function - Interpolation103.784255319149
Midmean - Closest Observation103.784255319149
Midmean - True Basic - Statistics Graphics Toolkit103.784255319149
Midmean - MS Excel (old versions)103.784255319149
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')