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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 09 Oct 2015 11:20:24 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Oct/09/t1444386051hywcjutx3br5ti9.htm/, Retrieved Tue, 14 May 2024 18:31:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=281809, Retrieved Tue, 14 May 2024 18:31:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2015-10-09 10:20:24] [5460c453892b15ffecb85c645e1cdda5] [Current]
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Dataseries X:
94,3
94,6
94,9
95,6
95,4
97,4
98,4
100,5
106,6
106,7
106,8
109
109,3
110,5
113,4
113
113,6
121,2
120,5
120,9
125,8
125,4
125,7
127,7
128,1
130
130,5
130,1
129,6
128,8
128,4
128,3
127,6
127,3
127,7
126,9
125,1
119
118,7
118,9
116,9
117
117
115,5
115,6
117,5
117,6
117,8
119,3
120
120,2
109,4
109
108,8
96,3
96,9
97
111,4
111,8
111,7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281809&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]2 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=281809&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281809&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean114.9816666666671.4401751534771879.8386685043502
Geometric Mean114.430316888886
Harmonic Mean113.860621255249
Quadratic Mean115.51257868013
Winsorized Mean ( 1 / 20 )114.981.4377630930944179.9714504790463
Winsorized Mean ( 2 / 20 )114.9866666666671.4347827384629880.142214973848
Winsorized Mean ( 3 / 20 )114.9916666666671.4253937738555480.6736136889572
Winsorized Mean ( 4 / 20 )114.9516666666671.4132314448669981.3395902590364
Winsorized Mean ( 5 / 20 )114.9766666666671.394351734975382.4588687220327
Winsorized Mean ( 6 / 20 )115.0266666666671.3792261538368283.3994239064264
Winsorized Mean ( 7 / 20 )115.0151.3728415518746883.7787870296771
Winsorized Mean ( 8 / 20 )115.0151.3524759153844285.040331359475
Winsorized Mean ( 9 / 20 )115.1651.3197667680442287.2616304551024
Winsorized Mean ( 10 / 20 )115.4983333333331.2435426241202192.8784676078533
Winsorized Mean ( 11 / 20 )116.5616666666671.02566801069998113.644634960505
Winsorized Mean ( 12 / 20 )116.5016666666671.00828346517205115.544557350037
Winsorized Mean ( 13 / 20 )116.2850.963904562521476120.639536860175
Winsorized Mean ( 14 / 20 )116.7283333333330.885476320689008131.82547133785
Winsorized Mean ( 15 / 20 )116.7033333333330.865078836636862134.904853050199
Winsorized Mean ( 16 / 20 )116.6233333333330.851513662773987136.960025930069
Winsorized Mean ( 17 / 20 )115.6033333333330.664405629058537173.995114245409
Winsorized Mean ( 18 / 20 )115.5433333333330.646836572705252178.628324694287
Winsorized Mean ( 19 / 20 )115.7650.573914229108219201.711325714789
Winsorized Mean ( 20 / 20 )115.9650.513995235089699225.61493197454
Trimmed Mean ( 1 / 20 )115.0706896551721.4207561882763980.9925662155815
Trimmed Mean ( 2 / 20 )115.1678571428571.3989632226510682.3237203652945
Trimmed Mean ( 3 / 20 )115.2685185185191.3731650587765683.9436728904382
Trimmed Mean ( 4 / 20 )115.3751.344756519983985.796200490912
Trimmed Mean ( 5 / 20 )115.5021.3129977850984687.9681605794471
Trimmed Mean ( 6 / 20 )115.6333333333331.2785406038331890.4416590186138
Trimmed Mean ( 7 / 20 )115.7652173913041.2385951890864393.4649338309562
Trimmed Mean ( 8 / 20 )115.9113636363641.188031469626797.5659034291282
Trimmed Mean ( 9 / 20 )116.0714285714291.12713488601378102.979182005382
Trimmed Mean ( 10 / 20 )116.22251.0558960679964110.070018747713
Trimmed Mean ( 11 / 20 )116.3368421052630.984274801835436118.195489601403
Trimmed Mean ( 12 / 20 )116.3027777777780.954142897280242121.892410570047
Trimmed Mean ( 13 / 20 )116.2735294117650.916547315097031126.860367704482
Trimmed Mean ( 14 / 20 )116.2718750.876464608055218132.660091384631
Trimmed Mean ( 15 / 20 )116.2066666666670.842272969285654137.96794020972
Trimmed Mean ( 16 / 20 )116.1357142857140.797320484277512145.657507333391
Trimmed Mean ( 17 / 20 )116.0653846153850.732959067126426158.351795920092
Trimmed Mean ( 18 / 20 )116.1333333333330.708326939442583163.95442113881
Trimmed Mean ( 19 / 20 )116.2227272727270.672139821897967172.914508984963
Trimmed Mean ( 20 / 20 )116.2950.643938334739724180.59959118136
Median117
Midrange112.4
Midmean - Weighted Average at Xnp115.967741935484
Midmean - Weighted Average at X(n+1)p116.206666666667
Midmean - Empirical Distribution Function115.967741935484
Midmean - Empirical Distribution Function - Averaging116.206666666667
Midmean - Empirical Distribution Function - Interpolation116.206666666667
Midmean - Closest Observation115.967741935484
Midmean - True Basic - Statistics Graphics Toolkit116.206666666667
Midmean - MS Excel (old versions)116.271875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 114.981666666667 & 1.44017515347718 & 79.8386685043502 \tabularnewline
Geometric Mean & 114.430316888886 &  &  \tabularnewline
Harmonic Mean & 113.860621255249 &  &  \tabularnewline
Quadratic Mean & 115.51257868013 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 114.98 & 1.43776309309441 & 79.9714504790463 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 114.986666666667 & 1.43478273846298 & 80.142214973848 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 114.991666666667 & 1.42539377385554 & 80.6736136889572 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 114.951666666667 & 1.41323144486699 & 81.3395902590364 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 114.976666666667 & 1.3943517349753 & 82.4588687220327 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 115.026666666667 & 1.37922615383682 & 83.3994239064264 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 115.015 & 1.37284155187468 & 83.7787870296771 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 115.015 & 1.35247591538442 & 85.040331359475 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 115.165 & 1.31976676804422 & 87.2616304551024 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 115.498333333333 & 1.24354262412021 & 92.8784676078533 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 116.561666666667 & 1.02566801069998 & 113.644634960505 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 116.501666666667 & 1.00828346517205 & 115.544557350037 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 116.285 & 0.963904562521476 & 120.639536860175 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 116.728333333333 & 0.885476320689008 & 131.82547133785 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 116.703333333333 & 0.865078836636862 & 134.904853050199 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 116.623333333333 & 0.851513662773987 & 136.960025930069 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 115.603333333333 & 0.664405629058537 & 173.995114245409 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 115.543333333333 & 0.646836572705252 & 178.628324694287 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 115.765 & 0.573914229108219 & 201.711325714789 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 115.965 & 0.513995235089699 & 225.61493197454 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 115.070689655172 & 1.42075618827639 & 80.9925662155815 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 115.167857142857 & 1.39896322265106 & 82.3237203652945 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 115.268518518519 & 1.37316505877656 & 83.9436728904382 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 115.375 & 1.3447565199839 & 85.796200490912 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 115.502 & 1.31299778509846 & 87.9681605794471 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 115.633333333333 & 1.27854060383318 & 90.4416590186138 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 115.765217391304 & 1.23859518908643 & 93.4649338309562 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 115.911363636364 & 1.1880314696267 & 97.5659034291282 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 116.071428571429 & 1.12713488601378 & 102.979182005382 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 116.2225 & 1.0558960679964 & 110.070018747713 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 116.336842105263 & 0.984274801835436 & 118.195489601403 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 116.302777777778 & 0.954142897280242 & 121.892410570047 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 116.273529411765 & 0.916547315097031 & 126.860367704482 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 116.271875 & 0.876464608055218 & 132.660091384631 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 116.206666666667 & 0.842272969285654 & 137.96794020972 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 116.135714285714 & 0.797320484277512 & 145.657507333391 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 116.065384615385 & 0.732959067126426 & 158.351795920092 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 116.133333333333 & 0.708326939442583 & 163.95442113881 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 116.222727272727 & 0.672139821897967 & 172.914508984963 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 116.295 & 0.643938334739724 & 180.59959118136 \tabularnewline
Median & 117 &  &  \tabularnewline
Midrange & 112.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 115.967741935484 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 116.206666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 115.967741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 116.206666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 116.206666666667 &  &  \tabularnewline
Midmean - Closest Observation & 115.967741935484 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 116.206666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 116.271875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=281809&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]114.981666666667[/C][C]1.44017515347718[/C][C]79.8386685043502[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]114.430316888886[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]113.860621255249[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]115.51257868013[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]114.98[/C][C]1.43776309309441[/C][C]79.9714504790463[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]114.986666666667[/C][C]1.43478273846298[/C][C]80.142214973848[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]114.991666666667[/C][C]1.42539377385554[/C][C]80.6736136889572[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]114.951666666667[/C][C]1.41323144486699[/C][C]81.3395902590364[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]114.976666666667[/C][C]1.3943517349753[/C][C]82.4588687220327[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]115.026666666667[/C][C]1.37922615383682[/C][C]83.3994239064264[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]115.015[/C][C]1.37284155187468[/C][C]83.7787870296771[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]115.015[/C][C]1.35247591538442[/C][C]85.040331359475[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]115.165[/C][C]1.31976676804422[/C][C]87.2616304551024[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]115.498333333333[/C][C]1.24354262412021[/C][C]92.8784676078533[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]116.561666666667[/C][C]1.02566801069998[/C][C]113.644634960505[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]116.501666666667[/C][C]1.00828346517205[/C][C]115.544557350037[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]116.285[/C][C]0.963904562521476[/C][C]120.639536860175[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]116.728333333333[/C][C]0.885476320689008[/C][C]131.82547133785[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]116.703333333333[/C][C]0.865078836636862[/C][C]134.904853050199[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]116.623333333333[/C][C]0.851513662773987[/C][C]136.960025930069[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]115.603333333333[/C][C]0.664405629058537[/C][C]173.995114245409[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]115.543333333333[/C][C]0.646836572705252[/C][C]178.628324694287[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]115.765[/C][C]0.573914229108219[/C][C]201.711325714789[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]115.965[/C][C]0.513995235089699[/C][C]225.61493197454[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]115.070689655172[/C][C]1.42075618827639[/C][C]80.9925662155815[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]115.167857142857[/C][C]1.39896322265106[/C][C]82.3237203652945[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]115.268518518519[/C][C]1.37316505877656[/C][C]83.9436728904382[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]115.375[/C][C]1.3447565199839[/C][C]85.796200490912[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]115.502[/C][C]1.31299778509846[/C][C]87.9681605794471[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]115.633333333333[/C][C]1.27854060383318[/C][C]90.4416590186138[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]115.765217391304[/C][C]1.23859518908643[/C][C]93.4649338309562[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]115.911363636364[/C][C]1.1880314696267[/C][C]97.5659034291282[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]116.071428571429[/C][C]1.12713488601378[/C][C]102.979182005382[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]116.2225[/C][C]1.0558960679964[/C][C]110.070018747713[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]116.336842105263[/C][C]0.984274801835436[/C][C]118.195489601403[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]116.302777777778[/C][C]0.954142897280242[/C][C]121.892410570047[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]116.273529411765[/C][C]0.916547315097031[/C][C]126.860367704482[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]116.271875[/C][C]0.876464608055218[/C][C]132.660091384631[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]116.206666666667[/C][C]0.842272969285654[/C][C]137.96794020972[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]116.135714285714[/C][C]0.797320484277512[/C][C]145.657507333391[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]116.065384615385[/C][C]0.732959067126426[/C][C]158.351795920092[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]116.133333333333[/C][C]0.708326939442583[/C][C]163.95442113881[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]116.222727272727[/C][C]0.672139821897967[/C][C]172.914508984963[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]116.295[/C][C]0.643938334739724[/C][C]180.59959118136[/C][/ROW]
[ROW][C]Median[/C][C]117[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]112.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]115.967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]116.206666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]115.967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]116.206666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]116.206666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]115.967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]116.206666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]116.271875[/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=281809&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=281809&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 Mean114.9816666666671.4401751534771879.8386685043502
Geometric Mean114.430316888886
Harmonic Mean113.860621255249
Quadratic Mean115.51257868013
Winsorized Mean ( 1 / 20 )114.981.4377630930944179.9714504790463
Winsorized Mean ( 2 / 20 )114.9866666666671.4347827384629880.142214973848
Winsorized Mean ( 3 / 20 )114.9916666666671.4253937738555480.6736136889572
Winsorized Mean ( 4 / 20 )114.9516666666671.4132314448669981.3395902590364
Winsorized Mean ( 5 / 20 )114.9766666666671.394351734975382.4588687220327
Winsorized Mean ( 6 / 20 )115.0266666666671.3792261538368283.3994239064264
Winsorized Mean ( 7 / 20 )115.0151.3728415518746883.7787870296771
Winsorized Mean ( 8 / 20 )115.0151.3524759153844285.040331359475
Winsorized Mean ( 9 / 20 )115.1651.3197667680442287.2616304551024
Winsorized Mean ( 10 / 20 )115.4983333333331.2435426241202192.8784676078533
Winsorized Mean ( 11 / 20 )116.5616666666671.02566801069998113.644634960505
Winsorized Mean ( 12 / 20 )116.5016666666671.00828346517205115.544557350037
Winsorized Mean ( 13 / 20 )116.2850.963904562521476120.639536860175
Winsorized Mean ( 14 / 20 )116.7283333333330.885476320689008131.82547133785
Winsorized Mean ( 15 / 20 )116.7033333333330.865078836636862134.904853050199
Winsorized Mean ( 16 / 20 )116.6233333333330.851513662773987136.960025930069
Winsorized Mean ( 17 / 20 )115.6033333333330.664405629058537173.995114245409
Winsorized Mean ( 18 / 20 )115.5433333333330.646836572705252178.628324694287
Winsorized Mean ( 19 / 20 )115.7650.573914229108219201.711325714789
Winsorized Mean ( 20 / 20 )115.9650.513995235089699225.61493197454
Trimmed Mean ( 1 / 20 )115.0706896551721.4207561882763980.9925662155815
Trimmed Mean ( 2 / 20 )115.1678571428571.3989632226510682.3237203652945
Trimmed Mean ( 3 / 20 )115.2685185185191.3731650587765683.9436728904382
Trimmed Mean ( 4 / 20 )115.3751.344756519983985.796200490912
Trimmed Mean ( 5 / 20 )115.5021.3129977850984687.9681605794471
Trimmed Mean ( 6 / 20 )115.6333333333331.2785406038331890.4416590186138
Trimmed Mean ( 7 / 20 )115.7652173913041.2385951890864393.4649338309562
Trimmed Mean ( 8 / 20 )115.9113636363641.188031469626797.5659034291282
Trimmed Mean ( 9 / 20 )116.0714285714291.12713488601378102.979182005382
Trimmed Mean ( 10 / 20 )116.22251.0558960679964110.070018747713
Trimmed Mean ( 11 / 20 )116.3368421052630.984274801835436118.195489601403
Trimmed Mean ( 12 / 20 )116.3027777777780.954142897280242121.892410570047
Trimmed Mean ( 13 / 20 )116.2735294117650.916547315097031126.860367704482
Trimmed Mean ( 14 / 20 )116.2718750.876464608055218132.660091384631
Trimmed Mean ( 15 / 20 )116.2066666666670.842272969285654137.96794020972
Trimmed Mean ( 16 / 20 )116.1357142857140.797320484277512145.657507333391
Trimmed Mean ( 17 / 20 )116.0653846153850.732959067126426158.351795920092
Trimmed Mean ( 18 / 20 )116.1333333333330.708326939442583163.95442113881
Trimmed Mean ( 19 / 20 )116.2227272727270.672139821897967172.914508984963
Trimmed Mean ( 20 / 20 )116.2950.643938334739724180.59959118136
Median117
Midrange112.4
Midmean - Weighted Average at Xnp115.967741935484
Midmean - Weighted Average at X(n+1)p116.206666666667
Midmean - Empirical Distribution Function115.967741935484
Midmean - Empirical Distribution Function - Averaging116.206666666667
Midmean - Empirical Distribution Function - Interpolation116.206666666667
Midmean - Closest Observation115.967741935484
Midmean - True Basic - Statistics Graphics Toolkit116.206666666667
Midmean - MS Excel (old versions)116.271875
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')