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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 14:08:41 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/20/t1224533419wo3z8u3vblatvvk.htm/, Retrieved Sat, 18 May 2024 23:23:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18055, Retrieved Sat, 18 May 2024 23:23:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact143
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Investigating Ass...] [2007-10-22 10:34:53] [b9964c45117f7aac638ab9056d451faa]
-    D    [Central Tendency] [Q9 Intermediare g...] [2008-10-20 20:08:41] [2ba2a74112fb2c960057a572bf2825d3] [Current]
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Dataseries X:
97,60
99,50
110,70
104,40
99,80
108,40
91,80
90,20
109,20
111,40
102,80
91,50
98,90
100,80
112,10
106,70
103,50
111,30
100,80
94,20
115,50
114,10
105,00
94,00
98,30
96,00
101,80
102,50
98,70
110,70
88,70
89,20
106,80
104,10
103,20
93,70
100,50
98,70
111,10
104,50
105,00
109,70
92,60
94,20
111,70
113,40
106,80
98,00
104,20
105,40
117,50
107,90
107,00
113,30
97,60
98,20
111,30
116,00
108,10
95,60
110,80




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18055&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18055&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18055&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean103.3934426229510.948181661747705109.043917209255
Geometric Mean103.129881594946
Harmonic Mean102.863871110368
Quadratic Mean103.653976697693
Winsorized Mean ( 1 / 20 )103.3770491803280.940292343339716109.941392070848
Winsorized Mean ( 2 / 20 )103.3934426229510.928674561844307111.334418827642
Winsorized Mean ( 3 / 20 )103.3885245901640.899736143351959114.909827013274
Winsorized Mean ( 4 / 20 )103.3622950819670.886545342580072116.589970210837
Winsorized Mean ( 5 / 20 )103.4196721311480.87108003958697118.725797207091
Winsorized Mean ( 6 / 20 )103.4098360655740.827784933256794124.923554308634
Winsorized Mean ( 7 / 20 )103.3983606557380.813182010703371127.152789037109
Winsorized Mean ( 8 / 20 )103.3852459016390.801524626654904128.985738508259
Winsorized Mean ( 9 / 20 )103.3704918032790.799075094654931129.362675041096
Winsorized Mean ( 10 / 20 )103.60.756862953284573136.880791364414
Winsorized Mean ( 11 / 20 )103.6360655737700.738193159621478140.391527912439
Winsorized Mean ( 12 / 20 )103.8918032786890.676556271440928153.559737252040
Winsorized Mean ( 13 / 20 )103.8704918032790.672940469692711154.353165668145
Winsorized Mean ( 14 / 20 )103.9622950819670.658886973127805157.784717746729
Winsorized Mean ( 15 / 20 )103.7655737704920.610530922073736169.959571282713
Winsorized Mean ( 16 / 20 )103.6606557377050.585570007147417177.025213847075
Winsorized Mean ( 17 / 20 )103.5491803278690.534148742872878193.858324501407
Winsorized Mean ( 18 / 20 )103.4606557377050.520877143190166198.627751457953
Winsorized Mean ( 19 / 20 )103.4606557377050.502204314160419206.013076392364
Winsorized Mean ( 20 / 20 )103.3622950819670.429964822137292240.397097065217
Trimmed Mean ( 1 / 20 )103.4033898305080.916696754873522112.799995506448
Trimmed Mean ( 2 / 20 )103.4315789473680.88767019934157116.520278617091
Trimmed Mean ( 3 / 20 )103.4527272727270.859570225967643120.354014305542
Trimmed Mean ( 4 / 20 )103.4773584905660.838599121753685123.393115740657
Trimmed Mean ( 5 / 20 )103.5117647058820.81728218689164126.653641014210
Trimmed Mean ( 6 / 20 )103.5346938775510.795494065343462130.151434672047
Trimmed Mean ( 7 / 20 )103.5617021276600.780856483154762132.625782537217
Trimmed Mean ( 8 / 20 )103.5933333333330.765594771099799135.310920664359
Trimmed Mean ( 9 / 20 )103.6302325581400.748313237098209138.485098780284
Trimmed Mean ( 10 / 20 )103.6731707317070.725611805694994142.876907346358
Trimmed Mean ( 11 / 20 )103.6846153846150.706691923340496146.718268541267
Trimmed Mean ( 12 / 20 )103.6918918918920.685591504751235151.24442349897
Trimmed Mean ( 13 / 20 )103.6628571428570.672647918370997154.111615172920
Trimmed Mean ( 14 / 20 )103.6333333333330.654322264837921158.382709717212
Trimmed Mean ( 15 / 20 )103.5870967741940.631072511476763164.144523632936
Trimmed Mean ( 16 / 20 )103.5620689655170.611837533433361169.264001154641
Trimmed Mean ( 17 / 20 )103.5481481481480.590146303999705175.461826069828
Trimmed Mean ( 18 / 20 )103.5480.573646813524373180.508280633203
Trimmed Mean ( 19 / 20 )103.5608695652170.550269036981606188.200430344547
Trimmed Mean ( 20 / 20 )103.5761904761900.517912695433027199.987741929343
Median104.1
Midrange103.1
Midmean - Weighted Average at Xnp103.383333333333
Midmean - Weighted Average at X(n+1)p103.587096774194
Midmean - Empirical Distribution Function103.587096774194
Midmean - Empirical Distribution Function - Averaging103.587096774194
Midmean - Empirical Distribution Function - Interpolation103.587096774194
Midmean - Closest Observation103.4125
Midmean - True Basic - Statistics Graphics Toolkit103.587096774194
Midmean - MS Excel (old versions)103.587096774194
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 103.393442622951 & 0.948181661747705 & 109.043917209255 \tabularnewline
Geometric Mean & 103.129881594946 &  &  \tabularnewline
Harmonic Mean & 102.863871110368 &  &  \tabularnewline
Quadratic Mean & 103.653976697693 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 103.377049180328 & 0.940292343339716 & 109.941392070848 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 103.393442622951 & 0.928674561844307 & 111.334418827642 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 103.388524590164 & 0.899736143351959 & 114.909827013274 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 103.362295081967 & 0.886545342580072 & 116.589970210837 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 103.419672131148 & 0.87108003958697 & 118.725797207091 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 103.409836065574 & 0.827784933256794 & 124.923554308634 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 103.398360655738 & 0.813182010703371 & 127.152789037109 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 103.385245901639 & 0.801524626654904 & 128.985738508259 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 103.370491803279 & 0.799075094654931 & 129.362675041096 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 103.6 & 0.756862953284573 & 136.880791364414 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 103.636065573770 & 0.738193159621478 & 140.391527912439 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 103.891803278689 & 0.676556271440928 & 153.559737252040 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 103.870491803279 & 0.672940469692711 & 154.353165668145 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 103.962295081967 & 0.658886973127805 & 157.784717746729 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 103.765573770492 & 0.610530922073736 & 169.959571282713 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 103.660655737705 & 0.585570007147417 & 177.025213847075 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 103.549180327869 & 0.534148742872878 & 193.858324501407 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 103.460655737705 & 0.520877143190166 & 198.627751457953 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 103.460655737705 & 0.502204314160419 & 206.013076392364 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 103.362295081967 & 0.429964822137292 & 240.397097065217 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 103.403389830508 & 0.916696754873522 & 112.799995506448 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 103.431578947368 & 0.88767019934157 & 116.520278617091 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 103.452727272727 & 0.859570225967643 & 120.354014305542 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 103.477358490566 & 0.838599121753685 & 123.393115740657 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 103.511764705882 & 0.81728218689164 & 126.653641014210 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 103.534693877551 & 0.795494065343462 & 130.151434672047 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 103.561702127660 & 0.780856483154762 & 132.625782537217 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 103.593333333333 & 0.765594771099799 & 135.310920664359 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 103.630232558140 & 0.748313237098209 & 138.485098780284 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 103.673170731707 & 0.725611805694994 & 142.876907346358 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 103.684615384615 & 0.706691923340496 & 146.718268541267 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 103.691891891892 & 0.685591504751235 & 151.24442349897 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 103.662857142857 & 0.672647918370997 & 154.111615172920 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 103.633333333333 & 0.654322264837921 & 158.382709717212 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 103.587096774194 & 0.631072511476763 & 164.144523632936 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 103.562068965517 & 0.611837533433361 & 169.264001154641 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 103.548148148148 & 0.590146303999705 & 175.461826069828 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 103.548 & 0.573646813524373 & 180.508280633203 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 103.560869565217 & 0.550269036981606 & 188.200430344547 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 103.576190476190 & 0.517912695433027 & 199.987741929343 \tabularnewline
Median & 104.1 &  &  \tabularnewline
Midrange & 103.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 103.383333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 103.587096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 103.587096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 103.587096774194 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 103.587096774194 &  &  \tabularnewline
Midmean - Closest Observation & 103.4125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 103.587096774194 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 103.587096774194 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18055&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]103.393442622951[/C][C]0.948181661747705[/C][C]109.043917209255[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]103.129881594946[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]102.863871110368[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]103.653976697693[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]103.377049180328[/C][C]0.940292343339716[/C][C]109.941392070848[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]103.393442622951[/C][C]0.928674561844307[/C][C]111.334418827642[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]103.388524590164[/C][C]0.899736143351959[/C][C]114.909827013274[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]103.362295081967[/C][C]0.886545342580072[/C][C]116.589970210837[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]103.419672131148[/C][C]0.87108003958697[/C][C]118.725797207091[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]103.409836065574[/C][C]0.827784933256794[/C][C]124.923554308634[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]103.398360655738[/C][C]0.813182010703371[/C][C]127.152789037109[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]103.385245901639[/C][C]0.801524626654904[/C][C]128.985738508259[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]103.370491803279[/C][C]0.799075094654931[/C][C]129.362675041096[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]103.6[/C][C]0.756862953284573[/C][C]136.880791364414[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]103.636065573770[/C][C]0.738193159621478[/C][C]140.391527912439[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]103.891803278689[/C][C]0.676556271440928[/C][C]153.559737252040[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]103.870491803279[/C][C]0.672940469692711[/C][C]154.353165668145[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]103.962295081967[/C][C]0.658886973127805[/C][C]157.784717746729[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]103.765573770492[/C][C]0.610530922073736[/C][C]169.959571282713[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]103.660655737705[/C][C]0.585570007147417[/C][C]177.025213847075[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]103.549180327869[/C][C]0.534148742872878[/C][C]193.858324501407[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]103.460655737705[/C][C]0.520877143190166[/C][C]198.627751457953[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]103.460655737705[/C][C]0.502204314160419[/C][C]206.013076392364[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]103.362295081967[/C][C]0.429964822137292[/C][C]240.397097065217[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]103.403389830508[/C][C]0.916696754873522[/C][C]112.799995506448[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]103.431578947368[/C][C]0.88767019934157[/C][C]116.520278617091[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]103.452727272727[/C][C]0.859570225967643[/C][C]120.354014305542[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]103.477358490566[/C][C]0.838599121753685[/C][C]123.393115740657[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]103.511764705882[/C][C]0.81728218689164[/C][C]126.653641014210[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]103.534693877551[/C][C]0.795494065343462[/C][C]130.151434672047[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]103.561702127660[/C][C]0.780856483154762[/C][C]132.625782537217[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]103.593333333333[/C][C]0.765594771099799[/C][C]135.310920664359[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]103.630232558140[/C][C]0.748313237098209[/C][C]138.485098780284[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]103.673170731707[/C][C]0.725611805694994[/C][C]142.876907346358[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]103.684615384615[/C][C]0.706691923340496[/C][C]146.718268541267[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]103.691891891892[/C][C]0.685591504751235[/C][C]151.24442349897[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]103.662857142857[/C][C]0.672647918370997[/C][C]154.111615172920[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]103.633333333333[/C][C]0.654322264837921[/C][C]158.382709717212[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]103.587096774194[/C][C]0.631072511476763[/C][C]164.144523632936[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]103.562068965517[/C][C]0.611837533433361[/C][C]169.264001154641[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]103.548148148148[/C][C]0.590146303999705[/C][C]175.461826069828[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]103.548[/C][C]0.573646813524373[/C][C]180.508280633203[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]103.560869565217[/C][C]0.550269036981606[/C][C]188.200430344547[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]103.576190476190[/C][C]0.517912695433027[/C][C]199.987741929343[/C][/ROW]
[ROW][C]Median[/C][C]104.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]103.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]103.383333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]103.587096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]103.587096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]103.587096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]103.587096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]103.4125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]103.587096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]103.587096774194[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18055&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18055&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 Mean103.3934426229510.948181661747705109.043917209255
Geometric Mean103.129881594946
Harmonic Mean102.863871110368
Quadratic Mean103.653976697693
Winsorized Mean ( 1 / 20 )103.3770491803280.940292343339716109.941392070848
Winsorized Mean ( 2 / 20 )103.3934426229510.928674561844307111.334418827642
Winsorized Mean ( 3 / 20 )103.3885245901640.899736143351959114.909827013274
Winsorized Mean ( 4 / 20 )103.3622950819670.886545342580072116.589970210837
Winsorized Mean ( 5 / 20 )103.4196721311480.87108003958697118.725797207091
Winsorized Mean ( 6 / 20 )103.4098360655740.827784933256794124.923554308634
Winsorized Mean ( 7 / 20 )103.3983606557380.813182010703371127.152789037109
Winsorized Mean ( 8 / 20 )103.3852459016390.801524626654904128.985738508259
Winsorized Mean ( 9 / 20 )103.3704918032790.799075094654931129.362675041096
Winsorized Mean ( 10 / 20 )103.60.756862953284573136.880791364414
Winsorized Mean ( 11 / 20 )103.6360655737700.738193159621478140.391527912439
Winsorized Mean ( 12 / 20 )103.8918032786890.676556271440928153.559737252040
Winsorized Mean ( 13 / 20 )103.8704918032790.672940469692711154.353165668145
Winsorized Mean ( 14 / 20 )103.9622950819670.658886973127805157.784717746729
Winsorized Mean ( 15 / 20 )103.7655737704920.610530922073736169.959571282713
Winsorized Mean ( 16 / 20 )103.6606557377050.585570007147417177.025213847075
Winsorized Mean ( 17 / 20 )103.5491803278690.534148742872878193.858324501407
Winsorized Mean ( 18 / 20 )103.4606557377050.520877143190166198.627751457953
Winsorized Mean ( 19 / 20 )103.4606557377050.502204314160419206.013076392364
Winsorized Mean ( 20 / 20 )103.3622950819670.429964822137292240.397097065217
Trimmed Mean ( 1 / 20 )103.4033898305080.916696754873522112.799995506448
Trimmed Mean ( 2 / 20 )103.4315789473680.88767019934157116.520278617091
Trimmed Mean ( 3 / 20 )103.4527272727270.859570225967643120.354014305542
Trimmed Mean ( 4 / 20 )103.4773584905660.838599121753685123.393115740657
Trimmed Mean ( 5 / 20 )103.5117647058820.81728218689164126.653641014210
Trimmed Mean ( 6 / 20 )103.5346938775510.795494065343462130.151434672047
Trimmed Mean ( 7 / 20 )103.5617021276600.780856483154762132.625782537217
Trimmed Mean ( 8 / 20 )103.5933333333330.765594771099799135.310920664359
Trimmed Mean ( 9 / 20 )103.6302325581400.748313237098209138.485098780284
Trimmed Mean ( 10 / 20 )103.6731707317070.725611805694994142.876907346358
Trimmed Mean ( 11 / 20 )103.6846153846150.706691923340496146.718268541267
Trimmed Mean ( 12 / 20 )103.6918918918920.685591504751235151.24442349897
Trimmed Mean ( 13 / 20 )103.6628571428570.672647918370997154.111615172920
Trimmed Mean ( 14 / 20 )103.6333333333330.654322264837921158.382709717212
Trimmed Mean ( 15 / 20 )103.5870967741940.631072511476763164.144523632936
Trimmed Mean ( 16 / 20 )103.5620689655170.611837533433361169.264001154641
Trimmed Mean ( 17 / 20 )103.5481481481480.590146303999705175.461826069828
Trimmed Mean ( 18 / 20 )103.5480.573646813524373180.508280633203
Trimmed Mean ( 19 / 20 )103.5608695652170.550269036981606188.200430344547
Trimmed Mean ( 20 / 20 )103.5761904761900.517912695433027199.987741929343
Median104.1
Midrange103.1
Midmean - Weighted Average at Xnp103.383333333333
Midmean - Weighted Average at X(n+1)p103.587096774194
Midmean - Empirical Distribution Function103.587096774194
Midmean - Empirical Distribution Function - Averaging103.587096774194
Midmean - Empirical Distribution Function - Interpolation103.587096774194
Midmean - Closest Observation103.4125
Midmean - True Basic - Statistics Graphics Toolkit103.587096774194
Midmean - MS Excel (old versions)103.587096774194
Number of observations61



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')