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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 08 Mar 2016 21:24:57 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Mar/08/t1457472322a3gz38t9t73fa1b.htm/, Retrieved Mon, 29 Apr 2024 07:39:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293778, Retrieved Mon, 29 Apr 2024 07:39:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten eige...] [2016-03-08 21:24:57] [ca27af53963d179bfb9e7ceb75b255dc] [Current]
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Dataseries X:
90,66
91,08
91,12
91,02
90,58
90,92
91,79
91,97
92,53
92,44
92,7
93,12
94,23
94,18
93,89
94,08
95,59
96,55
97,01
96,87
97,96
97,94
98,57
98,67
98,58
99,04
98,89
98,63
98,52
98,07
98,15
98,4
99,22
99,35
100,05
99,86
100,31
100,7
100,78
99,78
99,55
99,46
99,66
99,43
99,68
100,21
100,31
100,13
100,27
100,23
99,93
100,66
100,55
100,43
101,22
101,07
101,43
101,35
101,58
101,59
102,03
102,48
102,63
103,54
103,97
104,34
104,29
104,17
104,55
104,58
104,74
104,73




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293778&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293778&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293778&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean98.59152777777780.468616636102822210.38845013634
Geometric Mean98.5111450022836
Harmonic Mean98.4294533694453
Quadratic Mean98.6705683561325
Winsorized Mean ( 1 / 24 )98.59250.468324676627929210.521684891546
Winsorized Mean ( 2 / 24 )98.59555555555560.46586365724279211.6403673536
Winsorized Mean ( 3 / 24 )98.59847222222220.464675819642064212.187654391338
Winsorized Mean ( 4 / 24 )98.59013888888890.461835975676867213.474359039257
Winsorized Mean ( 5 / 24 )98.58944444444450.46059356856402214.048677995687
Winsorized Mean ( 6 / 24 )98.63527777777780.446438259352864220.938227652699
Winsorized Mean ( 7 / 24 )98.63333333333330.439317919896041224.514705333836
Winsorized Mean ( 8 / 24 )98.63777777777780.42029817561461234.685238958123
Winsorized Mean ( 9 / 24 )98.53527777777780.400378389699384246.105385087744
Winsorized Mean ( 10 / 24 )98.53805555555560.392436195330742251.093188467257
Winsorized Mean ( 11 / 24 )98.53347222222220.369641430519607266.565011621433
Winsorized Mean ( 12 / 24 )98.58847222222220.334134287691872295.056436450298
Winsorized Mean ( 13 / 24 )98.62097222222220.327154180133949301.451053389698
Winsorized Mean ( 14 / 24 )98.611250.319686058436287308.46277902248
Winsorized Mean ( 15 / 24 )98.6050.315596474291601312.440119051812
Winsorized Mean ( 16 / 24 )98.87833333333330.254776974488011388.097603922157
Winsorized Mean ( 17 / 24 )99.06958333333330.210246654228411471.206467931255
Winsorized Mean ( 18 / 24 )99.07708333333330.187339961695426528.862515165937
Winsorized Mean ( 19 / 24 )99.09291666666670.178549125451598554.989650137095
Winsorized Mean ( 20 / 24 )99.34013888888890.136925709649612725.503918461307
Winsorized Mean ( 21 / 24 )99.31388888888890.131785403696195753.60310097647
Winsorized Mean ( 22 / 24 )99.31083333333330.122158589745107812.966436012011
Winsorized Mean ( 23 / 24 )99.29805555555550.113632172785939873.855116214435
Winsorized Mean ( 24 / 24 )99.38138888888890.102043729609245973.909805820003
Trimmed Mean ( 1 / 24 )98.61814285714290.45967070276855214.540849053846
Trimmed Mean ( 2 / 24 )98.64529411764710.449325974118925219.540600364977
Trimmed Mean ( 3 / 24 )98.67242424242420.438496799743052225.024274522058
Trimmed Mean ( 4 / 24 )98.700156250.426003745383452231.688470628723
Trimmed Mean ( 5 / 24 )98.73209677419360.411940445417728239.675656693711
Trimmed Mean ( 6 / 24 )98.76633333333330.39519772399979249.916250361265
Trimmed Mean ( 7 / 24 )98.79344827586210.379037095660197260.643217793198
Trimmed Mean ( 8 / 24 )98.82285714285710.361079524489503273.687236302234
Trimmed Mean ( 9 / 24 )98.85370370370370.343920880535371287.431526547098
Trimmed Mean ( 10 / 24 )98.90269230769230.327329465275358302.150288317285
Trimmed Mean ( 11 / 24 )98.95520.308213448434552321.060617252763
Trimmed Mean ( 12 / 24 )99.01270833333330.289500324535783342.012426038213
Trimmed Mean ( 13 / 24 )99.06804347826090.274566785618281360.81583304104
Trimmed Mean ( 14 / 24 )99.12431818181820.256749356996066386.074260678039
Trimmed Mean ( 15 / 24 )99.18714285714290.23462335094295422.750516768729
Trimmed Mean ( 16 / 24 )99.2570.204667397476353484.967323686558
Trimmed Mean ( 17 / 24 )99.30184210526320.18471032076711537.608519615245
Trimmed Mean ( 18 / 24 )99.32916666666670.171926236951726577.742922940591
Trimmed Mean ( 19 / 24 )99.35882352941180.160939623263398617.367069182203
Trimmed Mean ( 20 / 24 )99.39031250.147950027237158671.782995623794
Trimmed Mean ( 21 / 24 )99.39633333333330.143828987960626691.073021806591
Trimmed Mean ( 22 / 24 )99.40642857142860.138971290748505715.301901824627
Trimmed Mean ( 23 / 24 )99.41846153846150.134525596429358739.030074404227
Trimmed Mean ( 24 / 24 )99.43416666666670.130171175857617763.872385814731
Median99.505
Midrange97.66
Midmean - Weighted Average at Xnp99.2540540540541
Midmean - Weighted Average at X(n+1)p99.3291666666667
Midmean - Empirical Distribution Function99.2540540540541
Midmean - Empirical Distribution Function - Averaging99.3291666666667
Midmean - Empirical Distribution Function - Interpolation99.3291666666667
Midmean - Closest Observation99.2540540540541
Midmean - True Basic - Statistics Graphics Toolkit99.3291666666667
Midmean - MS Excel (old versions)99.3018421052632
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 98.5915277777778 & 0.468616636102822 & 210.38845013634 \tabularnewline
Geometric Mean & 98.5111450022836 &  &  \tabularnewline
Harmonic Mean & 98.4294533694453 &  &  \tabularnewline
Quadratic Mean & 98.6705683561325 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 98.5925 & 0.468324676627929 & 210.521684891546 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 98.5955555555556 & 0.46586365724279 & 211.6403673536 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 98.5984722222222 & 0.464675819642064 & 212.187654391338 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 98.5901388888889 & 0.461835975676867 & 213.474359039257 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 98.5894444444445 & 0.46059356856402 & 214.048677995687 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 98.6352777777778 & 0.446438259352864 & 220.938227652699 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 98.6333333333333 & 0.439317919896041 & 224.514705333836 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 98.6377777777778 & 0.42029817561461 & 234.685238958123 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 98.5352777777778 & 0.400378389699384 & 246.105385087744 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 98.5380555555556 & 0.392436195330742 & 251.093188467257 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 98.5334722222222 & 0.369641430519607 & 266.565011621433 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 98.5884722222222 & 0.334134287691872 & 295.056436450298 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 98.6209722222222 & 0.327154180133949 & 301.451053389698 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 98.61125 & 0.319686058436287 & 308.46277902248 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 98.605 & 0.315596474291601 & 312.440119051812 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 98.8783333333333 & 0.254776974488011 & 388.097603922157 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 99.0695833333333 & 0.210246654228411 & 471.206467931255 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 99.0770833333333 & 0.187339961695426 & 528.862515165937 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 99.0929166666667 & 0.178549125451598 & 554.989650137095 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 99.3401388888889 & 0.136925709649612 & 725.503918461307 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 99.3138888888889 & 0.131785403696195 & 753.60310097647 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 99.3108333333333 & 0.122158589745107 & 812.966436012011 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 99.2980555555555 & 0.113632172785939 & 873.855116214435 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 99.3813888888889 & 0.102043729609245 & 973.909805820003 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 98.6181428571429 & 0.45967070276855 & 214.540849053846 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 98.6452941176471 & 0.449325974118925 & 219.540600364977 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 98.6724242424242 & 0.438496799743052 & 225.024274522058 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 98.70015625 & 0.426003745383452 & 231.688470628723 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 98.7320967741936 & 0.411940445417728 & 239.675656693711 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 98.7663333333333 & 0.39519772399979 & 249.916250361265 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 98.7934482758621 & 0.379037095660197 & 260.643217793198 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 98.8228571428571 & 0.361079524489503 & 273.687236302234 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 98.8537037037037 & 0.343920880535371 & 287.431526547098 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 98.9026923076923 & 0.327329465275358 & 302.150288317285 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 98.9552 & 0.308213448434552 & 321.060617252763 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 99.0127083333333 & 0.289500324535783 & 342.012426038213 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 99.0680434782609 & 0.274566785618281 & 360.81583304104 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 99.1243181818182 & 0.256749356996066 & 386.074260678039 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 99.1871428571429 & 0.23462335094295 & 422.750516768729 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 99.257 & 0.204667397476353 & 484.967323686558 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 99.3018421052632 & 0.18471032076711 & 537.608519615245 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 99.3291666666667 & 0.171926236951726 & 577.742922940591 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 99.3588235294118 & 0.160939623263398 & 617.367069182203 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 99.3903125 & 0.147950027237158 & 671.782995623794 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 99.3963333333333 & 0.143828987960626 & 691.073021806591 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 99.4064285714286 & 0.138971290748505 & 715.301901824627 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 99.4184615384615 & 0.134525596429358 & 739.030074404227 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 99.4341666666667 & 0.130171175857617 & 763.872385814731 \tabularnewline
Median & 99.505 &  &  \tabularnewline
Midrange & 97.66 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 99.2540540540541 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 99.3291666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 99.2540540540541 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 99.3291666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 99.3291666666667 &  &  \tabularnewline
Midmean - Closest Observation & 99.2540540540541 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 99.3291666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 99.3018421052632 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293778&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]98.5915277777778[/C][C]0.468616636102822[/C][C]210.38845013634[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]98.5111450022836[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]98.4294533694453[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]98.6705683561325[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]98.5925[/C][C]0.468324676627929[/C][C]210.521684891546[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]98.5955555555556[/C][C]0.46586365724279[/C][C]211.6403673536[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]98.5984722222222[/C][C]0.464675819642064[/C][C]212.187654391338[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]98.5901388888889[/C][C]0.461835975676867[/C][C]213.474359039257[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]98.5894444444445[/C][C]0.46059356856402[/C][C]214.048677995687[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]98.6352777777778[/C][C]0.446438259352864[/C][C]220.938227652699[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]98.6333333333333[/C][C]0.439317919896041[/C][C]224.514705333836[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]98.6377777777778[/C][C]0.42029817561461[/C][C]234.685238958123[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]98.5352777777778[/C][C]0.400378389699384[/C][C]246.105385087744[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]98.5380555555556[/C][C]0.392436195330742[/C][C]251.093188467257[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]98.5334722222222[/C][C]0.369641430519607[/C][C]266.565011621433[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]98.5884722222222[/C][C]0.334134287691872[/C][C]295.056436450298[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]98.6209722222222[/C][C]0.327154180133949[/C][C]301.451053389698[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]98.61125[/C][C]0.319686058436287[/C][C]308.46277902248[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]98.605[/C][C]0.315596474291601[/C][C]312.440119051812[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]98.8783333333333[/C][C]0.254776974488011[/C][C]388.097603922157[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]99.0695833333333[/C][C]0.210246654228411[/C][C]471.206467931255[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]99.0770833333333[/C][C]0.187339961695426[/C][C]528.862515165937[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]99.0929166666667[/C][C]0.178549125451598[/C][C]554.989650137095[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]99.3401388888889[/C][C]0.136925709649612[/C][C]725.503918461307[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]99.3138888888889[/C][C]0.131785403696195[/C][C]753.60310097647[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]99.3108333333333[/C][C]0.122158589745107[/C][C]812.966436012011[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]99.2980555555555[/C][C]0.113632172785939[/C][C]873.855116214435[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]99.3813888888889[/C][C]0.102043729609245[/C][C]973.909805820003[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]98.6181428571429[/C][C]0.45967070276855[/C][C]214.540849053846[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]98.6452941176471[/C][C]0.449325974118925[/C][C]219.540600364977[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]98.6724242424242[/C][C]0.438496799743052[/C][C]225.024274522058[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]98.70015625[/C][C]0.426003745383452[/C][C]231.688470628723[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]98.7320967741936[/C][C]0.411940445417728[/C][C]239.675656693711[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]98.7663333333333[/C][C]0.39519772399979[/C][C]249.916250361265[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]98.7934482758621[/C][C]0.379037095660197[/C][C]260.643217793198[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]98.8228571428571[/C][C]0.361079524489503[/C][C]273.687236302234[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]98.8537037037037[/C][C]0.343920880535371[/C][C]287.431526547098[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]98.9026923076923[/C][C]0.327329465275358[/C][C]302.150288317285[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]98.9552[/C][C]0.308213448434552[/C][C]321.060617252763[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]99.0127083333333[/C][C]0.289500324535783[/C][C]342.012426038213[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]99.0680434782609[/C][C]0.274566785618281[/C][C]360.81583304104[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]99.1243181818182[/C][C]0.256749356996066[/C][C]386.074260678039[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]99.1871428571429[/C][C]0.23462335094295[/C][C]422.750516768729[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]99.257[/C][C]0.204667397476353[/C][C]484.967323686558[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]99.3018421052632[/C][C]0.18471032076711[/C][C]537.608519615245[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]99.3291666666667[/C][C]0.171926236951726[/C][C]577.742922940591[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]99.3588235294118[/C][C]0.160939623263398[/C][C]617.367069182203[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]99.3903125[/C][C]0.147950027237158[/C][C]671.782995623794[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]99.3963333333333[/C][C]0.143828987960626[/C][C]691.073021806591[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]99.4064285714286[/C][C]0.138971290748505[/C][C]715.301901824627[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]99.4184615384615[/C][C]0.134525596429358[/C][C]739.030074404227[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]99.4341666666667[/C][C]0.130171175857617[/C][C]763.872385814731[/C][/ROW]
[ROW][C]Median[/C][C]99.505[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]97.66[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]99.2540540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]99.3291666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]99.2540540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]99.3291666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]99.3291666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]99.2540540540541[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]99.3291666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]99.3018421052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293778&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293778&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 Mean98.59152777777780.468616636102822210.38845013634
Geometric Mean98.5111450022836
Harmonic Mean98.4294533694453
Quadratic Mean98.6705683561325
Winsorized Mean ( 1 / 24 )98.59250.468324676627929210.521684891546
Winsorized Mean ( 2 / 24 )98.59555555555560.46586365724279211.6403673536
Winsorized Mean ( 3 / 24 )98.59847222222220.464675819642064212.187654391338
Winsorized Mean ( 4 / 24 )98.59013888888890.461835975676867213.474359039257
Winsorized Mean ( 5 / 24 )98.58944444444450.46059356856402214.048677995687
Winsorized Mean ( 6 / 24 )98.63527777777780.446438259352864220.938227652699
Winsorized Mean ( 7 / 24 )98.63333333333330.439317919896041224.514705333836
Winsorized Mean ( 8 / 24 )98.63777777777780.42029817561461234.685238958123
Winsorized Mean ( 9 / 24 )98.53527777777780.400378389699384246.105385087744
Winsorized Mean ( 10 / 24 )98.53805555555560.392436195330742251.093188467257
Winsorized Mean ( 11 / 24 )98.53347222222220.369641430519607266.565011621433
Winsorized Mean ( 12 / 24 )98.58847222222220.334134287691872295.056436450298
Winsorized Mean ( 13 / 24 )98.62097222222220.327154180133949301.451053389698
Winsorized Mean ( 14 / 24 )98.611250.319686058436287308.46277902248
Winsorized Mean ( 15 / 24 )98.6050.315596474291601312.440119051812
Winsorized Mean ( 16 / 24 )98.87833333333330.254776974488011388.097603922157
Winsorized Mean ( 17 / 24 )99.06958333333330.210246654228411471.206467931255
Winsorized Mean ( 18 / 24 )99.07708333333330.187339961695426528.862515165937
Winsorized Mean ( 19 / 24 )99.09291666666670.178549125451598554.989650137095
Winsorized Mean ( 20 / 24 )99.34013888888890.136925709649612725.503918461307
Winsorized Mean ( 21 / 24 )99.31388888888890.131785403696195753.60310097647
Winsorized Mean ( 22 / 24 )99.31083333333330.122158589745107812.966436012011
Winsorized Mean ( 23 / 24 )99.29805555555550.113632172785939873.855116214435
Winsorized Mean ( 24 / 24 )99.38138888888890.102043729609245973.909805820003
Trimmed Mean ( 1 / 24 )98.61814285714290.45967070276855214.540849053846
Trimmed Mean ( 2 / 24 )98.64529411764710.449325974118925219.540600364977
Trimmed Mean ( 3 / 24 )98.67242424242420.438496799743052225.024274522058
Trimmed Mean ( 4 / 24 )98.700156250.426003745383452231.688470628723
Trimmed Mean ( 5 / 24 )98.73209677419360.411940445417728239.675656693711
Trimmed Mean ( 6 / 24 )98.76633333333330.39519772399979249.916250361265
Trimmed Mean ( 7 / 24 )98.79344827586210.379037095660197260.643217793198
Trimmed Mean ( 8 / 24 )98.82285714285710.361079524489503273.687236302234
Trimmed Mean ( 9 / 24 )98.85370370370370.343920880535371287.431526547098
Trimmed Mean ( 10 / 24 )98.90269230769230.327329465275358302.150288317285
Trimmed Mean ( 11 / 24 )98.95520.308213448434552321.060617252763
Trimmed Mean ( 12 / 24 )99.01270833333330.289500324535783342.012426038213
Trimmed Mean ( 13 / 24 )99.06804347826090.274566785618281360.81583304104
Trimmed Mean ( 14 / 24 )99.12431818181820.256749356996066386.074260678039
Trimmed Mean ( 15 / 24 )99.18714285714290.23462335094295422.750516768729
Trimmed Mean ( 16 / 24 )99.2570.204667397476353484.967323686558
Trimmed Mean ( 17 / 24 )99.30184210526320.18471032076711537.608519615245
Trimmed Mean ( 18 / 24 )99.32916666666670.171926236951726577.742922940591
Trimmed Mean ( 19 / 24 )99.35882352941180.160939623263398617.367069182203
Trimmed Mean ( 20 / 24 )99.39031250.147950027237158671.782995623794
Trimmed Mean ( 21 / 24 )99.39633333333330.143828987960626691.073021806591
Trimmed Mean ( 22 / 24 )99.40642857142860.138971290748505715.301901824627
Trimmed Mean ( 23 / 24 )99.41846153846150.134525596429358739.030074404227
Trimmed Mean ( 24 / 24 )99.43416666666670.130171175857617763.872385814731
Median99.505
Midrange97.66
Midmean - Weighted Average at Xnp99.2540540540541
Midmean - Weighted Average at X(n+1)p99.3291666666667
Midmean - Empirical Distribution Function99.2540540540541
Midmean - Empirical Distribution Function - Averaging99.3291666666667
Midmean - Empirical Distribution Function - Interpolation99.3291666666667
Midmean - Closest Observation99.2540540540541
Midmean - True Basic - Statistics Graphics Toolkit99.3291666666667
Midmean - MS Excel (old versions)99.3018421052632
Number of observations72



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