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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 07 Mar 2016 16:11:13 +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/07/t14573671144erbmcpjaeghalw.htm/, Retrieved Tue, 30 Apr 2024 22:30:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293589, Retrieved Tue, 30 Apr 2024 22:30:00 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Moerman Nicolaï] [2016-03-07 16:11:13] [ab100cc47aff291ae023e643a55282f8] [Current]
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Dataseries X:
96,4
96,9
98,1
99,2
100
100,3
100,3
100,8
101,3
101,4
101,9
103,4
105,6
107,5
109
110,5
109,8
109,6
109,6
108,8
109,4
109,1
109
109,2
110,5
112,2
113,2
113,6
113,2
112,2
112,2
113,2
113,8
113,8
113,7
113,9
114
114,3
114,3
112,8
112,3
112,2
112,6
111,9
111,7
111
110,8
111,1
110,5
110,5
109,8
109
109
109,4
108,8
108,4
108,3
108,2
106,8
103,6




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' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293589&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293589&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293589&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' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean108.5650.633770998047482171.300044234379
Geometric Mean108.452347789887
Harmonic Mean108.336131819224
Quadratic Mean108.674088447983
Winsorized Mean ( 1 / 20 )108.5733333333330.631109088615098172.035762583591
Winsorized Mean ( 2 / 20 )108.6033333333330.617558371937041175.859219579012
Winsorized Mean ( 3 / 20 )108.6533333333330.601558553286391180.619713143046
Winsorized Mean ( 4 / 20 )108.70.586765528393356185.252873149579
Winsorized Mean ( 5 / 20 )108.7250.580549248021674187.279546688761
Winsorized Mean ( 6 / 20 )108.7150.579078876002888187.737810003378
Winsorized Mean ( 7 / 20 )108.7616666666670.563203567108525193.112531628744
Winsorized Mean ( 8 / 20 )108.7750.539798167972894201.51050235773
Winsorized Mean ( 9 / 20 )108.790.536286140841582202.858123145376
Winsorized Mean ( 10 / 20 )108.8733333333330.517025754566562210.57622830531
Winsorized Mean ( 11 / 20 )109.0750.445369300198523244.909112395893
Winsorized Mean ( 12 / 20 )109.0750.431137144407827252.993743208593
Winsorized Mean ( 13 / 20 )109.4433333333330.332278273776823329.372522883761
Winsorized Mean ( 14 / 20 )109.70.276203069485515397.171545574561
Winsorized Mean ( 15 / 20 )109.8750.246255861153684446.182273531467
Winsorized Mean ( 16 / 20 )110.0616666666670.217342600578822506.397118528778
Winsorized Mean ( 17 / 20 )110.090.213270206055512516.199623173547
Winsorized Mean ( 18 / 20 )110.030.194097942543024566.878754913183
Winsorized Mean ( 19 / 20 )110.0933333333330.166330734895864661.894107557814
Winsorized Mean ( 20 / 20 )109.8933333333330.134644681317742816.172850333398
Trimmed Mean ( 1 / 20 )108.6758620689660.612509789024224177.427143233245
Trimmed Mean ( 2 / 20 )108.7857142857140.58922372755446184.625481287428
Trimmed Mean ( 3 / 20 )108.8870370370370.569244637214246191.283377863524
Trimmed Mean ( 4 / 20 )108.9769230769230.551978584140762197.429621742594
Trimmed Mean ( 5 / 20 )109.060.535978982225754203.47812809209
Trimmed Mean ( 6 / 20 )109.143750.517545919520246210.887084379245
Trimmed Mean ( 7 / 20 )109.2369565217390.493879043022415221.181599148724
Trimmed Mean ( 8 / 20 )109.3295454545450.467953797179215233.633205059078
Trimmed Mean ( 9 / 20 )109.4285714285710.440703240599721248.30444014811
Trimmed Mean ( 10 / 20 )109.5350.404550240929229270.757470687458
Trimmed Mean ( 11 / 20 )109.6394736842110.360940360931187303.760636248472
Trimmed Mean ( 12 / 20 )109.7250.326097049533242336.47958531687
Trimmed Mean ( 13 / 20 )109.8205882352940.279889824636766392.370777958135
Trimmed Mean ( 14 / 20 )109.8750.253682554996747433.120046435235
Trimmed Mean ( 15 / 20 )109.90.237225340275793463.272599260403
Trimmed Mean ( 16 / 20 )109.9035714285710.22393086038846490.792431368853
Trimmed Mean ( 17 / 20 )109.8807692307690.213830934710236513.867506493714
Trimmed Mean ( 18 / 20 )109.850.198818976728195552.512651496924
Trimmed Mean ( 19 / 20 )109.8227272727270.183157942650388599.606687449842
Trimmed Mean ( 20 / 20 )109.780.169301972506929648.427176449508
Median109.6
Midrange105.35
Midmean - Weighted Average at Xnp109.875
Midmean - Weighted Average at X(n+1)p109.974193548387
Midmean - Empirical Distribution Function109.875
Midmean - Empirical Distribution Function - Averaging109.974193548387
Midmean - Empirical Distribution Function - Interpolation109.974193548387
Midmean - Closest Observation109.875
Midmean - True Basic - Statistics Graphics Toolkit109.974193548387
Midmean - MS Excel (old versions)109.875
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 108.565 & 0.633770998047482 & 171.300044234379 \tabularnewline
Geometric Mean & 108.452347789887 &  &  \tabularnewline
Harmonic Mean & 108.336131819224 &  &  \tabularnewline
Quadratic Mean & 108.674088447983 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 108.573333333333 & 0.631109088615098 & 172.035762583591 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 108.603333333333 & 0.617558371937041 & 175.859219579012 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 108.653333333333 & 0.601558553286391 & 180.619713143046 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 108.7 & 0.586765528393356 & 185.252873149579 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 108.725 & 0.580549248021674 & 187.279546688761 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 108.715 & 0.579078876002888 & 187.737810003378 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 108.761666666667 & 0.563203567108525 & 193.112531628744 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 108.775 & 0.539798167972894 & 201.51050235773 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 108.79 & 0.536286140841582 & 202.858123145376 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 108.873333333333 & 0.517025754566562 & 210.57622830531 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 109.075 & 0.445369300198523 & 244.909112395893 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 109.075 & 0.431137144407827 & 252.993743208593 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 109.443333333333 & 0.332278273776823 & 329.372522883761 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 109.7 & 0.276203069485515 & 397.171545574561 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 109.875 & 0.246255861153684 & 446.182273531467 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 110.061666666667 & 0.217342600578822 & 506.397118528778 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 110.09 & 0.213270206055512 & 516.199623173547 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 110.03 & 0.194097942543024 & 566.878754913183 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 110.093333333333 & 0.166330734895864 & 661.894107557814 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 109.893333333333 & 0.134644681317742 & 816.172850333398 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 108.675862068966 & 0.612509789024224 & 177.427143233245 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 108.785714285714 & 0.58922372755446 & 184.625481287428 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 108.887037037037 & 0.569244637214246 & 191.283377863524 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 108.976923076923 & 0.551978584140762 & 197.429621742594 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 109.06 & 0.535978982225754 & 203.47812809209 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 109.14375 & 0.517545919520246 & 210.887084379245 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 109.236956521739 & 0.493879043022415 & 221.181599148724 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 109.329545454545 & 0.467953797179215 & 233.633205059078 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 109.428571428571 & 0.440703240599721 & 248.30444014811 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 109.535 & 0.404550240929229 & 270.757470687458 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 109.639473684211 & 0.360940360931187 & 303.760636248472 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 109.725 & 0.326097049533242 & 336.47958531687 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 109.820588235294 & 0.279889824636766 & 392.370777958135 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 109.875 & 0.253682554996747 & 433.120046435235 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 109.9 & 0.237225340275793 & 463.272599260403 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 109.903571428571 & 0.22393086038846 & 490.792431368853 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 109.880769230769 & 0.213830934710236 & 513.867506493714 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 109.85 & 0.198818976728195 & 552.512651496924 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 109.822727272727 & 0.183157942650388 & 599.606687449842 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 109.78 & 0.169301972506929 & 648.427176449508 \tabularnewline
Median & 109.6 &  &  \tabularnewline
Midrange & 105.35 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 109.875 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 109.974193548387 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 109.875 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 109.974193548387 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 109.974193548387 &  &  \tabularnewline
Midmean - Closest Observation & 109.875 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 109.974193548387 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 109.875 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293589&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]108.565[/C][C]0.633770998047482[/C][C]171.300044234379[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]108.452347789887[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]108.336131819224[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]108.674088447983[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]108.573333333333[/C][C]0.631109088615098[/C][C]172.035762583591[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]108.603333333333[/C][C]0.617558371937041[/C][C]175.859219579012[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]108.653333333333[/C][C]0.601558553286391[/C][C]180.619713143046[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]108.7[/C][C]0.586765528393356[/C][C]185.252873149579[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]108.725[/C][C]0.580549248021674[/C][C]187.279546688761[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]108.715[/C][C]0.579078876002888[/C][C]187.737810003378[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]108.761666666667[/C][C]0.563203567108525[/C][C]193.112531628744[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]108.775[/C][C]0.539798167972894[/C][C]201.51050235773[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]108.79[/C][C]0.536286140841582[/C][C]202.858123145376[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]108.873333333333[/C][C]0.517025754566562[/C][C]210.57622830531[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]109.075[/C][C]0.445369300198523[/C][C]244.909112395893[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]109.075[/C][C]0.431137144407827[/C][C]252.993743208593[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]109.443333333333[/C][C]0.332278273776823[/C][C]329.372522883761[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]109.7[/C][C]0.276203069485515[/C][C]397.171545574561[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]109.875[/C][C]0.246255861153684[/C][C]446.182273531467[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]110.061666666667[/C][C]0.217342600578822[/C][C]506.397118528778[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]110.09[/C][C]0.213270206055512[/C][C]516.199623173547[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]110.03[/C][C]0.194097942543024[/C][C]566.878754913183[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]110.093333333333[/C][C]0.166330734895864[/C][C]661.894107557814[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]109.893333333333[/C][C]0.134644681317742[/C][C]816.172850333398[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]108.675862068966[/C][C]0.612509789024224[/C][C]177.427143233245[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]108.785714285714[/C][C]0.58922372755446[/C][C]184.625481287428[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]108.887037037037[/C][C]0.569244637214246[/C][C]191.283377863524[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]108.976923076923[/C][C]0.551978584140762[/C][C]197.429621742594[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]109.06[/C][C]0.535978982225754[/C][C]203.47812809209[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]109.14375[/C][C]0.517545919520246[/C][C]210.887084379245[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]109.236956521739[/C][C]0.493879043022415[/C][C]221.181599148724[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]109.329545454545[/C][C]0.467953797179215[/C][C]233.633205059078[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]109.428571428571[/C][C]0.440703240599721[/C][C]248.30444014811[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]109.535[/C][C]0.404550240929229[/C][C]270.757470687458[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]109.639473684211[/C][C]0.360940360931187[/C][C]303.760636248472[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]109.725[/C][C]0.326097049533242[/C][C]336.47958531687[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]109.820588235294[/C][C]0.279889824636766[/C][C]392.370777958135[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]109.875[/C][C]0.253682554996747[/C][C]433.120046435235[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]109.9[/C][C]0.237225340275793[/C][C]463.272599260403[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]109.903571428571[/C][C]0.22393086038846[/C][C]490.792431368853[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]109.880769230769[/C][C]0.213830934710236[/C][C]513.867506493714[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]109.85[/C][C]0.198818976728195[/C][C]552.512651496924[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]109.822727272727[/C][C]0.183157942650388[/C][C]599.606687449842[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]109.78[/C][C]0.169301972506929[/C][C]648.427176449508[/C][/ROW]
[ROW][C]Median[/C][C]109.6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]105.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]109.875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]109.974193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]109.875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]109.974193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]109.974193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]109.875[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]109.974193548387[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]109.875[/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=293589&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293589&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 Mean108.5650.633770998047482171.300044234379
Geometric Mean108.452347789887
Harmonic Mean108.336131819224
Quadratic Mean108.674088447983
Winsorized Mean ( 1 / 20 )108.5733333333330.631109088615098172.035762583591
Winsorized Mean ( 2 / 20 )108.6033333333330.617558371937041175.859219579012
Winsorized Mean ( 3 / 20 )108.6533333333330.601558553286391180.619713143046
Winsorized Mean ( 4 / 20 )108.70.586765528393356185.252873149579
Winsorized Mean ( 5 / 20 )108.7250.580549248021674187.279546688761
Winsorized Mean ( 6 / 20 )108.7150.579078876002888187.737810003378
Winsorized Mean ( 7 / 20 )108.7616666666670.563203567108525193.112531628744
Winsorized Mean ( 8 / 20 )108.7750.539798167972894201.51050235773
Winsorized Mean ( 9 / 20 )108.790.536286140841582202.858123145376
Winsorized Mean ( 10 / 20 )108.8733333333330.517025754566562210.57622830531
Winsorized Mean ( 11 / 20 )109.0750.445369300198523244.909112395893
Winsorized Mean ( 12 / 20 )109.0750.431137144407827252.993743208593
Winsorized Mean ( 13 / 20 )109.4433333333330.332278273776823329.372522883761
Winsorized Mean ( 14 / 20 )109.70.276203069485515397.171545574561
Winsorized Mean ( 15 / 20 )109.8750.246255861153684446.182273531467
Winsorized Mean ( 16 / 20 )110.0616666666670.217342600578822506.397118528778
Winsorized Mean ( 17 / 20 )110.090.213270206055512516.199623173547
Winsorized Mean ( 18 / 20 )110.030.194097942543024566.878754913183
Winsorized Mean ( 19 / 20 )110.0933333333330.166330734895864661.894107557814
Winsorized Mean ( 20 / 20 )109.8933333333330.134644681317742816.172850333398
Trimmed Mean ( 1 / 20 )108.6758620689660.612509789024224177.427143233245
Trimmed Mean ( 2 / 20 )108.7857142857140.58922372755446184.625481287428
Trimmed Mean ( 3 / 20 )108.8870370370370.569244637214246191.283377863524
Trimmed Mean ( 4 / 20 )108.9769230769230.551978584140762197.429621742594
Trimmed Mean ( 5 / 20 )109.060.535978982225754203.47812809209
Trimmed Mean ( 6 / 20 )109.143750.517545919520246210.887084379245
Trimmed Mean ( 7 / 20 )109.2369565217390.493879043022415221.181599148724
Trimmed Mean ( 8 / 20 )109.3295454545450.467953797179215233.633205059078
Trimmed Mean ( 9 / 20 )109.4285714285710.440703240599721248.30444014811
Trimmed Mean ( 10 / 20 )109.5350.404550240929229270.757470687458
Trimmed Mean ( 11 / 20 )109.6394736842110.360940360931187303.760636248472
Trimmed Mean ( 12 / 20 )109.7250.326097049533242336.47958531687
Trimmed Mean ( 13 / 20 )109.8205882352940.279889824636766392.370777958135
Trimmed Mean ( 14 / 20 )109.8750.253682554996747433.120046435235
Trimmed Mean ( 15 / 20 )109.90.237225340275793463.272599260403
Trimmed Mean ( 16 / 20 )109.9035714285710.22393086038846490.792431368853
Trimmed Mean ( 17 / 20 )109.8807692307690.213830934710236513.867506493714
Trimmed Mean ( 18 / 20 )109.850.198818976728195552.512651496924
Trimmed Mean ( 19 / 20 )109.8227272727270.183157942650388599.606687449842
Trimmed Mean ( 20 / 20 )109.780.169301972506929648.427176449508
Median109.6
Midrange105.35
Midmean - Weighted Average at Xnp109.875
Midmean - Weighted Average at X(n+1)p109.974193548387
Midmean - Empirical Distribution Function109.875
Midmean - Empirical Distribution Function - Averaging109.974193548387
Midmean - Empirical Distribution Function - Interpolation109.974193548387
Midmean - Closest Observation109.875
Midmean - True Basic - Statistics Graphics Toolkit109.974193548387
Midmean - MS Excel (old versions)109.875
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')