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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 computationTue, 20 Oct 2009 13:44:46 -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/2009/Oct/20/t12560679148kp8ph5fztqyxzd.htm/, Retrieved Thu, 02 May 2024 15:03:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49085, Retrieved Thu, 02 May 2024 15:03:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD      [Central Tendency] [Workshop 3: Part ...] [2009-10-20 17:47:21] [03d5b865e91ca35b5a5d21b8d6da5aba]
-    D        [Central Tendency] [WS3-PArt2] [2009-10-20 19:42:58] [408e92805dcb18620260f240a7fb9d53]
-    D            [Central Tendency] [WS3-Part 2] [2009-10-20 19:44:46] [b32ceebc68d054278e6bda97f3d57f91] [Current]
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Dataseries X:
0,77
0,815217391
0,826086957
0,821052632
0,8125
0,821052632
0,824175824
0,842696629
0,788888889
0,742574257
0,72815534
0,745098039
0,802083333
0,836956522
0,849462366
0,861702128
0,872340426
0,891304348
0,911111111
0,877777778
0,811111111
0,704081633
0,66
0,683673469
0,741935484
0,777777778
0,788888889
0,791208791
0,78021978
0,758241758
0,760869565
0,772727273
0,771084337
0,797619048
0,814814815
0,831168831
0,797468354
0,784810127
0,8125
0,860759494
0,894736842
0,901408451
0,897058824
0,892307692
0,884057971
0,87804878
0,83908046
0,831325301
0,772151899
0,773333333
0,794871795
0,855421687
0,916666667
0,963414634
1
1,027777778
1,02739726
0,987654321
0,952941176




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=49085&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=49085&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49085&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 Mean0.831031390.010208901887665281.4026228427254
Geometric Mean0.827475467836476
Harmonic Mean0.823989831792831
Quadratic Mean0.834660427045003
Winsorized Mean ( 1 / 19 )0.8314261857796610.010098150983373282.3344973895343
Winsorized Mean ( 2 / 19 )0.8311892672711860.0096360355421095686.25842688509
Winsorized Mean ( 3 / 19 )0.8317856076779660.0091907233279055790.502736074367
Winsorized Mean ( 4 / 19 )0.8310764861186440.0085555979129552597.1383291470714
Winsorized Mean ( 5 / 19 )0.8302430382372880.0083144681964962599.8552184717185
Winsorized Mean ( 6 / 19 )0.8268107609152540.00740688370901959111.627344696721
Winsorized Mean ( 7 / 19 )0.8277110514406780.00698771824155625118.452264791995
Winsorized Mean ( 8 / 19 )0.8267517493389830.0066641949387943124.058758324462
Winsorized Mean ( 9 / 19 )0.8274810251355930.00630865460620041131.166005557240
Winsorized Mean ( 10 / 19 )0.827271254796610.00620556518539985133.311186021053
Winsorized Mean ( 11 / 19 )0.827017399406780.00609026443848559135.793348180531
Winsorized Mean ( 12 / 19 )0.8269303546610170.00603448745458885137.034066419707
Winsorized Mean ( 13 / 19 )0.8254672339661020.00572583282770312144.165444365101
Winsorized Mean ( 14 / 19 )0.8250959383050850.00531362067956021155.27942020381
Winsorized Mean ( 15 / 19 )0.8256478874576270.0052073941905614158.552983938521
Winsorized Mean ( 16 / 19 )0.825418191186440.00476992400802198173.046402793476
Winsorized Mean ( 17 / 19 )0.823528155389830.00409025269962009201.339187543674
Winsorized Mean ( 18 / 19 )0.8232405721355930.00404411382730555203.565133745033
Winsorized Mean ( 19 / 19 )0.8222687044237290.00366302992515542224.477746899335
Trimmed Mean ( 1 / 19 )0.830580249684210.0095098238126117587.3391837799046
Trimmed Mean ( 2 / 19 )0.8296727909636360.0087676761988305294.628584832353
Trimmed Mean ( 3 / 19 )0.8288287145283020.00815951312573383101.578207149922
Trimmed Mean ( 4 / 19 )0.8276884746862740.00761991731105676108.621713451571
Trimmed Mean ( 5 / 19 )0.826668614102040.00720906444606596114.670720491778
Trimmed Mean ( 6 / 19 )0.8257712054893620.00677306260866529121.919913221072
Trimmed Mean ( 7 / 19 )0.8255440433777780.00652918608549919126.439043483727
Trimmed Mean ( 8 / 19 )0.8251192810.00633806101981216130.184811793506
Trimmed Mean ( 9 / 19 )0.8248256357804880.00617811138139019133.507731548033
Trimmed Mean ( 10 / 19 )0.8243792882820510.00605674945883058136.109194194937
Trimmed Mean ( 11 / 19 )0.8239181368648650.00591275403671253139.345917612863
Trimmed Mean ( 12 / 19 )0.8234431849428570.00573964757556165143.465809372848
Trimmed Mean ( 13 / 19 )0.8229236318787880.00550625338059694149.452554213837
Trimmed Mean ( 14 / 19 )0.8225512434838710.00526867151180542156.12118569943
Trimmed Mean ( 15 / 19 )0.8221814479310350.00505233339373142162.733015392678
Trimmed Mean ( 16 / 19 )0.8216764604444440.00475444794344332172.822685245211
Trimmed Mean ( 17 / 19 )0.821124555160.00446000248314694184.108542150546
Trimmed Mean ( 18 / 19 )0.8207618635652170.00427472352156012192.003496699985
Trimmed Mean ( 19 / 19 )0.8203749751904760.00397235382933068206.521123353381
Median0.821052632
Midrange0.843888889
Midmean - Weighted Average at Xnp0.8207013256
Midmean - Weighted Average at X(n+1)p0.822551243483871
Midmean - Empirical Distribution Function0.822551243483871
Midmean - Empirical Distribution Function - Averaging0.822551243483871
Midmean - Empirical Distribution Function - Interpolation0.822181447931035
Midmean - Closest Observation0.8207013256
Midmean - True Basic - Statistics Graphics Toolkit0.822551243483871
Midmean - MS Excel (old versions)0.822551243483871
Number of observations59

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.83103139 & 0.0102089018876652 & 81.4026228427254 \tabularnewline
Geometric Mean & 0.827475467836476 &  &  \tabularnewline
Harmonic Mean & 0.823989831792831 &  &  \tabularnewline
Quadratic Mean & 0.834660427045003 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 0.831426185779661 & 0.0100981509833732 & 82.3344973895343 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 0.831189267271186 & 0.00963603554210956 & 86.25842688509 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 0.831785607677966 & 0.00919072332790557 & 90.502736074367 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 0.831076486118644 & 0.00855559791295525 & 97.1383291470714 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 0.830243038237288 & 0.00831446819649625 & 99.8552184717185 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 0.826810760915254 & 0.00740688370901959 & 111.627344696721 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 0.827711051440678 & 0.00698771824155625 & 118.452264791995 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 0.826751749338983 & 0.0066641949387943 & 124.058758324462 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 0.827481025135593 & 0.00630865460620041 & 131.166005557240 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 0.82727125479661 & 0.00620556518539985 & 133.311186021053 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 0.82701739940678 & 0.00609026443848559 & 135.793348180531 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 0.826930354661017 & 0.00603448745458885 & 137.034066419707 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 0.825467233966102 & 0.00572583282770312 & 144.165444365101 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 0.825095938305085 & 0.00531362067956021 & 155.27942020381 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 0.825647887457627 & 0.0052073941905614 & 158.552983938521 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 0.82541819118644 & 0.00476992400802198 & 173.046402793476 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 0.82352815538983 & 0.00409025269962009 & 201.339187543674 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 0.823240572135593 & 0.00404411382730555 & 203.565133745033 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 0.822268704423729 & 0.00366302992515542 & 224.477746899335 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 0.83058024968421 & 0.00950982381261175 & 87.3391837799046 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 0.829672790963636 & 0.00876767619883052 & 94.628584832353 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 0.828828714528302 & 0.00815951312573383 & 101.578207149922 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 0.827688474686274 & 0.00761991731105676 & 108.621713451571 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 0.82666861410204 & 0.00720906444606596 & 114.670720491778 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 0.825771205489362 & 0.00677306260866529 & 121.919913221072 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 0.825544043377778 & 0.00652918608549919 & 126.439043483727 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 0.825119281 & 0.00633806101981216 & 130.184811793506 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 0.824825635780488 & 0.00617811138139019 & 133.507731548033 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 0.824379288282051 & 0.00605674945883058 & 136.109194194937 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 0.823918136864865 & 0.00591275403671253 & 139.345917612863 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 0.823443184942857 & 0.00573964757556165 & 143.465809372848 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 0.822923631878788 & 0.00550625338059694 & 149.452554213837 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 0.822551243483871 & 0.00526867151180542 & 156.12118569943 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 0.822181447931035 & 0.00505233339373142 & 162.733015392678 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 0.821676460444444 & 0.00475444794344332 & 172.822685245211 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 0.82112455516 & 0.00446000248314694 & 184.108542150546 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 0.820761863565217 & 0.00427472352156012 & 192.003496699985 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 0.820374975190476 & 0.00397235382933068 & 206.521123353381 \tabularnewline
Median & 0.821052632 &  &  \tabularnewline
Midrange & 0.843888889 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.8207013256 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.822551243483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.822551243483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.822551243483871 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.822181447931035 &  &  \tabularnewline
Midmean - Closest Observation & 0.8207013256 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.822551243483871 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.822551243483871 &  &  \tabularnewline
Number of observations & 59 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49085&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]0.83103139[/C][C]0.0102089018876652[/C][C]81.4026228427254[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.827475467836476[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.823989831792831[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.834660427045003[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]0.831426185779661[/C][C]0.0100981509833732[/C][C]82.3344973895343[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]0.831189267271186[/C][C]0.00963603554210956[/C][C]86.25842688509[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]0.831785607677966[/C][C]0.00919072332790557[/C][C]90.502736074367[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]0.831076486118644[/C][C]0.00855559791295525[/C][C]97.1383291470714[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]0.830243038237288[/C][C]0.00831446819649625[/C][C]99.8552184717185[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]0.826810760915254[/C][C]0.00740688370901959[/C][C]111.627344696721[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]0.827711051440678[/C][C]0.00698771824155625[/C][C]118.452264791995[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]0.826751749338983[/C][C]0.0066641949387943[/C][C]124.058758324462[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]0.827481025135593[/C][C]0.00630865460620041[/C][C]131.166005557240[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]0.82727125479661[/C][C]0.00620556518539985[/C][C]133.311186021053[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]0.82701739940678[/C][C]0.00609026443848559[/C][C]135.793348180531[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]0.826930354661017[/C][C]0.00603448745458885[/C][C]137.034066419707[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]0.825467233966102[/C][C]0.00572583282770312[/C][C]144.165444365101[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]0.825095938305085[/C][C]0.00531362067956021[/C][C]155.27942020381[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]0.825647887457627[/C][C]0.0052073941905614[/C][C]158.552983938521[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]0.82541819118644[/C][C]0.00476992400802198[/C][C]173.046402793476[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]0.82352815538983[/C][C]0.00409025269962009[/C][C]201.339187543674[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]0.823240572135593[/C][C]0.00404411382730555[/C][C]203.565133745033[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]0.822268704423729[/C][C]0.00366302992515542[/C][C]224.477746899335[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]0.83058024968421[/C][C]0.00950982381261175[/C][C]87.3391837799046[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]0.829672790963636[/C][C]0.00876767619883052[/C][C]94.628584832353[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]0.828828714528302[/C][C]0.00815951312573383[/C][C]101.578207149922[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]0.827688474686274[/C][C]0.00761991731105676[/C][C]108.621713451571[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]0.82666861410204[/C][C]0.00720906444606596[/C][C]114.670720491778[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]0.825771205489362[/C][C]0.00677306260866529[/C][C]121.919913221072[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]0.825544043377778[/C][C]0.00652918608549919[/C][C]126.439043483727[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]0.825119281[/C][C]0.00633806101981216[/C][C]130.184811793506[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]0.824825635780488[/C][C]0.00617811138139019[/C][C]133.507731548033[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]0.824379288282051[/C][C]0.00605674945883058[/C][C]136.109194194937[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]0.823918136864865[/C][C]0.00591275403671253[/C][C]139.345917612863[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]0.823443184942857[/C][C]0.00573964757556165[/C][C]143.465809372848[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]0.822923631878788[/C][C]0.00550625338059694[/C][C]149.452554213837[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]0.822551243483871[/C][C]0.00526867151180542[/C][C]156.12118569943[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]0.822181447931035[/C][C]0.00505233339373142[/C][C]162.733015392678[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]0.821676460444444[/C][C]0.00475444794344332[/C][C]172.822685245211[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]0.82112455516[/C][C]0.00446000248314694[/C][C]184.108542150546[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]0.820761863565217[/C][C]0.00427472352156012[/C][C]192.003496699985[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]0.820374975190476[/C][C]0.00397235382933068[/C][C]206.521123353381[/C][/ROW]
[ROW][C]Median[/C][C]0.821052632[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.843888889[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.8207013256[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.822551243483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.822551243483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.822551243483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.822181447931035[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.8207013256[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.822551243483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.822551243483871[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]59[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49085&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49085&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 Mean0.831031390.010208901887665281.4026228427254
Geometric Mean0.827475467836476
Harmonic Mean0.823989831792831
Quadratic Mean0.834660427045003
Winsorized Mean ( 1 / 19 )0.8314261857796610.010098150983373282.3344973895343
Winsorized Mean ( 2 / 19 )0.8311892672711860.0096360355421095686.25842688509
Winsorized Mean ( 3 / 19 )0.8317856076779660.0091907233279055790.502736074367
Winsorized Mean ( 4 / 19 )0.8310764861186440.0085555979129552597.1383291470714
Winsorized Mean ( 5 / 19 )0.8302430382372880.0083144681964962599.8552184717185
Winsorized Mean ( 6 / 19 )0.8268107609152540.00740688370901959111.627344696721
Winsorized Mean ( 7 / 19 )0.8277110514406780.00698771824155625118.452264791995
Winsorized Mean ( 8 / 19 )0.8267517493389830.0066641949387943124.058758324462
Winsorized Mean ( 9 / 19 )0.8274810251355930.00630865460620041131.166005557240
Winsorized Mean ( 10 / 19 )0.827271254796610.00620556518539985133.311186021053
Winsorized Mean ( 11 / 19 )0.827017399406780.00609026443848559135.793348180531
Winsorized Mean ( 12 / 19 )0.8269303546610170.00603448745458885137.034066419707
Winsorized Mean ( 13 / 19 )0.8254672339661020.00572583282770312144.165444365101
Winsorized Mean ( 14 / 19 )0.8250959383050850.00531362067956021155.27942020381
Winsorized Mean ( 15 / 19 )0.8256478874576270.0052073941905614158.552983938521
Winsorized Mean ( 16 / 19 )0.825418191186440.00476992400802198173.046402793476
Winsorized Mean ( 17 / 19 )0.823528155389830.00409025269962009201.339187543674
Winsorized Mean ( 18 / 19 )0.8232405721355930.00404411382730555203.565133745033
Winsorized Mean ( 19 / 19 )0.8222687044237290.00366302992515542224.477746899335
Trimmed Mean ( 1 / 19 )0.830580249684210.0095098238126117587.3391837799046
Trimmed Mean ( 2 / 19 )0.8296727909636360.0087676761988305294.628584832353
Trimmed Mean ( 3 / 19 )0.8288287145283020.00815951312573383101.578207149922
Trimmed Mean ( 4 / 19 )0.8276884746862740.00761991731105676108.621713451571
Trimmed Mean ( 5 / 19 )0.826668614102040.00720906444606596114.670720491778
Trimmed Mean ( 6 / 19 )0.8257712054893620.00677306260866529121.919913221072
Trimmed Mean ( 7 / 19 )0.8255440433777780.00652918608549919126.439043483727
Trimmed Mean ( 8 / 19 )0.8251192810.00633806101981216130.184811793506
Trimmed Mean ( 9 / 19 )0.8248256357804880.00617811138139019133.507731548033
Trimmed Mean ( 10 / 19 )0.8243792882820510.00605674945883058136.109194194937
Trimmed Mean ( 11 / 19 )0.8239181368648650.00591275403671253139.345917612863
Trimmed Mean ( 12 / 19 )0.8234431849428570.00573964757556165143.465809372848
Trimmed Mean ( 13 / 19 )0.8229236318787880.00550625338059694149.452554213837
Trimmed Mean ( 14 / 19 )0.8225512434838710.00526867151180542156.12118569943
Trimmed Mean ( 15 / 19 )0.8221814479310350.00505233339373142162.733015392678
Trimmed Mean ( 16 / 19 )0.8216764604444440.00475444794344332172.822685245211
Trimmed Mean ( 17 / 19 )0.821124555160.00446000248314694184.108542150546
Trimmed Mean ( 18 / 19 )0.8207618635652170.00427472352156012192.003496699985
Trimmed Mean ( 19 / 19 )0.8203749751904760.00397235382933068206.521123353381
Median0.821052632
Midrange0.843888889
Midmean - Weighted Average at Xnp0.8207013256
Midmean - Weighted Average at X(n+1)p0.822551243483871
Midmean - Empirical Distribution Function0.822551243483871
Midmean - Empirical Distribution Function - Averaging0.822551243483871
Midmean - Empirical Distribution Function - Interpolation0.822181447931035
Midmean - Closest Observation0.8207013256
Midmean - True Basic - Statistics Graphics Toolkit0.822551243483871
Midmean - MS Excel (old versions)0.822551243483871
Number of observations59



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')