Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 24 Oct 2009 03:23:42 -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/24/t1256376260p329l50ip23fj1p.htm/, Retrieved Sun, 05 May 2024 12:57:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50043, Retrieved Sun, 05 May 2024 12:57:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact130
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]
-   PD      [Univariate Data Series] [y[t]/x[t]= c+e[t]] [2009-10-17 12:00:47] [f7fc9270f813d017f9fa5b506fdc7682]
- RMPD        [Univariate Explorative Data Analysis] [WS 3 Review 1 part 2] [2009-10-24 09:15:42] [83058a88a37d754675a5cd22dab372fc]
- RMP             [Central Tendency] [WS 3 Review 1 part 2] [2009-10-24 09:23:42] [eba9f01697e64705b70041e6f338cb22] [Current]
Feedback Forum

Post a new message
Dataseries X:
4.241
4.336
4.452
4.567
4.737
4.800
4.091
3.738
3.750
3.914
4.092
4.206
4.269
4.355
4.421
4.534
4.684
4.720
3.959
3.662
3.667
3.814
4.032
4.143
4.212
4.297
4.396
4.485
4.632
4.641
3.765
3.559
3.568
3.733
3.907
3.997
4.086
4.208
4.332
4.484
4.622
4.564
3.777
3.643
3.660
3.827
3.980
4.052
4.130
4.217
4.423
4.543
4.701
4.671
3.884
3.776
3.806
4.090
4.268
4.424
4.534
4.655
4.775
4.884
5.060
5.041
4.174
4.000
3.996
4.173
4.361
4.520
4.735
4.808
4.972
5.049
5.172
5.111
4.316
4.174
4.156
4.374
4.611
4.820
4.809
4.933
5.082
5.166
5.405
5.359
4.474
4.331
4.370
4.584
4.831
4.901
4.933
5.011
5.210
5.257
5.586
5.459
4.560
4.434
4.427
4.652
4.802
4.835
4.831
4.883
4.953
5.036
5.278
5.181
4.489
4.341
4.310




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50043&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50043&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50043&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4.459213675213680.0433938481575692102.761425053193
Geometric Mean4.43465726997809
Harmonic Mean4.41006316007498
Quadratic Mean4.48363888197206
Winsorized Mean ( 1 / 39 )4.458205128205130.043150086152103103.318568414674
Winsorized Mean ( 2 / 39 )4.45856410256410.0427502314004788104.293332609053
Winsorized Mean ( 3 / 39 )4.457820512820510.0424586041968934104.992158765942
Winsorized Mean ( 4 / 39 )4.455119658119660.0419599495413928106.17552468038
Winsorized Mean ( 5 / 39 )4.45443589743590.0417750004292383106.629224456410
Winsorized Mean ( 6 / 39 )4.455410256410260.0408502403761904109.066928747061
Winsorized Mean ( 7 / 39 )4.453974358974360.0405323557529676109.886886074917
Winsorized Mean ( 8 / 39 )4.454179487179490.0403132930889246110.48910039064
Winsorized Mean ( 9 / 39 )4.45487179487180.0400700582664365111.177073046666
Winsorized Mean ( 10 / 39 )4.451111111111110.0392299191598855113.462153540775
Winsorized Mean ( 11 / 39 )4.448478632478630.0388264663393568114.573358121169
Winsorized Mean ( 12 / 39 )4.449196581196580.0380733567608149116.858532047684
Winsorized Mean ( 13 / 39 )4.448863247863250.0377760239433233117.769494601603
Winsorized Mean ( 14 / 39 )4.449461538461540.0374210270479045118.902710306843
Winsorized Mean ( 15 / 39 )4.45612820512820.0363125869322387122.715801367817
Winsorized Mean ( 16 / 39 )4.45585470085470.0354225519424022125.791464943012
Winsorized Mean ( 17 / 39 )4.451205128205130.034535116352614128.889246607916
Winsorized Mean ( 18 / 39 )4.455205128205130.0332465216563925134.005150200382
Winsorized Mean ( 19 / 39 )4.455367521367520.032395329186824137.531169869378
Winsorized Mean ( 20 / 39 )4.458102564102560.032052359133096139.088125950121
Winsorized Mean ( 21 / 39 )4.452538461538460.0313083843955623142.215529402072
Winsorized Mean ( 22 / 39 )4.449905982905980.0308462550477759144.260817918214
Winsorized Mean ( 23 / 39 )4.4560.0300439823971259148.315890386964
Winsorized Mean ( 24 / 39 )4.450256410256410.0283665098159839156.884172184933
Winsorized Mean ( 25 / 39 )4.456666666666670.0274027202575315162.635921718092
Winsorized Mean ( 26 / 39 )4.457555555555560.0272993077246742163.284563861912
Winsorized Mean ( 27 / 39 )4.455247863247860.0269748436637581165.163065216711
Winsorized Mean ( 28 / 39 )4.45285470085470.0266418160760676167.137806527187
Winsorized Mean ( 29 / 39 )4.462025641025640.0255348113995829174.742846978636
Winsorized Mean ( 30 / 39 )4.463820512820510.0249838545429966178.668207707437
Winsorized Mean ( 31 / 39 )4.466735042735040.0245432799279183181.994218207733
Winsorized Mean ( 32 / 39 )4.464547008547010.0232440900896900192.072350060597
Winsorized Mean ( 33 / 39 )4.454111111111110.0220017106004370202.443855025647
Winsorized Mean ( 34 / 39 )4.453529914529920.0219373574732770203.011229586562
Winsorized Mean ( 35 / 39 )4.458615384615380.0204042762567054218.513772726938
Winsorized Mean ( 36 / 39 )4.453384615384620.0196987324427672226.074679085240
Winsorized Mean ( 37 / 39 )4.449273504273500.0189847947593842234.359842213950
Winsorized Mean ( 38 / 39 )4.446675213675210.0183623708193483242.162368760671
Winsorized Mean ( 39 / 39 )4.449341880341880.0169469542292145262.545223180679
Trimmed Mean ( 1 / 39 )4.457243478260870.0423165499886862105.330975220158
Trimmed Mean ( 2 / 39 )4.456247787610620.0413901615060444107.66442133742
Trimmed Mean ( 3 / 39 )4.455027027027030.0405933680923497109.747656732791
Trimmed Mean ( 4 / 39 )4.454027522935780.039824791390488111.840573859217
Trimmed Mean ( 5 / 39 )4.453728971962620.0391276651382828113.825574723728
Trimmed Mean ( 6 / 39 )4.453571428571430.0383975251442805115.985897836825
Trimmed Mean ( 7 / 39 )4.453223300970870.0377966090216928117.820709747137
Trimmed Mean ( 8 / 39 )4.453099009900990.0371876363595483119.746761177458
Trimmed Mean ( 9 / 39 )4.452939393939390.0365435128005635121.853074668583
Trimmed Mean ( 10 / 39 )4.452680412371130.0358599004838693124.168788878097
Trimmed Mean ( 11 / 39 )4.452873684210530.0352297188313695126.395379580650
Trimmed Mean ( 12 / 39 )4.453376344086020.0345793695570994128.787088981838
Trimmed Mean ( 13 / 39 )4.453824175824180.0339567763513051131.161572280786
Trimmed Mean ( 14 / 39 )4.454325842696630.033290652781758133.801096418795
Trimmed Mean ( 15 / 39 )4.454325842696630.0325808030040207136.716269459256
Trimmed Mean ( 16 / 39 )4.454670588235290.0319282300395005139.521375996230
Trimmed Mean ( 17 / 39 )4.454566265060240.0313032488100296142.303640497308
Trimmed Mean ( 18 / 39 )4.454851851851850.0307046821092379145.087053368696
Trimmed Mean ( 19 / 39 )4.454822784810130.0301870655870166147.573892930028
Trimmed Mean ( 20 / 39 )4.454779220779220.0296973433510633150.005984310368
Trimmed Mean ( 21 / 39 )4.454520.0291683177499211152.717754866479
Trimmed Mean ( 22 / 39 )4.454671232876710.0286465965555081155.504379874410
Trimmed Mean ( 23 / 39 )4.455028169014080.028092116165865158.586421283115
Trimmed Mean ( 24 / 39 )4.454956521739130.0275453855876218161.731499730433
Trimmed Mean ( 25 / 39 )4.455298507462690.0271236511850292164.258804136287
Trimmed Mean ( 26 / 39 )4.45520.0267453195042537166.578679282235
Trimmed Mean ( 27 / 39 )4.455031746031750.0262968789288745169.4129466117
Trimmed Mean ( 28 / 39 )4.455016393442620.0257954277708584172.705660592903
Trimmed Mean ( 29 / 39 )4.455169491525420.0252300479589928176.581887547997
Trimmed Mean ( 30 / 39 )4.455169491525420.0247041030083634180.341277318070
Trimmed Mean ( 31 / 39 )4.454036363636360.0241366475155619184.534176122208
Trimmed Mean ( 32 / 39 )4.45313207547170.0234976458342161189.513966926307
Trimmed Mean ( 33 / 39 )4.45231372549020.0229200569789539194.254042630805
Trimmed Mean ( 34 / 39 )4.452183673469390.0224089555080946198.678768042587
Trimmed Mean ( 35 / 39 )4.452085106382980.0217601046692067204.598515221447
Trimmed Mean ( 36 / 39 )4.45160.0212175456267741209.807490381102
Trimmed Mean ( 37 / 39 )4.451465116279070.0206460266177808215.608804477921
Trimmed Mean ( 38 / 39 )4.451634146341460.0200366358386016222.174729440616
Trimmed Mean ( 39 / 39 )4.452025641025640.0193557674011189230.010288342702
Median4.434
Midrange4.5725
Midmean - Weighted Average at Xnp4.44908620689655
Midmean - Weighted Average at X(n+1)p4.45516949152542
Midmean - Empirical Distribution Function4.45516949152542
Midmean - Empirical Distribution Function - Averaging4.45516949152542
Midmean - Empirical Distribution Function - Interpolation4.45516949152542
Midmean - Closest Observation4.44911666666667
Midmean - True Basic - Statistics Graphics Toolkit4.45516949152542
Midmean - MS Excel (old versions)4.45516949152542
Number of observations117

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4.45921367521368 & 0.0433938481575692 & 102.761425053193 \tabularnewline
Geometric Mean & 4.43465726997809 &  &  \tabularnewline
Harmonic Mean & 4.41006316007498 &  &  \tabularnewline
Quadratic Mean & 4.48363888197206 &  &  \tabularnewline
Winsorized Mean ( 1 / 39 ) & 4.45820512820513 & 0.043150086152103 & 103.318568414674 \tabularnewline
Winsorized Mean ( 2 / 39 ) & 4.4585641025641 & 0.0427502314004788 & 104.293332609053 \tabularnewline
Winsorized Mean ( 3 / 39 ) & 4.45782051282051 & 0.0424586041968934 & 104.992158765942 \tabularnewline
Winsorized Mean ( 4 / 39 ) & 4.45511965811966 & 0.0419599495413928 & 106.17552468038 \tabularnewline
Winsorized Mean ( 5 / 39 ) & 4.4544358974359 & 0.0417750004292383 & 106.629224456410 \tabularnewline
Winsorized Mean ( 6 / 39 ) & 4.45541025641026 & 0.0408502403761904 & 109.066928747061 \tabularnewline
Winsorized Mean ( 7 / 39 ) & 4.45397435897436 & 0.0405323557529676 & 109.886886074917 \tabularnewline
Winsorized Mean ( 8 / 39 ) & 4.45417948717949 & 0.0403132930889246 & 110.48910039064 \tabularnewline
Winsorized Mean ( 9 / 39 ) & 4.4548717948718 & 0.0400700582664365 & 111.177073046666 \tabularnewline
Winsorized Mean ( 10 / 39 ) & 4.45111111111111 & 0.0392299191598855 & 113.462153540775 \tabularnewline
Winsorized Mean ( 11 / 39 ) & 4.44847863247863 & 0.0388264663393568 & 114.573358121169 \tabularnewline
Winsorized Mean ( 12 / 39 ) & 4.44919658119658 & 0.0380733567608149 & 116.858532047684 \tabularnewline
Winsorized Mean ( 13 / 39 ) & 4.44886324786325 & 0.0377760239433233 & 117.769494601603 \tabularnewline
Winsorized Mean ( 14 / 39 ) & 4.44946153846154 & 0.0374210270479045 & 118.902710306843 \tabularnewline
Winsorized Mean ( 15 / 39 ) & 4.4561282051282 & 0.0363125869322387 & 122.715801367817 \tabularnewline
Winsorized Mean ( 16 / 39 ) & 4.4558547008547 & 0.0354225519424022 & 125.791464943012 \tabularnewline
Winsorized Mean ( 17 / 39 ) & 4.45120512820513 & 0.034535116352614 & 128.889246607916 \tabularnewline
Winsorized Mean ( 18 / 39 ) & 4.45520512820513 & 0.0332465216563925 & 134.005150200382 \tabularnewline
Winsorized Mean ( 19 / 39 ) & 4.45536752136752 & 0.032395329186824 & 137.531169869378 \tabularnewline
Winsorized Mean ( 20 / 39 ) & 4.45810256410256 & 0.032052359133096 & 139.088125950121 \tabularnewline
Winsorized Mean ( 21 / 39 ) & 4.45253846153846 & 0.0313083843955623 & 142.215529402072 \tabularnewline
Winsorized Mean ( 22 / 39 ) & 4.44990598290598 & 0.0308462550477759 & 144.260817918214 \tabularnewline
Winsorized Mean ( 23 / 39 ) & 4.456 & 0.0300439823971259 & 148.315890386964 \tabularnewline
Winsorized Mean ( 24 / 39 ) & 4.45025641025641 & 0.0283665098159839 & 156.884172184933 \tabularnewline
Winsorized Mean ( 25 / 39 ) & 4.45666666666667 & 0.0274027202575315 & 162.635921718092 \tabularnewline
Winsorized Mean ( 26 / 39 ) & 4.45755555555556 & 0.0272993077246742 & 163.284563861912 \tabularnewline
Winsorized Mean ( 27 / 39 ) & 4.45524786324786 & 0.0269748436637581 & 165.163065216711 \tabularnewline
Winsorized Mean ( 28 / 39 ) & 4.4528547008547 & 0.0266418160760676 & 167.137806527187 \tabularnewline
Winsorized Mean ( 29 / 39 ) & 4.46202564102564 & 0.0255348113995829 & 174.742846978636 \tabularnewline
Winsorized Mean ( 30 / 39 ) & 4.46382051282051 & 0.0249838545429966 & 178.668207707437 \tabularnewline
Winsorized Mean ( 31 / 39 ) & 4.46673504273504 & 0.0245432799279183 & 181.994218207733 \tabularnewline
Winsorized Mean ( 32 / 39 ) & 4.46454700854701 & 0.0232440900896900 & 192.072350060597 \tabularnewline
Winsorized Mean ( 33 / 39 ) & 4.45411111111111 & 0.0220017106004370 & 202.443855025647 \tabularnewline
Winsorized Mean ( 34 / 39 ) & 4.45352991452992 & 0.0219373574732770 & 203.011229586562 \tabularnewline
Winsorized Mean ( 35 / 39 ) & 4.45861538461538 & 0.0204042762567054 & 218.513772726938 \tabularnewline
Winsorized Mean ( 36 / 39 ) & 4.45338461538462 & 0.0196987324427672 & 226.074679085240 \tabularnewline
Winsorized Mean ( 37 / 39 ) & 4.44927350427350 & 0.0189847947593842 & 234.359842213950 \tabularnewline
Winsorized Mean ( 38 / 39 ) & 4.44667521367521 & 0.0183623708193483 & 242.162368760671 \tabularnewline
Winsorized Mean ( 39 / 39 ) & 4.44934188034188 & 0.0169469542292145 & 262.545223180679 \tabularnewline
Trimmed Mean ( 1 / 39 ) & 4.45724347826087 & 0.0423165499886862 & 105.330975220158 \tabularnewline
Trimmed Mean ( 2 / 39 ) & 4.45624778761062 & 0.0413901615060444 & 107.66442133742 \tabularnewline
Trimmed Mean ( 3 / 39 ) & 4.45502702702703 & 0.0405933680923497 & 109.747656732791 \tabularnewline
Trimmed Mean ( 4 / 39 ) & 4.45402752293578 & 0.039824791390488 & 111.840573859217 \tabularnewline
Trimmed Mean ( 5 / 39 ) & 4.45372897196262 & 0.0391276651382828 & 113.825574723728 \tabularnewline
Trimmed Mean ( 6 / 39 ) & 4.45357142857143 & 0.0383975251442805 & 115.985897836825 \tabularnewline
Trimmed Mean ( 7 / 39 ) & 4.45322330097087 & 0.0377966090216928 & 117.820709747137 \tabularnewline
Trimmed Mean ( 8 / 39 ) & 4.45309900990099 & 0.0371876363595483 & 119.746761177458 \tabularnewline
Trimmed Mean ( 9 / 39 ) & 4.45293939393939 & 0.0365435128005635 & 121.853074668583 \tabularnewline
Trimmed Mean ( 10 / 39 ) & 4.45268041237113 & 0.0358599004838693 & 124.168788878097 \tabularnewline
Trimmed Mean ( 11 / 39 ) & 4.45287368421053 & 0.0352297188313695 & 126.395379580650 \tabularnewline
Trimmed Mean ( 12 / 39 ) & 4.45337634408602 & 0.0345793695570994 & 128.787088981838 \tabularnewline
Trimmed Mean ( 13 / 39 ) & 4.45382417582418 & 0.0339567763513051 & 131.161572280786 \tabularnewline
Trimmed Mean ( 14 / 39 ) & 4.45432584269663 & 0.033290652781758 & 133.801096418795 \tabularnewline
Trimmed Mean ( 15 / 39 ) & 4.45432584269663 & 0.0325808030040207 & 136.716269459256 \tabularnewline
Trimmed Mean ( 16 / 39 ) & 4.45467058823529 & 0.0319282300395005 & 139.521375996230 \tabularnewline
Trimmed Mean ( 17 / 39 ) & 4.45456626506024 & 0.0313032488100296 & 142.303640497308 \tabularnewline
Trimmed Mean ( 18 / 39 ) & 4.45485185185185 & 0.0307046821092379 & 145.087053368696 \tabularnewline
Trimmed Mean ( 19 / 39 ) & 4.45482278481013 & 0.0301870655870166 & 147.573892930028 \tabularnewline
Trimmed Mean ( 20 / 39 ) & 4.45477922077922 & 0.0296973433510633 & 150.005984310368 \tabularnewline
Trimmed Mean ( 21 / 39 ) & 4.45452 & 0.0291683177499211 & 152.717754866479 \tabularnewline
Trimmed Mean ( 22 / 39 ) & 4.45467123287671 & 0.0286465965555081 & 155.504379874410 \tabularnewline
Trimmed Mean ( 23 / 39 ) & 4.45502816901408 & 0.028092116165865 & 158.586421283115 \tabularnewline
Trimmed Mean ( 24 / 39 ) & 4.45495652173913 & 0.0275453855876218 & 161.731499730433 \tabularnewline
Trimmed Mean ( 25 / 39 ) & 4.45529850746269 & 0.0271236511850292 & 164.258804136287 \tabularnewline
Trimmed Mean ( 26 / 39 ) & 4.4552 & 0.0267453195042537 & 166.578679282235 \tabularnewline
Trimmed Mean ( 27 / 39 ) & 4.45503174603175 & 0.0262968789288745 & 169.4129466117 \tabularnewline
Trimmed Mean ( 28 / 39 ) & 4.45501639344262 & 0.0257954277708584 & 172.705660592903 \tabularnewline
Trimmed Mean ( 29 / 39 ) & 4.45516949152542 & 0.0252300479589928 & 176.581887547997 \tabularnewline
Trimmed Mean ( 30 / 39 ) & 4.45516949152542 & 0.0247041030083634 & 180.341277318070 \tabularnewline
Trimmed Mean ( 31 / 39 ) & 4.45403636363636 & 0.0241366475155619 & 184.534176122208 \tabularnewline
Trimmed Mean ( 32 / 39 ) & 4.4531320754717 & 0.0234976458342161 & 189.513966926307 \tabularnewline
Trimmed Mean ( 33 / 39 ) & 4.4523137254902 & 0.0229200569789539 & 194.254042630805 \tabularnewline
Trimmed Mean ( 34 / 39 ) & 4.45218367346939 & 0.0224089555080946 & 198.678768042587 \tabularnewline
Trimmed Mean ( 35 / 39 ) & 4.45208510638298 & 0.0217601046692067 & 204.598515221447 \tabularnewline
Trimmed Mean ( 36 / 39 ) & 4.4516 & 0.0212175456267741 & 209.807490381102 \tabularnewline
Trimmed Mean ( 37 / 39 ) & 4.45146511627907 & 0.0206460266177808 & 215.608804477921 \tabularnewline
Trimmed Mean ( 38 / 39 ) & 4.45163414634146 & 0.0200366358386016 & 222.174729440616 \tabularnewline
Trimmed Mean ( 39 / 39 ) & 4.45202564102564 & 0.0193557674011189 & 230.010288342702 \tabularnewline
Median & 4.434 &  &  \tabularnewline
Midrange & 4.5725 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4.44908620689655 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4.45516949152542 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4.45516949152542 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4.45516949152542 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4.45516949152542 &  &  \tabularnewline
Midmean - Closest Observation & 4.44911666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4.45516949152542 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4.45516949152542 &  &  \tabularnewline
Number of observations & 117 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50043&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]4.45921367521368[/C][C]0.0433938481575692[/C][C]102.761425053193[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4.43465726997809[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4.41006316007498[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4.48363888197206[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 39 )[/C][C]4.45820512820513[/C][C]0.043150086152103[/C][C]103.318568414674[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 39 )[/C][C]4.4585641025641[/C][C]0.0427502314004788[/C][C]104.293332609053[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 39 )[/C][C]4.45782051282051[/C][C]0.0424586041968934[/C][C]104.992158765942[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 39 )[/C][C]4.45511965811966[/C][C]0.0419599495413928[/C][C]106.17552468038[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 39 )[/C][C]4.4544358974359[/C][C]0.0417750004292383[/C][C]106.629224456410[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 39 )[/C][C]4.45541025641026[/C][C]0.0408502403761904[/C][C]109.066928747061[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 39 )[/C][C]4.45397435897436[/C][C]0.0405323557529676[/C][C]109.886886074917[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 39 )[/C][C]4.45417948717949[/C][C]0.0403132930889246[/C][C]110.48910039064[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 39 )[/C][C]4.4548717948718[/C][C]0.0400700582664365[/C][C]111.177073046666[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 39 )[/C][C]4.45111111111111[/C][C]0.0392299191598855[/C][C]113.462153540775[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 39 )[/C][C]4.44847863247863[/C][C]0.0388264663393568[/C][C]114.573358121169[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 39 )[/C][C]4.44919658119658[/C][C]0.0380733567608149[/C][C]116.858532047684[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 39 )[/C][C]4.44886324786325[/C][C]0.0377760239433233[/C][C]117.769494601603[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 39 )[/C][C]4.44946153846154[/C][C]0.0374210270479045[/C][C]118.902710306843[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 39 )[/C][C]4.4561282051282[/C][C]0.0363125869322387[/C][C]122.715801367817[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 39 )[/C][C]4.4558547008547[/C][C]0.0354225519424022[/C][C]125.791464943012[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 39 )[/C][C]4.45120512820513[/C][C]0.034535116352614[/C][C]128.889246607916[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 39 )[/C][C]4.45520512820513[/C][C]0.0332465216563925[/C][C]134.005150200382[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 39 )[/C][C]4.45536752136752[/C][C]0.032395329186824[/C][C]137.531169869378[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 39 )[/C][C]4.45810256410256[/C][C]0.032052359133096[/C][C]139.088125950121[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 39 )[/C][C]4.45253846153846[/C][C]0.0313083843955623[/C][C]142.215529402072[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 39 )[/C][C]4.44990598290598[/C][C]0.0308462550477759[/C][C]144.260817918214[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 39 )[/C][C]4.456[/C][C]0.0300439823971259[/C][C]148.315890386964[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 39 )[/C][C]4.45025641025641[/C][C]0.0283665098159839[/C][C]156.884172184933[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 39 )[/C][C]4.45666666666667[/C][C]0.0274027202575315[/C][C]162.635921718092[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 39 )[/C][C]4.45755555555556[/C][C]0.0272993077246742[/C][C]163.284563861912[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 39 )[/C][C]4.45524786324786[/C][C]0.0269748436637581[/C][C]165.163065216711[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 39 )[/C][C]4.4528547008547[/C][C]0.0266418160760676[/C][C]167.137806527187[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 39 )[/C][C]4.46202564102564[/C][C]0.0255348113995829[/C][C]174.742846978636[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 39 )[/C][C]4.46382051282051[/C][C]0.0249838545429966[/C][C]178.668207707437[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 39 )[/C][C]4.46673504273504[/C][C]0.0245432799279183[/C][C]181.994218207733[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 39 )[/C][C]4.46454700854701[/C][C]0.0232440900896900[/C][C]192.072350060597[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 39 )[/C][C]4.45411111111111[/C][C]0.0220017106004370[/C][C]202.443855025647[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 39 )[/C][C]4.45352991452992[/C][C]0.0219373574732770[/C][C]203.011229586562[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 39 )[/C][C]4.45861538461538[/C][C]0.0204042762567054[/C][C]218.513772726938[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 39 )[/C][C]4.45338461538462[/C][C]0.0196987324427672[/C][C]226.074679085240[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 39 )[/C][C]4.44927350427350[/C][C]0.0189847947593842[/C][C]234.359842213950[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 39 )[/C][C]4.44667521367521[/C][C]0.0183623708193483[/C][C]242.162368760671[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 39 )[/C][C]4.44934188034188[/C][C]0.0169469542292145[/C][C]262.545223180679[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 39 )[/C][C]4.45724347826087[/C][C]0.0423165499886862[/C][C]105.330975220158[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 39 )[/C][C]4.45624778761062[/C][C]0.0413901615060444[/C][C]107.66442133742[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 39 )[/C][C]4.45502702702703[/C][C]0.0405933680923497[/C][C]109.747656732791[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 39 )[/C][C]4.45402752293578[/C][C]0.039824791390488[/C][C]111.840573859217[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 39 )[/C][C]4.45372897196262[/C][C]0.0391276651382828[/C][C]113.825574723728[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 39 )[/C][C]4.45357142857143[/C][C]0.0383975251442805[/C][C]115.985897836825[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 39 )[/C][C]4.45322330097087[/C][C]0.0377966090216928[/C][C]117.820709747137[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 39 )[/C][C]4.45309900990099[/C][C]0.0371876363595483[/C][C]119.746761177458[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 39 )[/C][C]4.45293939393939[/C][C]0.0365435128005635[/C][C]121.853074668583[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 39 )[/C][C]4.45268041237113[/C][C]0.0358599004838693[/C][C]124.168788878097[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 39 )[/C][C]4.45287368421053[/C][C]0.0352297188313695[/C][C]126.395379580650[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 39 )[/C][C]4.45337634408602[/C][C]0.0345793695570994[/C][C]128.787088981838[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 39 )[/C][C]4.45382417582418[/C][C]0.0339567763513051[/C][C]131.161572280786[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 39 )[/C][C]4.45432584269663[/C][C]0.033290652781758[/C][C]133.801096418795[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 39 )[/C][C]4.45432584269663[/C][C]0.0325808030040207[/C][C]136.716269459256[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 39 )[/C][C]4.45467058823529[/C][C]0.0319282300395005[/C][C]139.521375996230[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 39 )[/C][C]4.45456626506024[/C][C]0.0313032488100296[/C][C]142.303640497308[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 39 )[/C][C]4.45485185185185[/C][C]0.0307046821092379[/C][C]145.087053368696[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 39 )[/C][C]4.45482278481013[/C][C]0.0301870655870166[/C][C]147.573892930028[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 39 )[/C][C]4.45477922077922[/C][C]0.0296973433510633[/C][C]150.005984310368[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 39 )[/C][C]4.45452[/C][C]0.0291683177499211[/C][C]152.717754866479[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 39 )[/C][C]4.45467123287671[/C][C]0.0286465965555081[/C][C]155.504379874410[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 39 )[/C][C]4.45502816901408[/C][C]0.028092116165865[/C][C]158.586421283115[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 39 )[/C][C]4.45495652173913[/C][C]0.0275453855876218[/C][C]161.731499730433[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 39 )[/C][C]4.45529850746269[/C][C]0.0271236511850292[/C][C]164.258804136287[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 39 )[/C][C]4.4552[/C][C]0.0267453195042537[/C][C]166.578679282235[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 39 )[/C][C]4.45503174603175[/C][C]0.0262968789288745[/C][C]169.4129466117[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 39 )[/C][C]4.45501639344262[/C][C]0.0257954277708584[/C][C]172.705660592903[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 39 )[/C][C]4.45516949152542[/C][C]0.0252300479589928[/C][C]176.581887547997[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 39 )[/C][C]4.45516949152542[/C][C]0.0247041030083634[/C][C]180.341277318070[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 39 )[/C][C]4.45403636363636[/C][C]0.0241366475155619[/C][C]184.534176122208[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 39 )[/C][C]4.4531320754717[/C][C]0.0234976458342161[/C][C]189.513966926307[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 39 )[/C][C]4.4523137254902[/C][C]0.0229200569789539[/C][C]194.254042630805[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 39 )[/C][C]4.45218367346939[/C][C]0.0224089555080946[/C][C]198.678768042587[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 39 )[/C][C]4.45208510638298[/C][C]0.0217601046692067[/C][C]204.598515221447[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 39 )[/C][C]4.4516[/C][C]0.0212175456267741[/C][C]209.807490381102[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 39 )[/C][C]4.45146511627907[/C][C]0.0206460266177808[/C][C]215.608804477921[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 39 )[/C][C]4.45163414634146[/C][C]0.0200366358386016[/C][C]222.174729440616[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 39 )[/C][C]4.45202564102564[/C][C]0.0193557674011189[/C][C]230.010288342702[/C][/ROW]
[ROW][C]Median[/C][C]4.434[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4.5725[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4.44908620689655[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4.45516949152542[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4.45516949152542[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4.45516949152542[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4.45516949152542[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4.44911666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4.45516949152542[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4.45516949152542[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]117[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50043&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50043&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 Mean4.459213675213680.0433938481575692102.761425053193
Geometric Mean4.43465726997809
Harmonic Mean4.41006316007498
Quadratic Mean4.48363888197206
Winsorized Mean ( 1 / 39 )4.458205128205130.043150086152103103.318568414674
Winsorized Mean ( 2 / 39 )4.45856410256410.0427502314004788104.293332609053
Winsorized Mean ( 3 / 39 )4.457820512820510.0424586041968934104.992158765942
Winsorized Mean ( 4 / 39 )4.455119658119660.0419599495413928106.17552468038
Winsorized Mean ( 5 / 39 )4.45443589743590.0417750004292383106.629224456410
Winsorized Mean ( 6 / 39 )4.455410256410260.0408502403761904109.066928747061
Winsorized Mean ( 7 / 39 )4.453974358974360.0405323557529676109.886886074917
Winsorized Mean ( 8 / 39 )4.454179487179490.0403132930889246110.48910039064
Winsorized Mean ( 9 / 39 )4.45487179487180.0400700582664365111.177073046666
Winsorized Mean ( 10 / 39 )4.451111111111110.0392299191598855113.462153540775
Winsorized Mean ( 11 / 39 )4.448478632478630.0388264663393568114.573358121169
Winsorized Mean ( 12 / 39 )4.449196581196580.0380733567608149116.858532047684
Winsorized Mean ( 13 / 39 )4.448863247863250.0377760239433233117.769494601603
Winsorized Mean ( 14 / 39 )4.449461538461540.0374210270479045118.902710306843
Winsorized Mean ( 15 / 39 )4.45612820512820.0363125869322387122.715801367817
Winsorized Mean ( 16 / 39 )4.45585470085470.0354225519424022125.791464943012
Winsorized Mean ( 17 / 39 )4.451205128205130.034535116352614128.889246607916
Winsorized Mean ( 18 / 39 )4.455205128205130.0332465216563925134.005150200382
Winsorized Mean ( 19 / 39 )4.455367521367520.032395329186824137.531169869378
Winsorized Mean ( 20 / 39 )4.458102564102560.032052359133096139.088125950121
Winsorized Mean ( 21 / 39 )4.452538461538460.0313083843955623142.215529402072
Winsorized Mean ( 22 / 39 )4.449905982905980.0308462550477759144.260817918214
Winsorized Mean ( 23 / 39 )4.4560.0300439823971259148.315890386964
Winsorized Mean ( 24 / 39 )4.450256410256410.0283665098159839156.884172184933
Winsorized Mean ( 25 / 39 )4.456666666666670.0274027202575315162.635921718092
Winsorized Mean ( 26 / 39 )4.457555555555560.0272993077246742163.284563861912
Winsorized Mean ( 27 / 39 )4.455247863247860.0269748436637581165.163065216711
Winsorized Mean ( 28 / 39 )4.45285470085470.0266418160760676167.137806527187
Winsorized Mean ( 29 / 39 )4.462025641025640.0255348113995829174.742846978636
Winsorized Mean ( 30 / 39 )4.463820512820510.0249838545429966178.668207707437
Winsorized Mean ( 31 / 39 )4.466735042735040.0245432799279183181.994218207733
Winsorized Mean ( 32 / 39 )4.464547008547010.0232440900896900192.072350060597
Winsorized Mean ( 33 / 39 )4.454111111111110.0220017106004370202.443855025647
Winsorized Mean ( 34 / 39 )4.453529914529920.0219373574732770203.011229586562
Winsorized Mean ( 35 / 39 )4.458615384615380.0204042762567054218.513772726938
Winsorized Mean ( 36 / 39 )4.453384615384620.0196987324427672226.074679085240
Winsorized Mean ( 37 / 39 )4.449273504273500.0189847947593842234.359842213950
Winsorized Mean ( 38 / 39 )4.446675213675210.0183623708193483242.162368760671
Winsorized Mean ( 39 / 39 )4.449341880341880.0169469542292145262.545223180679
Trimmed Mean ( 1 / 39 )4.457243478260870.0423165499886862105.330975220158
Trimmed Mean ( 2 / 39 )4.456247787610620.0413901615060444107.66442133742
Trimmed Mean ( 3 / 39 )4.455027027027030.0405933680923497109.747656732791
Trimmed Mean ( 4 / 39 )4.454027522935780.039824791390488111.840573859217
Trimmed Mean ( 5 / 39 )4.453728971962620.0391276651382828113.825574723728
Trimmed Mean ( 6 / 39 )4.453571428571430.0383975251442805115.985897836825
Trimmed Mean ( 7 / 39 )4.453223300970870.0377966090216928117.820709747137
Trimmed Mean ( 8 / 39 )4.453099009900990.0371876363595483119.746761177458
Trimmed Mean ( 9 / 39 )4.452939393939390.0365435128005635121.853074668583
Trimmed Mean ( 10 / 39 )4.452680412371130.0358599004838693124.168788878097
Trimmed Mean ( 11 / 39 )4.452873684210530.0352297188313695126.395379580650
Trimmed Mean ( 12 / 39 )4.453376344086020.0345793695570994128.787088981838
Trimmed Mean ( 13 / 39 )4.453824175824180.0339567763513051131.161572280786
Trimmed Mean ( 14 / 39 )4.454325842696630.033290652781758133.801096418795
Trimmed Mean ( 15 / 39 )4.454325842696630.0325808030040207136.716269459256
Trimmed Mean ( 16 / 39 )4.454670588235290.0319282300395005139.521375996230
Trimmed Mean ( 17 / 39 )4.454566265060240.0313032488100296142.303640497308
Trimmed Mean ( 18 / 39 )4.454851851851850.0307046821092379145.087053368696
Trimmed Mean ( 19 / 39 )4.454822784810130.0301870655870166147.573892930028
Trimmed Mean ( 20 / 39 )4.454779220779220.0296973433510633150.005984310368
Trimmed Mean ( 21 / 39 )4.454520.0291683177499211152.717754866479
Trimmed Mean ( 22 / 39 )4.454671232876710.0286465965555081155.504379874410
Trimmed Mean ( 23 / 39 )4.455028169014080.028092116165865158.586421283115
Trimmed Mean ( 24 / 39 )4.454956521739130.0275453855876218161.731499730433
Trimmed Mean ( 25 / 39 )4.455298507462690.0271236511850292164.258804136287
Trimmed Mean ( 26 / 39 )4.45520.0267453195042537166.578679282235
Trimmed Mean ( 27 / 39 )4.455031746031750.0262968789288745169.4129466117
Trimmed Mean ( 28 / 39 )4.455016393442620.0257954277708584172.705660592903
Trimmed Mean ( 29 / 39 )4.455169491525420.0252300479589928176.581887547997
Trimmed Mean ( 30 / 39 )4.455169491525420.0247041030083634180.341277318070
Trimmed Mean ( 31 / 39 )4.454036363636360.0241366475155619184.534176122208
Trimmed Mean ( 32 / 39 )4.45313207547170.0234976458342161189.513966926307
Trimmed Mean ( 33 / 39 )4.45231372549020.0229200569789539194.254042630805
Trimmed Mean ( 34 / 39 )4.452183673469390.0224089555080946198.678768042587
Trimmed Mean ( 35 / 39 )4.452085106382980.0217601046692067204.598515221447
Trimmed Mean ( 36 / 39 )4.45160.0212175456267741209.807490381102
Trimmed Mean ( 37 / 39 )4.451465116279070.0206460266177808215.608804477921
Trimmed Mean ( 38 / 39 )4.451634146341460.0200366358386016222.174729440616
Trimmed Mean ( 39 / 39 )4.452025641025640.0193557674011189230.010288342702
Median4.434
Midrange4.5725
Midmean - Weighted Average at Xnp4.44908620689655
Midmean - Weighted Average at X(n+1)p4.45516949152542
Midmean - Empirical Distribution Function4.45516949152542
Midmean - Empirical Distribution Function - Averaging4.45516949152542
Midmean - Empirical Distribution Function - Interpolation4.45516949152542
Midmean - Closest Observation4.44911666666667
Midmean - True Basic - Statistics Graphics Toolkit4.45516949152542
Midmean - MS Excel (old versions)4.45516949152542
Number of observations117



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')