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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 18 Aug 2009 11:06:21 -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/Aug/18/t1250615239mefdy03rhyok3uv.htm/, Retrieved Tue, 07 May 2024 04:02:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42852, Retrieved Tue, 07 May 2024 04:02:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Opgave 5 - Oefeni...] [2009-08-18 17:06:21] [594470f14259f7e0de407f0568e168f2] [Current]
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Dataseries X:
12,11
11,42
11,71
12,04
12,21
12
12,36
12,32
12,96
12,79
13,19
12,34
13,25
12,54
12,77
12,96
13
13,61
13,8
14,16
14,27
14,69
15,01
15,09
15,14
14,2
13,83
14,31
14,04
14,9
14,92
15,36
15,5
15,65
16,18
15,44
15,58
15,24
15,33
16,07
15,82
15,87
15,72
17,07
16,83
17,52
17,76
17,36
17,95
16,71
17,14
16,72
17,26
17,24
17,69
18,13
18,08
18,18
18,18
17,64
17,89
16,82
16,61
16,66
17,02
16,91
17,18
18,06
17,58
17,48
17,54
17,44
17,79
16,79
16,19
16,62
16,39
16,54
17,26
18
17,29
18,16
17,82
17,48
18,31
17,04
17,03
16,97
17,11
17,12
17,69
18,5
18,27
18,45
18,35
18,03
18,49
18,07
17,8
17,88
18,12
18,68
18,8
19,64
19,56
19,3
20,07
19,82
20,29
19,36
18,74
18,87
18,87
18,91
19,31
20,06
20,72
20,42
20,58
20,58
21,18
19,87
19,83
19,48
19,49
19,4
19,89
20,44
20,07
19,75
19,54
19,07




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42852&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42852&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42852&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean16.86742424242420.20721431010531981.4008657696043
Geometric Mean16.6889329127468
Harmonic Mean16.4984231063723
Quadratic Mean17.0333451936150
Winsorized Mean ( 1 / 44 )16.86613636363640.20625881254635881.7717127109206
Winsorized Mean ( 2 / 44 )16.86840909090910.20514374455030982.2272652177914
Winsorized Mean ( 3 / 44 )16.86931818181820.20497965102656882.2975261072705
Winsorized Mean ( 4 / 44 )16.86719696969700.20402341292923582.6728497848788
Winsorized Mean ( 5 / 44 )16.87022727272730.20325367697680883.0008466447187
Winsorized Mean ( 6 / 44 )16.86931818181820.20160884804553083.673501165031
Winsorized Mean ( 7 / 44 )16.85871212121210.19995518828601684.3124515333774
Winsorized Mean ( 8 / 44 )16.85992424242420.19974641268418484.4066434829106
Winsorized Mean ( 9 / 44 )16.87151515151520.19758024646180985.3906979753478
Winsorized Mean ( 10 / 44 )16.87606060606060.19314737234460287.3740108457254
Winsorized Mean ( 11 / 44 )16.87606060606060.19267912670036787.5863457296251
Winsorized Mean ( 12 / 44 )16.88787878787880.18977627935339288.9883543160367
Winsorized Mean ( 13 / 44 )16.88689393939390.18965987101473589.0377803646295
Winsorized Mean ( 14 / 44 )16.88371212121210.18812030264859489.7495479408762
Winsorized Mean ( 15 / 44 )16.89280303030300.18331183966683592.15336587645
Winsorized Mean ( 16 / 44 )16.89037878787880.18109277119766293.2692049283567
Winsorized Mean ( 17 / 44 )16.93416666666670.17385616539666997.403313986765
Winsorized Mean ( 18 / 44 )16.95325757575760.169343464799296100.111673018208
Winsorized Mean ( 19 / 44 )16.95613636363640.168566353115958100.590278250679
Winsorized Mean ( 20 / 44 )16.97583333333330.162740312944172104.312404383522
Winsorized Mean ( 21 / 44 )16.98856060606060.159409516920558106.571809100500
Winsorized Mean ( 22 / 44 )16.98689393939390.157565811994852107.808246753102
Winsorized Mean ( 23 / 44 )16.99734848484850.155730682809951109.145790528586
Winsorized Mean ( 24 / 44 )16.96280303030300.150152028532350112.970854913548
Winsorized Mean ( 25 / 44 )17.00446969696970.137435254429987123.727130767835
Winsorized Mean ( 26 / 44 )17.03795454545450.131368917516408129.695477952968
Winsorized Mean ( 27 / 44 )17.04204545454550.130861605802444130.229530273938
Winsorized Mean ( 28 / 44 )17.04628787878790.126936146011579134.290258641010
Winsorized Mean ( 29 / 44 )17.05068181818180.123410185737686138.162678520101
Winsorized Mean ( 30 / 44 )17.04840909090910.120618242658442141.341879264362
Winsorized Mean ( 31 / 44 )17.02962121212120.113511314301589150.025760135902
Winsorized Mean ( 32 / 44 )17.04901515151510.110664243685754154.060738895285
Winsorized Mean ( 33 / 44 )17.04651515151520.108786334758627156.697210080086
Winsorized Mean ( 34 / 44 )17.04136363636360.103846158654104164.102012604297
Winsorized Mean ( 35 / 44 )17.04666666666670.100962787515748168.841085771406
Winsorized Mean ( 36 / 44 )17.05757575757580.0973838995231262175.158068644859
Winsorized Mean ( 37 / 44 )17.05196969696970.0927448799767445183.858879339166
Winsorized Mean ( 38 / 44 )17.07212121212120.090432048933123188.783969992171
Winsorized Mean ( 39 / 44 )17.09575757575760.0865291299024563197.572281092269
Winsorized Mean ( 40 / 44 )17.10181818181820.0839765244135355203.649987913309
Winsorized Mean ( 41 / 44 )17.16083333333330.0768343449163223.348469386023
Winsorized Mean ( 42 / 44 )17.18310606060610.0718591816777234239.121927907132
Winsorized Mean ( 43 / 44 )17.18310606060610.0712021401872314241.328505230626
Winsorized Mean ( 44 / 44 )17.24643939393940.0639158172725233269.830538509807
Trimmed Mean ( 1 / 44 )16.87615384615380.20345807051905582.946593384573
Trimmed Mean ( 2 / 44 )16.8864843750.20038092997951684.2719133838048
Trimmed Mean ( 3 / 44 )16.89595238095240.19763494256214485.4907141516215
Trimmed Mean ( 4 / 44 )16.90540322580650.19467482484167886.8391854958904
Trimmed Mean ( 5 / 44 )16.91573770491800.19170623152053388.2378082900568
Trimmed Mean ( 6 / 44 )16.925750.18862738239915389.7311396930884
Trimmed Mean ( 7 / 44 )16.93627118644070.18559260582121591.2550966753263
Trimmed Mean ( 8 / 44 )16.94887931034480.18255597287314492.8420968297894
Trimmed Mean ( 9 / 44 )16.96175438596490.17921837079721294.6429448639358
Trimmed Mean ( 10 / 44 )16.97357142857140.17588559964513896.5034742060568
Trimmed Mean ( 11 / 44 )16.98527272727270.17289241830814698.2418598425751
Trimmed Mean ( 12 / 44 )16.99740740740740.169616847266441100.210608093117
Trimmed Mean ( 13 / 44 )17.00877358490570.166386127028033102.224710008665
Trimmed Mean ( 14 / 44 )17.02067307692310.162773425070919104.566658037129
Trimmed Mean ( 15 / 44 )17.03333333333330.158920678480785107.181352962779
Trimmed Mean ( 16 / 44 )17.04570.155246253065602109.797819035265
Trimmed Mean ( 17 / 44 )17.05877551020410.151386763430407112.683401927977
Trimmed Mean ( 18 / 44 )17.06885416666670.148012332774421115.320486115711
Trimmed Mean ( 19 / 44 )17.07787234042550.144779818654871117.957547530406
Trimmed Mean ( 20 / 44 )17.08706521739130.141199940754502121.013260530327
Trimmed Mean ( 21 / 44 )17.09522222222220.137879357765483123.986813539552
Trimmed Mean ( 22 / 44 )17.10284090909090.134513126936656127.146259243121
Trimmed Mean ( 23 / 44 )17.11093023255810.130882684482395130.734866114851
Trimmed Mean ( 24 / 44 )17.11869047619050.126945195298400134.851031076449
Trimmed Mean ( 25 / 44 )17.12914634146340.123099243313236139.149079071729
Trimmed Mean ( 26 / 44 )17.1373750.120338886429223142.40928687735
Trimmed Mean ( 27 / 44 )17.14384615384620.117918204656102145.387611724964
Trimmed Mean ( 28 / 44 )17.15039473684210.115153054638655148.935647349167
Trimmed Mean ( 29 / 44 )17.15702702702700.11242468040658152.609079829974
Trimmed Mean ( 30 / 44 )17.163750.109680043546076156.489270473252
Trimmed Mean ( 31 / 44 )17.1710.106805322019056160.769142168182
Trimmed Mean ( 32 / 44 )17.17985294117650.104336713619483164.657792498925
Trimmed Mean ( 33 / 44 )17.18803030303030.101795585585103168.848483991094
Trimmed Mean ( 34 / 44 )17.1968750.0989969223006453173.711208392666
Trimmed Mean ( 35 / 44 )17.20661290322580.0963273063553463178.626534409169
Trimmed Mean ( 36 / 44 )17.21666666666670.0935141509176316184.107608289480
Trimmed Mean ( 37 / 44 )17.22672413793100.0906434576484185190.049283035394
Trimmed Mean ( 38 / 44 )17.23785714285710.087833118877788196.256917243735
Trimmed Mean ( 39 / 44 )17.24851851851850.0847644029749436203.487760346961
Trimmed Mean ( 40 / 44 )17.25846153846150.0816655360290734211.331026252218
Trimmed Mean ( 41 / 44 )17.26880.078230762778449220.741807783539
Trimmed Mean ( 42 / 44 )17.27604166666670.0754124237178777229.087474118288
Trimmed Mean ( 43 / 44 )17.28239130434780.0728324029275025237.289868378375
Trimmed Mean ( 44 / 44 )17.28931818181820.06959821093123248.416129530998
Median17.26
Midrange16.3
Midmean - Weighted Average at Xnp17.1602985074627
Midmean - Weighted Average at X(n+1)p17.1880303030303
Midmean - Empirical Distribution Function17.1602985074627
Midmean - Empirical Distribution Function - Averaging17.1880303030303
Midmean - Empirical Distribution Function - Interpolation17.1880303030303
Midmean - Closest Observation17.1602985074627
Midmean - True Basic - Statistics Graphics Toolkit17.1880303030303
Midmean - MS Excel (old versions)17.1798529411765
Number of observations132

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 16.8674242424242 & 0.207214310105319 & 81.4008657696043 \tabularnewline
Geometric Mean & 16.6889329127468 &  &  \tabularnewline
Harmonic Mean & 16.4984231063723 &  &  \tabularnewline
Quadratic Mean & 17.0333451936150 &  &  \tabularnewline
Winsorized Mean ( 1 / 44 ) & 16.8661363636364 & 0.206258812546358 & 81.7717127109206 \tabularnewline
Winsorized Mean ( 2 / 44 ) & 16.8684090909091 & 0.205143744550309 & 82.2272652177914 \tabularnewline
Winsorized Mean ( 3 / 44 ) & 16.8693181818182 & 0.204979651026568 & 82.2975261072705 \tabularnewline
Winsorized Mean ( 4 / 44 ) & 16.8671969696970 & 0.204023412929235 & 82.6728497848788 \tabularnewline
Winsorized Mean ( 5 / 44 ) & 16.8702272727273 & 0.203253676976808 & 83.0008466447187 \tabularnewline
Winsorized Mean ( 6 / 44 ) & 16.8693181818182 & 0.201608848045530 & 83.673501165031 \tabularnewline
Winsorized Mean ( 7 / 44 ) & 16.8587121212121 & 0.199955188286016 & 84.3124515333774 \tabularnewline
Winsorized Mean ( 8 / 44 ) & 16.8599242424242 & 0.199746412684184 & 84.4066434829106 \tabularnewline
Winsorized Mean ( 9 / 44 ) & 16.8715151515152 & 0.197580246461809 & 85.3906979753478 \tabularnewline
Winsorized Mean ( 10 / 44 ) & 16.8760606060606 & 0.193147372344602 & 87.3740108457254 \tabularnewline
Winsorized Mean ( 11 / 44 ) & 16.8760606060606 & 0.192679126700367 & 87.5863457296251 \tabularnewline
Winsorized Mean ( 12 / 44 ) & 16.8878787878788 & 0.189776279353392 & 88.9883543160367 \tabularnewline
Winsorized Mean ( 13 / 44 ) & 16.8868939393939 & 0.189659871014735 & 89.0377803646295 \tabularnewline
Winsorized Mean ( 14 / 44 ) & 16.8837121212121 & 0.188120302648594 & 89.7495479408762 \tabularnewline
Winsorized Mean ( 15 / 44 ) & 16.8928030303030 & 0.183311839666835 & 92.15336587645 \tabularnewline
Winsorized Mean ( 16 / 44 ) & 16.8903787878788 & 0.181092771197662 & 93.2692049283567 \tabularnewline
Winsorized Mean ( 17 / 44 ) & 16.9341666666667 & 0.173856165396669 & 97.403313986765 \tabularnewline
Winsorized Mean ( 18 / 44 ) & 16.9532575757576 & 0.169343464799296 & 100.111673018208 \tabularnewline
Winsorized Mean ( 19 / 44 ) & 16.9561363636364 & 0.168566353115958 & 100.590278250679 \tabularnewline
Winsorized Mean ( 20 / 44 ) & 16.9758333333333 & 0.162740312944172 & 104.312404383522 \tabularnewline
Winsorized Mean ( 21 / 44 ) & 16.9885606060606 & 0.159409516920558 & 106.571809100500 \tabularnewline
Winsorized Mean ( 22 / 44 ) & 16.9868939393939 & 0.157565811994852 & 107.808246753102 \tabularnewline
Winsorized Mean ( 23 / 44 ) & 16.9973484848485 & 0.155730682809951 & 109.145790528586 \tabularnewline
Winsorized Mean ( 24 / 44 ) & 16.9628030303030 & 0.150152028532350 & 112.970854913548 \tabularnewline
Winsorized Mean ( 25 / 44 ) & 17.0044696969697 & 0.137435254429987 & 123.727130767835 \tabularnewline
Winsorized Mean ( 26 / 44 ) & 17.0379545454545 & 0.131368917516408 & 129.695477952968 \tabularnewline
Winsorized Mean ( 27 / 44 ) & 17.0420454545455 & 0.130861605802444 & 130.229530273938 \tabularnewline
Winsorized Mean ( 28 / 44 ) & 17.0462878787879 & 0.126936146011579 & 134.290258641010 \tabularnewline
Winsorized Mean ( 29 / 44 ) & 17.0506818181818 & 0.123410185737686 & 138.162678520101 \tabularnewline
Winsorized Mean ( 30 / 44 ) & 17.0484090909091 & 0.120618242658442 & 141.341879264362 \tabularnewline
Winsorized Mean ( 31 / 44 ) & 17.0296212121212 & 0.113511314301589 & 150.025760135902 \tabularnewline
Winsorized Mean ( 32 / 44 ) & 17.0490151515151 & 0.110664243685754 & 154.060738895285 \tabularnewline
Winsorized Mean ( 33 / 44 ) & 17.0465151515152 & 0.108786334758627 & 156.697210080086 \tabularnewline
Winsorized Mean ( 34 / 44 ) & 17.0413636363636 & 0.103846158654104 & 164.102012604297 \tabularnewline
Winsorized Mean ( 35 / 44 ) & 17.0466666666667 & 0.100962787515748 & 168.841085771406 \tabularnewline
Winsorized Mean ( 36 / 44 ) & 17.0575757575758 & 0.0973838995231262 & 175.158068644859 \tabularnewline
Winsorized Mean ( 37 / 44 ) & 17.0519696969697 & 0.0927448799767445 & 183.858879339166 \tabularnewline
Winsorized Mean ( 38 / 44 ) & 17.0721212121212 & 0.090432048933123 & 188.783969992171 \tabularnewline
Winsorized Mean ( 39 / 44 ) & 17.0957575757576 & 0.0865291299024563 & 197.572281092269 \tabularnewline
Winsorized Mean ( 40 / 44 ) & 17.1018181818182 & 0.0839765244135355 & 203.649987913309 \tabularnewline
Winsorized Mean ( 41 / 44 ) & 17.1608333333333 & 0.0768343449163 & 223.348469386023 \tabularnewline
Winsorized Mean ( 42 / 44 ) & 17.1831060606061 & 0.0718591816777234 & 239.121927907132 \tabularnewline
Winsorized Mean ( 43 / 44 ) & 17.1831060606061 & 0.0712021401872314 & 241.328505230626 \tabularnewline
Winsorized Mean ( 44 / 44 ) & 17.2464393939394 & 0.0639158172725233 & 269.830538509807 \tabularnewline
Trimmed Mean ( 1 / 44 ) & 16.8761538461538 & 0.203458070519055 & 82.946593384573 \tabularnewline
Trimmed Mean ( 2 / 44 ) & 16.886484375 & 0.200380929979516 & 84.2719133838048 \tabularnewline
Trimmed Mean ( 3 / 44 ) & 16.8959523809524 & 0.197634942562144 & 85.4907141516215 \tabularnewline
Trimmed Mean ( 4 / 44 ) & 16.9054032258065 & 0.194674824841678 & 86.8391854958904 \tabularnewline
Trimmed Mean ( 5 / 44 ) & 16.9157377049180 & 0.191706231520533 & 88.2378082900568 \tabularnewline
Trimmed Mean ( 6 / 44 ) & 16.92575 & 0.188627382399153 & 89.7311396930884 \tabularnewline
Trimmed Mean ( 7 / 44 ) & 16.9362711864407 & 0.185592605821215 & 91.2550966753263 \tabularnewline
Trimmed Mean ( 8 / 44 ) & 16.9488793103448 & 0.182555972873144 & 92.8420968297894 \tabularnewline
Trimmed Mean ( 9 / 44 ) & 16.9617543859649 & 0.179218370797212 & 94.6429448639358 \tabularnewline
Trimmed Mean ( 10 / 44 ) & 16.9735714285714 & 0.175885599645138 & 96.5034742060568 \tabularnewline
Trimmed Mean ( 11 / 44 ) & 16.9852727272727 & 0.172892418308146 & 98.2418598425751 \tabularnewline
Trimmed Mean ( 12 / 44 ) & 16.9974074074074 & 0.169616847266441 & 100.210608093117 \tabularnewline
Trimmed Mean ( 13 / 44 ) & 17.0087735849057 & 0.166386127028033 & 102.224710008665 \tabularnewline
Trimmed Mean ( 14 / 44 ) & 17.0206730769231 & 0.162773425070919 & 104.566658037129 \tabularnewline
Trimmed Mean ( 15 / 44 ) & 17.0333333333333 & 0.158920678480785 & 107.181352962779 \tabularnewline
Trimmed Mean ( 16 / 44 ) & 17.0457 & 0.155246253065602 & 109.797819035265 \tabularnewline
Trimmed Mean ( 17 / 44 ) & 17.0587755102041 & 0.151386763430407 & 112.683401927977 \tabularnewline
Trimmed Mean ( 18 / 44 ) & 17.0688541666667 & 0.148012332774421 & 115.320486115711 \tabularnewline
Trimmed Mean ( 19 / 44 ) & 17.0778723404255 & 0.144779818654871 & 117.957547530406 \tabularnewline
Trimmed Mean ( 20 / 44 ) & 17.0870652173913 & 0.141199940754502 & 121.013260530327 \tabularnewline
Trimmed Mean ( 21 / 44 ) & 17.0952222222222 & 0.137879357765483 & 123.986813539552 \tabularnewline
Trimmed Mean ( 22 / 44 ) & 17.1028409090909 & 0.134513126936656 & 127.146259243121 \tabularnewline
Trimmed Mean ( 23 / 44 ) & 17.1109302325581 & 0.130882684482395 & 130.734866114851 \tabularnewline
Trimmed Mean ( 24 / 44 ) & 17.1186904761905 & 0.126945195298400 & 134.851031076449 \tabularnewline
Trimmed Mean ( 25 / 44 ) & 17.1291463414634 & 0.123099243313236 & 139.149079071729 \tabularnewline
Trimmed Mean ( 26 / 44 ) & 17.137375 & 0.120338886429223 & 142.40928687735 \tabularnewline
Trimmed Mean ( 27 / 44 ) & 17.1438461538462 & 0.117918204656102 & 145.387611724964 \tabularnewline
Trimmed Mean ( 28 / 44 ) & 17.1503947368421 & 0.115153054638655 & 148.935647349167 \tabularnewline
Trimmed Mean ( 29 / 44 ) & 17.1570270270270 & 0.11242468040658 & 152.609079829974 \tabularnewline
Trimmed Mean ( 30 / 44 ) & 17.16375 & 0.109680043546076 & 156.489270473252 \tabularnewline
Trimmed Mean ( 31 / 44 ) & 17.171 & 0.106805322019056 & 160.769142168182 \tabularnewline
Trimmed Mean ( 32 / 44 ) & 17.1798529411765 & 0.104336713619483 & 164.657792498925 \tabularnewline
Trimmed Mean ( 33 / 44 ) & 17.1880303030303 & 0.101795585585103 & 168.848483991094 \tabularnewline
Trimmed Mean ( 34 / 44 ) & 17.196875 & 0.0989969223006453 & 173.711208392666 \tabularnewline
Trimmed Mean ( 35 / 44 ) & 17.2066129032258 & 0.0963273063553463 & 178.626534409169 \tabularnewline
Trimmed Mean ( 36 / 44 ) & 17.2166666666667 & 0.0935141509176316 & 184.107608289480 \tabularnewline
Trimmed Mean ( 37 / 44 ) & 17.2267241379310 & 0.0906434576484185 & 190.049283035394 \tabularnewline
Trimmed Mean ( 38 / 44 ) & 17.2378571428571 & 0.087833118877788 & 196.256917243735 \tabularnewline
Trimmed Mean ( 39 / 44 ) & 17.2485185185185 & 0.0847644029749436 & 203.487760346961 \tabularnewline
Trimmed Mean ( 40 / 44 ) & 17.2584615384615 & 0.0816655360290734 & 211.331026252218 \tabularnewline
Trimmed Mean ( 41 / 44 ) & 17.2688 & 0.078230762778449 & 220.741807783539 \tabularnewline
Trimmed Mean ( 42 / 44 ) & 17.2760416666667 & 0.0754124237178777 & 229.087474118288 \tabularnewline
Trimmed Mean ( 43 / 44 ) & 17.2823913043478 & 0.0728324029275025 & 237.289868378375 \tabularnewline
Trimmed Mean ( 44 / 44 ) & 17.2893181818182 & 0.06959821093123 & 248.416129530998 \tabularnewline
Median & 17.26 &  &  \tabularnewline
Midrange & 16.3 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 17.1602985074627 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 17.1880303030303 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 17.1602985074627 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 17.1880303030303 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 17.1880303030303 &  &  \tabularnewline
Midmean - Closest Observation & 17.1602985074627 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 17.1880303030303 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 17.1798529411765 &  &  \tabularnewline
Number of observations & 132 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42852&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]16.8674242424242[/C][C]0.207214310105319[/C][C]81.4008657696043[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]16.6889329127468[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]16.4984231063723[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17.0333451936150[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 44 )[/C][C]16.8661363636364[/C][C]0.206258812546358[/C][C]81.7717127109206[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 44 )[/C][C]16.8684090909091[/C][C]0.205143744550309[/C][C]82.2272652177914[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 44 )[/C][C]16.8693181818182[/C][C]0.204979651026568[/C][C]82.2975261072705[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 44 )[/C][C]16.8671969696970[/C][C]0.204023412929235[/C][C]82.6728497848788[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 44 )[/C][C]16.8702272727273[/C][C]0.203253676976808[/C][C]83.0008466447187[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 44 )[/C][C]16.8693181818182[/C][C]0.201608848045530[/C][C]83.673501165031[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 44 )[/C][C]16.8587121212121[/C][C]0.199955188286016[/C][C]84.3124515333774[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 44 )[/C][C]16.8599242424242[/C][C]0.199746412684184[/C][C]84.4066434829106[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 44 )[/C][C]16.8715151515152[/C][C]0.197580246461809[/C][C]85.3906979753478[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 44 )[/C][C]16.8760606060606[/C][C]0.193147372344602[/C][C]87.3740108457254[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 44 )[/C][C]16.8760606060606[/C][C]0.192679126700367[/C][C]87.5863457296251[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 44 )[/C][C]16.8878787878788[/C][C]0.189776279353392[/C][C]88.9883543160367[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 44 )[/C][C]16.8868939393939[/C][C]0.189659871014735[/C][C]89.0377803646295[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 44 )[/C][C]16.8837121212121[/C][C]0.188120302648594[/C][C]89.7495479408762[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 44 )[/C][C]16.8928030303030[/C][C]0.183311839666835[/C][C]92.15336587645[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 44 )[/C][C]16.8903787878788[/C][C]0.181092771197662[/C][C]93.2692049283567[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 44 )[/C][C]16.9341666666667[/C][C]0.173856165396669[/C][C]97.403313986765[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 44 )[/C][C]16.9532575757576[/C][C]0.169343464799296[/C][C]100.111673018208[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 44 )[/C][C]16.9561363636364[/C][C]0.168566353115958[/C][C]100.590278250679[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 44 )[/C][C]16.9758333333333[/C][C]0.162740312944172[/C][C]104.312404383522[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 44 )[/C][C]16.9885606060606[/C][C]0.159409516920558[/C][C]106.571809100500[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 44 )[/C][C]16.9868939393939[/C][C]0.157565811994852[/C][C]107.808246753102[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 44 )[/C][C]16.9973484848485[/C][C]0.155730682809951[/C][C]109.145790528586[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 44 )[/C][C]16.9628030303030[/C][C]0.150152028532350[/C][C]112.970854913548[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 44 )[/C][C]17.0044696969697[/C][C]0.137435254429987[/C][C]123.727130767835[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 44 )[/C][C]17.0379545454545[/C][C]0.131368917516408[/C][C]129.695477952968[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 44 )[/C][C]17.0420454545455[/C][C]0.130861605802444[/C][C]130.229530273938[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 44 )[/C][C]17.0462878787879[/C][C]0.126936146011579[/C][C]134.290258641010[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 44 )[/C][C]17.0506818181818[/C][C]0.123410185737686[/C][C]138.162678520101[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 44 )[/C][C]17.0484090909091[/C][C]0.120618242658442[/C][C]141.341879264362[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 44 )[/C][C]17.0296212121212[/C][C]0.113511314301589[/C][C]150.025760135902[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 44 )[/C][C]17.0490151515151[/C][C]0.110664243685754[/C][C]154.060738895285[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 44 )[/C][C]17.0465151515152[/C][C]0.108786334758627[/C][C]156.697210080086[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 44 )[/C][C]17.0413636363636[/C][C]0.103846158654104[/C][C]164.102012604297[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 44 )[/C][C]17.0466666666667[/C][C]0.100962787515748[/C][C]168.841085771406[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 44 )[/C][C]17.0575757575758[/C][C]0.0973838995231262[/C][C]175.158068644859[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 44 )[/C][C]17.0519696969697[/C][C]0.0927448799767445[/C][C]183.858879339166[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 44 )[/C][C]17.0721212121212[/C][C]0.090432048933123[/C][C]188.783969992171[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 44 )[/C][C]17.0957575757576[/C][C]0.0865291299024563[/C][C]197.572281092269[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 44 )[/C][C]17.1018181818182[/C][C]0.0839765244135355[/C][C]203.649987913309[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 44 )[/C][C]17.1608333333333[/C][C]0.0768343449163[/C][C]223.348469386023[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 44 )[/C][C]17.1831060606061[/C][C]0.0718591816777234[/C][C]239.121927907132[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 44 )[/C][C]17.1831060606061[/C][C]0.0712021401872314[/C][C]241.328505230626[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 44 )[/C][C]17.2464393939394[/C][C]0.0639158172725233[/C][C]269.830538509807[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 44 )[/C][C]16.8761538461538[/C][C]0.203458070519055[/C][C]82.946593384573[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 44 )[/C][C]16.886484375[/C][C]0.200380929979516[/C][C]84.2719133838048[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 44 )[/C][C]16.8959523809524[/C][C]0.197634942562144[/C][C]85.4907141516215[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 44 )[/C][C]16.9054032258065[/C][C]0.194674824841678[/C][C]86.8391854958904[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 44 )[/C][C]16.9157377049180[/C][C]0.191706231520533[/C][C]88.2378082900568[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 44 )[/C][C]16.92575[/C][C]0.188627382399153[/C][C]89.7311396930884[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 44 )[/C][C]16.9362711864407[/C][C]0.185592605821215[/C][C]91.2550966753263[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 44 )[/C][C]16.9488793103448[/C][C]0.182555972873144[/C][C]92.8420968297894[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 44 )[/C][C]16.9617543859649[/C][C]0.179218370797212[/C][C]94.6429448639358[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 44 )[/C][C]16.9735714285714[/C][C]0.175885599645138[/C][C]96.5034742060568[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 44 )[/C][C]16.9852727272727[/C][C]0.172892418308146[/C][C]98.2418598425751[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 44 )[/C][C]16.9974074074074[/C][C]0.169616847266441[/C][C]100.210608093117[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 44 )[/C][C]17.0087735849057[/C][C]0.166386127028033[/C][C]102.224710008665[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 44 )[/C][C]17.0206730769231[/C][C]0.162773425070919[/C][C]104.566658037129[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 44 )[/C][C]17.0333333333333[/C][C]0.158920678480785[/C][C]107.181352962779[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 44 )[/C][C]17.0457[/C][C]0.155246253065602[/C][C]109.797819035265[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 44 )[/C][C]17.0587755102041[/C][C]0.151386763430407[/C][C]112.683401927977[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 44 )[/C][C]17.0688541666667[/C][C]0.148012332774421[/C][C]115.320486115711[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 44 )[/C][C]17.0778723404255[/C][C]0.144779818654871[/C][C]117.957547530406[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 44 )[/C][C]17.0870652173913[/C][C]0.141199940754502[/C][C]121.013260530327[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 44 )[/C][C]17.0952222222222[/C][C]0.137879357765483[/C][C]123.986813539552[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 44 )[/C][C]17.1028409090909[/C][C]0.134513126936656[/C][C]127.146259243121[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 44 )[/C][C]17.1109302325581[/C][C]0.130882684482395[/C][C]130.734866114851[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 44 )[/C][C]17.1186904761905[/C][C]0.126945195298400[/C][C]134.851031076449[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 44 )[/C][C]17.1291463414634[/C][C]0.123099243313236[/C][C]139.149079071729[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 44 )[/C][C]17.137375[/C][C]0.120338886429223[/C][C]142.40928687735[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 44 )[/C][C]17.1438461538462[/C][C]0.117918204656102[/C][C]145.387611724964[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 44 )[/C][C]17.1503947368421[/C][C]0.115153054638655[/C][C]148.935647349167[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 44 )[/C][C]17.1570270270270[/C][C]0.11242468040658[/C][C]152.609079829974[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 44 )[/C][C]17.16375[/C][C]0.109680043546076[/C][C]156.489270473252[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 44 )[/C][C]17.171[/C][C]0.106805322019056[/C][C]160.769142168182[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 44 )[/C][C]17.1798529411765[/C][C]0.104336713619483[/C][C]164.657792498925[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 44 )[/C][C]17.1880303030303[/C][C]0.101795585585103[/C][C]168.848483991094[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 44 )[/C][C]17.196875[/C][C]0.0989969223006453[/C][C]173.711208392666[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 44 )[/C][C]17.2066129032258[/C][C]0.0963273063553463[/C][C]178.626534409169[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 44 )[/C][C]17.2166666666667[/C][C]0.0935141509176316[/C][C]184.107608289480[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 44 )[/C][C]17.2267241379310[/C][C]0.0906434576484185[/C][C]190.049283035394[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 44 )[/C][C]17.2378571428571[/C][C]0.087833118877788[/C][C]196.256917243735[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 44 )[/C][C]17.2485185185185[/C][C]0.0847644029749436[/C][C]203.487760346961[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 44 )[/C][C]17.2584615384615[/C][C]0.0816655360290734[/C][C]211.331026252218[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 44 )[/C][C]17.2688[/C][C]0.078230762778449[/C][C]220.741807783539[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 44 )[/C][C]17.2760416666667[/C][C]0.0754124237178777[/C][C]229.087474118288[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 44 )[/C][C]17.2823913043478[/C][C]0.0728324029275025[/C][C]237.289868378375[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 44 )[/C][C]17.2893181818182[/C][C]0.06959821093123[/C][C]248.416129530998[/C][/ROW]
[ROW][C]Median[/C][C]17.26[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]16.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]17.1602985074627[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]17.1880303030303[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]17.1602985074627[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]17.1880303030303[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]17.1880303030303[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]17.1602985074627[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]17.1880303030303[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]17.1798529411765[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]132[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42852&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42852&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 Mean16.86742424242420.20721431010531981.4008657696043
Geometric Mean16.6889329127468
Harmonic Mean16.4984231063723
Quadratic Mean17.0333451936150
Winsorized Mean ( 1 / 44 )16.86613636363640.20625881254635881.7717127109206
Winsorized Mean ( 2 / 44 )16.86840909090910.20514374455030982.2272652177914
Winsorized Mean ( 3 / 44 )16.86931818181820.20497965102656882.2975261072705
Winsorized Mean ( 4 / 44 )16.86719696969700.20402341292923582.6728497848788
Winsorized Mean ( 5 / 44 )16.87022727272730.20325367697680883.0008466447187
Winsorized Mean ( 6 / 44 )16.86931818181820.20160884804553083.673501165031
Winsorized Mean ( 7 / 44 )16.85871212121210.19995518828601684.3124515333774
Winsorized Mean ( 8 / 44 )16.85992424242420.19974641268418484.4066434829106
Winsorized Mean ( 9 / 44 )16.87151515151520.19758024646180985.3906979753478
Winsorized Mean ( 10 / 44 )16.87606060606060.19314737234460287.3740108457254
Winsorized Mean ( 11 / 44 )16.87606060606060.19267912670036787.5863457296251
Winsorized Mean ( 12 / 44 )16.88787878787880.18977627935339288.9883543160367
Winsorized Mean ( 13 / 44 )16.88689393939390.18965987101473589.0377803646295
Winsorized Mean ( 14 / 44 )16.88371212121210.18812030264859489.7495479408762
Winsorized Mean ( 15 / 44 )16.89280303030300.18331183966683592.15336587645
Winsorized Mean ( 16 / 44 )16.89037878787880.18109277119766293.2692049283567
Winsorized Mean ( 17 / 44 )16.93416666666670.17385616539666997.403313986765
Winsorized Mean ( 18 / 44 )16.95325757575760.169343464799296100.111673018208
Winsorized Mean ( 19 / 44 )16.95613636363640.168566353115958100.590278250679
Winsorized Mean ( 20 / 44 )16.97583333333330.162740312944172104.312404383522
Winsorized Mean ( 21 / 44 )16.98856060606060.159409516920558106.571809100500
Winsorized Mean ( 22 / 44 )16.98689393939390.157565811994852107.808246753102
Winsorized Mean ( 23 / 44 )16.99734848484850.155730682809951109.145790528586
Winsorized Mean ( 24 / 44 )16.96280303030300.150152028532350112.970854913548
Winsorized Mean ( 25 / 44 )17.00446969696970.137435254429987123.727130767835
Winsorized Mean ( 26 / 44 )17.03795454545450.131368917516408129.695477952968
Winsorized Mean ( 27 / 44 )17.04204545454550.130861605802444130.229530273938
Winsorized Mean ( 28 / 44 )17.04628787878790.126936146011579134.290258641010
Winsorized Mean ( 29 / 44 )17.05068181818180.123410185737686138.162678520101
Winsorized Mean ( 30 / 44 )17.04840909090910.120618242658442141.341879264362
Winsorized Mean ( 31 / 44 )17.02962121212120.113511314301589150.025760135902
Winsorized Mean ( 32 / 44 )17.04901515151510.110664243685754154.060738895285
Winsorized Mean ( 33 / 44 )17.04651515151520.108786334758627156.697210080086
Winsorized Mean ( 34 / 44 )17.04136363636360.103846158654104164.102012604297
Winsorized Mean ( 35 / 44 )17.04666666666670.100962787515748168.841085771406
Winsorized Mean ( 36 / 44 )17.05757575757580.0973838995231262175.158068644859
Winsorized Mean ( 37 / 44 )17.05196969696970.0927448799767445183.858879339166
Winsorized Mean ( 38 / 44 )17.07212121212120.090432048933123188.783969992171
Winsorized Mean ( 39 / 44 )17.09575757575760.0865291299024563197.572281092269
Winsorized Mean ( 40 / 44 )17.10181818181820.0839765244135355203.649987913309
Winsorized Mean ( 41 / 44 )17.16083333333330.0768343449163223.348469386023
Winsorized Mean ( 42 / 44 )17.18310606060610.0718591816777234239.121927907132
Winsorized Mean ( 43 / 44 )17.18310606060610.0712021401872314241.328505230626
Winsorized Mean ( 44 / 44 )17.24643939393940.0639158172725233269.830538509807
Trimmed Mean ( 1 / 44 )16.87615384615380.20345807051905582.946593384573
Trimmed Mean ( 2 / 44 )16.8864843750.20038092997951684.2719133838048
Trimmed Mean ( 3 / 44 )16.89595238095240.19763494256214485.4907141516215
Trimmed Mean ( 4 / 44 )16.90540322580650.19467482484167886.8391854958904
Trimmed Mean ( 5 / 44 )16.91573770491800.19170623152053388.2378082900568
Trimmed Mean ( 6 / 44 )16.925750.18862738239915389.7311396930884
Trimmed Mean ( 7 / 44 )16.93627118644070.18559260582121591.2550966753263
Trimmed Mean ( 8 / 44 )16.94887931034480.18255597287314492.8420968297894
Trimmed Mean ( 9 / 44 )16.96175438596490.17921837079721294.6429448639358
Trimmed Mean ( 10 / 44 )16.97357142857140.17588559964513896.5034742060568
Trimmed Mean ( 11 / 44 )16.98527272727270.17289241830814698.2418598425751
Trimmed Mean ( 12 / 44 )16.99740740740740.169616847266441100.210608093117
Trimmed Mean ( 13 / 44 )17.00877358490570.166386127028033102.224710008665
Trimmed Mean ( 14 / 44 )17.02067307692310.162773425070919104.566658037129
Trimmed Mean ( 15 / 44 )17.03333333333330.158920678480785107.181352962779
Trimmed Mean ( 16 / 44 )17.04570.155246253065602109.797819035265
Trimmed Mean ( 17 / 44 )17.05877551020410.151386763430407112.683401927977
Trimmed Mean ( 18 / 44 )17.06885416666670.148012332774421115.320486115711
Trimmed Mean ( 19 / 44 )17.07787234042550.144779818654871117.957547530406
Trimmed Mean ( 20 / 44 )17.08706521739130.141199940754502121.013260530327
Trimmed Mean ( 21 / 44 )17.09522222222220.137879357765483123.986813539552
Trimmed Mean ( 22 / 44 )17.10284090909090.134513126936656127.146259243121
Trimmed Mean ( 23 / 44 )17.11093023255810.130882684482395130.734866114851
Trimmed Mean ( 24 / 44 )17.11869047619050.126945195298400134.851031076449
Trimmed Mean ( 25 / 44 )17.12914634146340.123099243313236139.149079071729
Trimmed Mean ( 26 / 44 )17.1373750.120338886429223142.40928687735
Trimmed Mean ( 27 / 44 )17.14384615384620.117918204656102145.387611724964
Trimmed Mean ( 28 / 44 )17.15039473684210.115153054638655148.935647349167
Trimmed Mean ( 29 / 44 )17.15702702702700.11242468040658152.609079829974
Trimmed Mean ( 30 / 44 )17.163750.109680043546076156.489270473252
Trimmed Mean ( 31 / 44 )17.1710.106805322019056160.769142168182
Trimmed Mean ( 32 / 44 )17.17985294117650.104336713619483164.657792498925
Trimmed Mean ( 33 / 44 )17.18803030303030.101795585585103168.848483991094
Trimmed Mean ( 34 / 44 )17.1968750.0989969223006453173.711208392666
Trimmed Mean ( 35 / 44 )17.20661290322580.0963273063553463178.626534409169
Trimmed Mean ( 36 / 44 )17.21666666666670.0935141509176316184.107608289480
Trimmed Mean ( 37 / 44 )17.22672413793100.0906434576484185190.049283035394
Trimmed Mean ( 38 / 44 )17.23785714285710.087833118877788196.256917243735
Trimmed Mean ( 39 / 44 )17.24851851851850.0847644029749436203.487760346961
Trimmed Mean ( 40 / 44 )17.25846153846150.0816655360290734211.331026252218
Trimmed Mean ( 41 / 44 )17.26880.078230762778449220.741807783539
Trimmed Mean ( 42 / 44 )17.27604166666670.0754124237178777229.087474118288
Trimmed Mean ( 43 / 44 )17.28239130434780.0728324029275025237.289868378375
Trimmed Mean ( 44 / 44 )17.28931818181820.06959821093123248.416129530998
Median17.26
Midrange16.3
Midmean - Weighted Average at Xnp17.1602985074627
Midmean - Weighted Average at X(n+1)p17.1880303030303
Midmean - Empirical Distribution Function17.1602985074627
Midmean - Empirical Distribution Function - Averaging17.1880303030303
Midmean - Empirical Distribution Function - Interpolation17.1880303030303
Midmean - Closest Observation17.1602985074627
Midmean - True Basic - Statistics Graphics Toolkit17.1880303030303
Midmean - MS Excel (old versions)17.1798529411765
Number of observations132



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')