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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 25 Nov 2010 20:43:28 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/25/t1290717755z8nerlxoftpgjbu.htm/, Retrieved Fri, 29 Mar 2024 06:38:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=101515, Retrieved Fri, 29 Mar 2024 06:38:09 +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)
-       [Central Tendency] [] [2010-11-25 20:43:28] [40b262140b988d7b8204c4955f8b7651] [Current]
-   PD    [Central Tendency] [Paper - Robustnes...] [2010-11-30 22:31:59] [8677c3f87cec9201607d40be65aa9670]
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Dataseries X:
1,00
1,10
0,20
0,20
-0,10
-0,20
-0,10
-0,40
0,00
-0,30
-0,20
0,30
1,80
2,40
2,90
3,60
3,90
4,90
5,20
5,80
6,00
7,60
7,70
8,70
8,70
8,90
9,20
9,70
10,20
10,50
10,10
11,40
11,60
11,60
12,40
12,40
11,40
11,60
11,90
11,00
10,70
10,30
11,00
10,20
10,10
9,90
9,30
8,50
8,40
8,10
7,80
8,40
8,80
8,90
8,40
7,80
7,50
7,30
7,60
7,90
8,30
8,20
8,00
7,60
7,30
6,80
6,40
6,60
6,80
6,60
6,00
5,80
5,90
5,50
5,30
5,30
4,90
5,40
6,20
6,20
6,40
7,10
7,40
7,90
7,60
8,40
8,80
8,60
8,70
8,90
8,20
8,10
7,30
6,90
7,00
6,90
7,10
7,00
7,00
7,20
7,70
7,40
7,40
7,40
7,80
8,00
7,80
7,40
6,90
5,90
5,60
5,40
4,40
3,90
3,80
3,90
3,90
4,10
3,90
4,20
4,20
4,70
4,40
4,60
5,50
5,90
6,00
5,80
4,90




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=101515&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=101515&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101515&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 Mean6.634883720930230.26479398887451725.0567762098045
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean7.27987030295918
Winsorized Mean ( 1 / 43 )6.635658914728680.2646341779175725.0748371466803
Winsorized Mean ( 2 / 43 )6.629457364341080.26305175286626925.2021029782356
Winsorized Mean ( 3 / 43 )6.622480620155040.26198787323923125.2778135807370
Winsorized Mean ( 4 / 43 )6.625581395348840.26136075938763925.3503296013999
Winsorized Mean ( 5 / 43 )6.625581395348840.26136075938763925.3503296013999
Winsorized Mean ( 6 / 43 )6.620930232558140.25906686871229825.5568389175649
Winsorized Mean ( 7 / 43 )6.631782945736430.25692205899722825.8124310992229
Winsorized Mean ( 8 / 43 )6.606976744186050.25344330772532826.0688546226931
Winsorized Mean ( 9 / 43 )6.61395348837210.25207170720686726.2383809815841
Winsorized Mean ( 10 / 43 )6.644961240310080.23861417876671827.8481407712429
Winsorized Mean ( 11 / 43 )6.636434108527130.23481225487474228.2627246694057
Winsorized Mean ( 12 / 43 )6.682945736434110.2207916189329830.2681132949285
Winsorized Mean ( 13 / 43 )6.733333333333330.20937433713111932.1593057945618
Winsorized Mean ( 14 / 43 )6.78759689922480.20087926801860933.7894346498515
Winsorized Mean ( 15 / 43 )6.857364341085270.18762842886425836.5475764125612
Winsorized Mean ( 16 / 43 )6.882170542635660.18432535171902137.3370807566752
Winsorized Mean ( 17 / 43 )6.868992248062010.17907018691853338.3592175016103
Winsorized Mean ( 18 / 43 )6.841085271317830.1754479745318338.9921017302865
Winsorized Mean ( 19 / 43 )6.782170542635660.16824752787241240.3106698113199
Winsorized Mean ( 20 / 43 )6.766666666666670.16645577742990340.6514377040246
Winsorized Mean ( 21 / 43 )6.717829457364340.16107924531371841.7051212543284
Winsorized Mean ( 22 / 43 )6.751937984496120.15648954806032343.1462552495416
Winsorized Mean ( 23 / 43 )6.769767441860470.15414808964321543.9172970455197
Winsorized Mean ( 24 / 43 )6.751162790697680.15216507683873644.3673603099648
Winsorized Mean ( 25 / 43 )6.789922480620160.14716657295493746.1376679791223
Winsorized Mean ( 26 / 43 )6.769767441860460.14504328348216746.6741187825688
Winsorized Mean ( 27 / 43 )6.811627906976740.13978296744633048.7300279241253
Winsorized Mean ( 28 / 43 )6.833333333333330.13712216115604149.8339092362845
Winsorized Mean ( 29 / 43 )6.855813953488370.12935208142853253.0011877487743
Winsorized Mean ( 30 / 43 )6.832558139534880.12693350930036753.8278518981681
Winsorized Mean ( 31 / 43 )6.808527131782950.12450011970235654.6869123343829
Winsorized Mean ( 32 / 43 )6.882945736434110.11581111425439659.4325145798593
Winsorized Mean ( 33 / 43 )6.908527131782950.11293537100021161.1723950662899
Winsorized Mean ( 34 / 43 )6.908527131782940.11293537100021161.1723950662899
Winsorized Mean ( 35 / 43 )6.908527131782950.10715687424227164.4711520435304
Winsorized Mean ( 36 / 43 )6.880620155038760.10436266939291465.9298980666541
Winsorized Mean ( 37 / 43 )6.90930232558140.10121262026808968.2652252977963
Winsorized Mean ( 38 / 43 )6.879844961240310.098316619947734369.9764186858506
Winsorized Mean ( 39 / 43 )6.910077519379850.095030626446123372.7142162247815
Winsorized Mean ( 40 / 43 )6.941085271317830.085431051939787981.2478029207686
Winsorized Mean ( 41 / 43 )6.941085271317830.085431051939787981.2478029207686
Winsorized Mean ( 42 / 43 )6.908527131782950.08232209358806983.9206928622646
Winsorized Mean ( 43 / 43 )6.941860465116280.07884751310407388.041590556617
Trimmed Mean ( 1 / 43 )6.644881889763780.25919102671240525.6370059336076
Trimmed Mean ( 2 / 43 )6.65440.25319252906472926.2819761095668
Trimmed Mean ( 3 / 43 )6.667479674796750.24748904537826826.9405042336562
Trimmed Mean ( 4 / 43 )6.683471074380170.24160946537087827.6622899029259
Trimmed Mean ( 5 / 43 )6.699159663865550.23529081121651928.4718286669549
Trimmed Mean ( 6 / 43 )6.715384615384620.22825603700029129.4204030861013
Trimmed Mean ( 7 / 43 )6.733043478260870.22095321454839430.4727111213229
Trimmed Mean ( 8 / 43 )6.74955752212390.21325069637280231.6508111669863
Trimmed Mean ( 9 / 43 )6.770270270270270.20528079327143632.9805344298245
Trimmed Mean ( 10 / 43 )6.79082568807340.19654050655689634.5517868404778
Trimmed Mean ( 11 / 43 )6.808411214953270.18917132440169135.9907149589762
Trimmed Mean ( 12 / 43 )6.827619047619050.18147490587327237.6229375337818
Trimmed Mean ( 13 / 43 )6.842718446601940.17514293171327739.0693382808278
Trimmed Mean ( 14 / 43 )6.853465346534650.16981390137987240.3586825980962
Trimmed Mean ( 15 / 43 )6.859595959595960.16508787907287041.5511786699261
Trimmed Mean ( 16 / 43 )6.859793814432990.16163801111186542.4392367070486
Trimmed Mean ( 17 / 43 )6.85789473684210.15817817039253943.3555067669792
Trimmed Mean ( 18 / 43 )6.856989247311830.15495100078682844.2526296215747
Trimmed Mean ( 19 / 43 )6.858241758241760.15175059815115445.1941662293184
Trimmed Mean ( 20 / 43 )6.864044943820220.14900287572386646.0665266389944
Trimmed Mean ( 21 / 43 )6.871264367816090.14606948768021447.0410657074335
Trimmed Mean ( 22 / 43 )6.882352941176470.14333147484875748.0170384658268
Trimmed Mean ( 23 / 43 )6.891566265060240.14076743626137048.9571057631846
Trimmed Mean ( 24 / 43 )6.90.13809774673875449.9646095823204
Trimmed Mean ( 25 / 43 )6.910126582278480.13522187684555151.102134828162
Trimmed Mean ( 26 / 43 )6.918181818181820.13253570009684852.1986288458619
Trimmed Mean ( 27 / 43 )6.9280.12963649803053853.4417398283006
Trimmed Mean ( 28 / 43 )6.935616438356160.12695008341728854.6326260815333
Trimmed Mean ( 29 / 43 )6.942253521126760.12414151028069855.9220965286273
Trimmed Mean ( 30 / 43 )6.947826086956520.12185705529513357.0161987759278
Trimmed Mean ( 31 / 43 )6.955223880597020.11942277086181958.2403492265701
Trimmed Mean ( 32 / 43 )6.964615384615380.11679680681782559.6301865981536
Trimmed Mean ( 33 / 43 )6.969841269841270.11490629145013360.6567419579983
Trimmed Mean ( 34 / 43 )6.973770491803280.11300422254657861.7124770618975
Trimmed Mean ( 35 / 43 )6.977966101694920.11065576269544263.0601238626893
Trimmed Mean ( 36 / 43 )6.982456140350880.10862327136283364.281401699158
Trimmed Mean ( 37 / 43 )6.989090909090910.10647940403344765.6379604350107
Trimmed Mean ( 38 / 43 )6.994339622641510.10431249434087067.0517915120076
Trimmed Mean ( 39 / 43 )7.001960784313730.10199923860071268.6471867865968
Trimmed Mean ( 40 / 43 )7.008163265306120.099652317979510370.3261440114929
Trimmed Mean ( 41 / 43 )7.012765957446810.098349798667947871.3043244869628
Trimmed Mean ( 42 / 43 )7.017777777777780.096571995903662872.6688696045849
Trimmed Mean ( 43 / 43 )7.025581395348840.094716048405989774.1751953716911
Median7.1
Midrange6
Midmean - Weighted Average at Xnp6.98636363636364
Midmean - Weighted Average at X(n+1)p6.98636363636364
Midmean - Empirical Distribution Function6.98636363636364
Midmean - Empirical Distribution Function - Averaging6.98636363636364
Midmean - Empirical Distribution Function - Interpolation6.98636363636364
Midmean - Closest Observation6.89565217391304
Midmean - True Basic - Statistics Graphics Toolkit6.98636363636364
Midmean - MS Excel (old versions)6.98636363636364
Number of observations129

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.63488372093023 & 0.264793988874517 & 25.0567762098045 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 7.27987030295918 &  &  \tabularnewline
Winsorized Mean ( 1 / 43 ) & 6.63565891472868 & 0.26463417791757 & 25.0748371466803 \tabularnewline
Winsorized Mean ( 2 / 43 ) & 6.62945736434108 & 0.263051752866269 & 25.2021029782356 \tabularnewline
Winsorized Mean ( 3 / 43 ) & 6.62248062015504 & 0.261987873239231 & 25.2778135807370 \tabularnewline
Winsorized Mean ( 4 / 43 ) & 6.62558139534884 & 0.261360759387639 & 25.3503296013999 \tabularnewline
Winsorized Mean ( 5 / 43 ) & 6.62558139534884 & 0.261360759387639 & 25.3503296013999 \tabularnewline
Winsorized Mean ( 6 / 43 ) & 6.62093023255814 & 0.259066868712298 & 25.5568389175649 \tabularnewline
Winsorized Mean ( 7 / 43 ) & 6.63178294573643 & 0.256922058997228 & 25.8124310992229 \tabularnewline
Winsorized Mean ( 8 / 43 ) & 6.60697674418605 & 0.253443307725328 & 26.0688546226931 \tabularnewline
Winsorized Mean ( 9 / 43 ) & 6.6139534883721 & 0.252071707206867 & 26.2383809815841 \tabularnewline
Winsorized Mean ( 10 / 43 ) & 6.64496124031008 & 0.238614178766718 & 27.8481407712429 \tabularnewline
Winsorized Mean ( 11 / 43 ) & 6.63643410852713 & 0.234812254874742 & 28.2627246694057 \tabularnewline
Winsorized Mean ( 12 / 43 ) & 6.68294573643411 & 0.22079161893298 & 30.2681132949285 \tabularnewline
Winsorized Mean ( 13 / 43 ) & 6.73333333333333 & 0.209374337131119 & 32.1593057945618 \tabularnewline
Winsorized Mean ( 14 / 43 ) & 6.7875968992248 & 0.200879268018609 & 33.7894346498515 \tabularnewline
Winsorized Mean ( 15 / 43 ) & 6.85736434108527 & 0.187628428864258 & 36.5475764125612 \tabularnewline
Winsorized Mean ( 16 / 43 ) & 6.88217054263566 & 0.184325351719021 & 37.3370807566752 \tabularnewline
Winsorized Mean ( 17 / 43 ) & 6.86899224806201 & 0.179070186918533 & 38.3592175016103 \tabularnewline
Winsorized Mean ( 18 / 43 ) & 6.84108527131783 & 0.17544797453183 & 38.9921017302865 \tabularnewline
Winsorized Mean ( 19 / 43 ) & 6.78217054263566 & 0.168247527872412 & 40.3106698113199 \tabularnewline
Winsorized Mean ( 20 / 43 ) & 6.76666666666667 & 0.166455777429903 & 40.6514377040246 \tabularnewline
Winsorized Mean ( 21 / 43 ) & 6.71782945736434 & 0.161079245313718 & 41.7051212543284 \tabularnewline
Winsorized Mean ( 22 / 43 ) & 6.75193798449612 & 0.156489548060323 & 43.1462552495416 \tabularnewline
Winsorized Mean ( 23 / 43 ) & 6.76976744186047 & 0.154148089643215 & 43.9172970455197 \tabularnewline
Winsorized Mean ( 24 / 43 ) & 6.75116279069768 & 0.152165076838736 & 44.3673603099648 \tabularnewline
Winsorized Mean ( 25 / 43 ) & 6.78992248062016 & 0.147166572954937 & 46.1376679791223 \tabularnewline
Winsorized Mean ( 26 / 43 ) & 6.76976744186046 & 0.145043283482167 & 46.6741187825688 \tabularnewline
Winsorized Mean ( 27 / 43 ) & 6.81162790697674 & 0.139782967446330 & 48.7300279241253 \tabularnewline
Winsorized Mean ( 28 / 43 ) & 6.83333333333333 & 0.137122161156041 & 49.8339092362845 \tabularnewline
Winsorized Mean ( 29 / 43 ) & 6.85581395348837 & 0.129352081428532 & 53.0011877487743 \tabularnewline
Winsorized Mean ( 30 / 43 ) & 6.83255813953488 & 0.126933509300367 & 53.8278518981681 \tabularnewline
Winsorized Mean ( 31 / 43 ) & 6.80852713178295 & 0.124500119702356 & 54.6869123343829 \tabularnewline
Winsorized Mean ( 32 / 43 ) & 6.88294573643411 & 0.115811114254396 & 59.4325145798593 \tabularnewline
Winsorized Mean ( 33 / 43 ) & 6.90852713178295 & 0.112935371000211 & 61.1723950662899 \tabularnewline
Winsorized Mean ( 34 / 43 ) & 6.90852713178294 & 0.112935371000211 & 61.1723950662899 \tabularnewline
Winsorized Mean ( 35 / 43 ) & 6.90852713178295 & 0.107156874242271 & 64.4711520435304 \tabularnewline
Winsorized Mean ( 36 / 43 ) & 6.88062015503876 & 0.104362669392914 & 65.9298980666541 \tabularnewline
Winsorized Mean ( 37 / 43 ) & 6.9093023255814 & 0.101212620268089 & 68.2652252977963 \tabularnewline
Winsorized Mean ( 38 / 43 ) & 6.87984496124031 & 0.0983166199477343 & 69.9764186858506 \tabularnewline
Winsorized Mean ( 39 / 43 ) & 6.91007751937985 & 0.0950306264461233 & 72.7142162247815 \tabularnewline
Winsorized Mean ( 40 / 43 ) & 6.94108527131783 & 0.0854310519397879 & 81.2478029207686 \tabularnewline
Winsorized Mean ( 41 / 43 ) & 6.94108527131783 & 0.0854310519397879 & 81.2478029207686 \tabularnewline
Winsorized Mean ( 42 / 43 ) & 6.90852713178295 & 0.082322093588069 & 83.9206928622646 \tabularnewline
Winsorized Mean ( 43 / 43 ) & 6.94186046511628 & 0.078847513104073 & 88.041590556617 \tabularnewline
Trimmed Mean ( 1 / 43 ) & 6.64488188976378 & 0.259191026712405 & 25.6370059336076 \tabularnewline
Trimmed Mean ( 2 / 43 ) & 6.6544 & 0.253192529064729 & 26.2819761095668 \tabularnewline
Trimmed Mean ( 3 / 43 ) & 6.66747967479675 & 0.247489045378268 & 26.9405042336562 \tabularnewline
Trimmed Mean ( 4 / 43 ) & 6.68347107438017 & 0.241609465370878 & 27.6622899029259 \tabularnewline
Trimmed Mean ( 5 / 43 ) & 6.69915966386555 & 0.235290811216519 & 28.4718286669549 \tabularnewline
Trimmed Mean ( 6 / 43 ) & 6.71538461538462 & 0.228256037000291 & 29.4204030861013 \tabularnewline
Trimmed Mean ( 7 / 43 ) & 6.73304347826087 & 0.220953214548394 & 30.4727111213229 \tabularnewline
Trimmed Mean ( 8 / 43 ) & 6.7495575221239 & 0.213250696372802 & 31.6508111669863 \tabularnewline
Trimmed Mean ( 9 / 43 ) & 6.77027027027027 & 0.205280793271436 & 32.9805344298245 \tabularnewline
Trimmed Mean ( 10 / 43 ) & 6.7908256880734 & 0.196540506556896 & 34.5517868404778 \tabularnewline
Trimmed Mean ( 11 / 43 ) & 6.80841121495327 & 0.189171324401691 & 35.9907149589762 \tabularnewline
Trimmed Mean ( 12 / 43 ) & 6.82761904761905 & 0.181474905873272 & 37.6229375337818 \tabularnewline
Trimmed Mean ( 13 / 43 ) & 6.84271844660194 & 0.175142931713277 & 39.0693382808278 \tabularnewline
Trimmed Mean ( 14 / 43 ) & 6.85346534653465 & 0.169813901379872 & 40.3586825980962 \tabularnewline
Trimmed Mean ( 15 / 43 ) & 6.85959595959596 & 0.165087879072870 & 41.5511786699261 \tabularnewline
Trimmed Mean ( 16 / 43 ) & 6.85979381443299 & 0.161638011111865 & 42.4392367070486 \tabularnewline
Trimmed Mean ( 17 / 43 ) & 6.8578947368421 & 0.158178170392539 & 43.3555067669792 \tabularnewline
Trimmed Mean ( 18 / 43 ) & 6.85698924731183 & 0.154951000786828 & 44.2526296215747 \tabularnewline
Trimmed Mean ( 19 / 43 ) & 6.85824175824176 & 0.151750598151154 & 45.1941662293184 \tabularnewline
Trimmed Mean ( 20 / 43 ) & 6.86404494382022 & 0.149002875723866 & 46.0665266389944 \tabularnewline
Trimmed Mean ( 21 / 43 ) & 6.87126436781609 & 0.146069487680214 & 47.0410657074335 \tabularnewline
Trimmed Mean ( 22 / 43 ) & 6.88235294117647 & 0.143331474848757 & 48.0170384658268 \tabularnewline
Trimmed Mean ( 23 / 43 ) & 6.89156626506024 & 0.140767436261370 & 48.9571057631846 \tabularnewline
Trimmed Mean ( 24 / 43 ) & 6.9 & 0.138097746738754 & 49.9646095823204 \tabularnewline
Trimmed Mean ( 25 / 43 ) & 6.91012658227848 & 0.135221876845551 & 51.102134828162 \tabularnewline
Trimmed Mean ( 26 / 43 ) & 6.91818181818182 & 0.132535700096848 & 52.1986288458619 \tabularnewline
Trimmed Mean ( 27 / 43 ) & 6.928 & 0.129636498030538 & 53.4417398283006 \tabularnewline
Trimmed Mean ( 28 / 43 ) & 6.93561643835616 & 0.126950083417288 & 54.6326260815333 \tabularnewline
Trimmed Mean ( 29 / 43 ) & 6.94225352112676 & 0.124141510280698 & 55.9220965286273 \tabularnewline
Trimmed Mean ( 30 / 43 ) & 6.94782608695652 & 0.121857055295133 & 57.0161987759278 \tabularnewline
Trimmed Mean ( 31 / 43 ) & 6.95522388059702 & 0.119422770861819 & 58.2403492265701 \tabularnewline
Trimmed Mean ( 32 / 43 ) & 6.96461538461538 & 0.116796806817825 & 59.6301865981536 \tabularnewline
Trimmed Mean ( 33 / 43 ) & 6.96984126984127 & 0.114906291450133 & 60.6567419579983 \tabularnewline
Trimmed Mean ( 34 / 43 ) & 6.97377049180328 & 0.113004222546578 & 61.7124770618975 \tabularnewline
Trimmed Mean ( 35 / 43 ) & 6.97796610169492 & 0.110655762695442 & 63.0601238626893 \tabularnewline
Trimmed Mean ( 36 / 43 ) & 6.98245614035088 & 0.108623271362833 & 64.281401699158 \tabularnewline
Trimmed Mean ( 37 / 43 ) & 6.98909090909091 & 0.106479404033447 & 65.6379604350107 \tabularnewline
Trimmed Mean ( 38 / 43 ) & 6.99433962264151 & 0.104312494340870 & 67.0517915120076 \tabularnewline
Trimmed Mean ( 39 / 43 ) & 7.00196078431373 & 0.101999238600712 & 68.6471867865968 \tabularnewline
Trimmed Mean ( 40 / 43 ) & 7.00816326530612 & 0.0996523179795103 & 70.3261440114929 \tabularnewline
Trimmed Mean ( 41 / 43 ) & 7.01276595744681 & 0.0983497986679478 & 71.3043244869628 \tabularnewline
Trimmed Mean ( 42 / 43 ) & 7.01777777777778 & 0.0965719959036628 & 72.6688696045849 \tabularnewline
Trimmed Mean ( 43 / 43 ) & 7.02558139534884 & 0.0947160484059897 & 74.1751953716911 \tabularnewline
Median & 7.1 &  &  \tabularnewline
Midrange & 6 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6.98636363636364 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6.98636363636364 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6.98636363636364 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6.98636363636364 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6.98636363636364 &  &  \tabularnewline
Midmean - Closest Observation & 6.89565217391304 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6.98636363636364 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6.98636363636364 &  &  \tabularnewline
Number of observations & 129 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=101515&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]6.63488372093023[/C][C]0.264793988874517[/C][C]25.0567762098045[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.27987030295918[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 43 )[/C][C]6.63565891472868[/C][C]0.26463417791757[/C][C]25.0748371466803[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 43 )[/C][C]6.62945736434108[/C][C]0.263051752866269[/C][C]25.2021029782356[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 43 )[/C][C]6.62248062015504[/C][C]0.261987873239231[/C][C]25.2778135807370[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 43 )[/C][C]6.62558139534884[/C][C]0.261360759387639[/C][C]25.3503296013999[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 43 )[/C][C]6.62558139534884[/C][C]0.261360759387639[/C][C]25.3503296013999[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 43 )[/C][C]6.62093023255814[/C][C]0.259066868712298[/C][C]25.5568389175649[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 43 )[/C][C]6.63178294573643[/C][C]0.256922058997228[/C][C]25.8124310992229[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 43 )[/C][C]6.60697674418605[/C][C]0.253443307725328[/C][C]26.0688546226931[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 43 )[/C][C]6.6139534883721[/C][C]0.252071707206867[/C][C]26.2383809815841[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 43 )[/C][C]6.64496124031008[/C][C]0.238614178766718[/C][C]27.8481407712429[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 43 )[/C][C]6.63643410852713[/C][C]0.234812254874742[/C][C]28.2627246694057[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 43 )[/C][C]6.68294573643411[/C][C]0.22079161893298[/C][C]30.2681132949285[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 43 )[/C][C]6.73333333333333[/C][C]0.209374337131119[/C][C]32.1593057945618[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 43 )[/C][C]6.7875968992248[/C][C]0.200879268018609[/C][C]33.7894346498515[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 43 )[/C][C]6.85736434108527[/C][C]0.187628428864258[/C][C]36.5475764125612[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 43 )[/C][C]6.88217054263566[/C][C]0.184325351719021[/C][C]37.3370807566752[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 43 )[/C][C]6.86899224806201[/C][C]0.179070186918533[/C][C]38.3592175016103[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 43 )[/C][C]6.84108527131783[/C][C]0.17544797453183[/C][C]38.9921017302865[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 43 )[/C][C]6.78217054263566[/C][C]0.168247527872412[/C][C]40.3106698113199[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 43 )[/C][C]6.76666666666667[/C][C]0.166455777429903[/C][C]40.6514377040246[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 43 )[/C][C]6.71782945736434[/C][C]0.161079245313718[/C][C]41.7051212543284[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 43 )[/C][C]6.75193798449612[/C][C]0.156489548060323[/C][C]43.1462552495416[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 43 )[/C][C]6.76976744186047[/C][C]0.154148089643215[/C][C]43.9172970455197[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 43 )[/C][C]6.75116279069768[/C][C]0.152165076838736[/C][C]44.3673603099648[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 43 )[/C][C]6.78992248062016[/C][C]0.147166572954937[/C][C]46.1376679791223[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 43 )[/C][C]6.76976744186046[/C][C]0.145043283482167[/C][C]46.6741187825688[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 43 )[/C][C]6.81162790697674[/C][C]0.139782967446330[/C][C]48.7300279241253[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 43 )[/C][C]6.83333333333333[/C][C]0.137122161156041[/C][C]49.8339092362845[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 43 )[/C][C]6.85581395348837[/C][C]0.129352081428532[/C][C]53.0011877487743[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 43 )[/C][C]6.83255813953488[/C][C]0.126933509300367[/C][C]53.8278518981681[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 43 )[/C][C]6.80852713178295[/C][C]0.124500119702356[/C][C]54.6869123343829[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 43 )[/C][C]6.88294573643411[/C][C]0.115811114254396[/C][C]59.4325145798593[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 43 )[/C][C]6.90852713178295[/C][C]0.112935371000211[/C][C]61.1723950662899[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 43 )[/C][C]6.90852713178294[/C][C]0.112935371000211[/C][C]61.1723950662899[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 43 )[/C][C]6.90852713178295[/C][C]0.107156874242271[/C][C]64.4711520435304[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 43 )[/C][C]6.88062015503876[/C][C]0.104362669392914[/C][C]65.9298980666541[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 43 )[/C][C]6.9093023255814[/C][C]0.101212620268089[/C][C]68.2652252977963[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 43 )[/C][C]6.87984496124031[/C][C]0.0983166199477343[/C][C]69.9764186858506[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 43 )[/C][C]6.91007751937985[/C][C]0.0950306264461233[/C][C]72.7142162247815[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 43 )[/C][C]6.94108527131783[/C][C]0.0854310519397879[/C][C]81.2478029207686[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 43 )[/C][C]6.94108527131783[/C][C]0.0854310519397879[/C][C]81.2478029207686[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 43 )[/C][C]6.90852713178295[/C][C]0.082322093588069[/C][C]83.9206928622646[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 43 )[/C][C]6.94186046511628[/C][C]0.078847513104073[/C][C]88.041590556617[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 43 )[/C][C]6.64488188976378[/C][C]0.259191026712405[/C][C]25.6370059336076[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 43 )[/C][C]6.6544[/C][C]0.253192529064729[/C][C]26.2819761095668[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 43 )[/C][C]6.66747967479675[/C][C]0.247489045378268[/C][C]26.9405042336562[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 43 )[/C][C]6.68347107438017[/C][C]0.241609465370878[/C][C]27.6622899029259[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 43 )[/C][C]6.69915966386555[/C][C]0.235290811216519[/C][C]28.4718286669549[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 43 )[/C][C]6.71538461538462[/C][C]0.228256037000291[/C][C]29.4204030861013[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 43 )[/C][C]6.73304347826087[/C][C]0.220953214548394[/C][C]30.4727111213229[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 43 )[/C][C]6.7495575221239[/C][C]0.213250696372802[/C][C]31.6508111669863[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 43 )[/C][C]6.77027027027027[/C][C]0.205280793271436[/C][C]32.9805344298245[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 43 )[/C][C]6.7908256880734[/C][C]0.196540506556896[/C][C]34.5517868404778[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 43 )[/C][C]6.80841121495327[/C][C]0.189171324401691[/C][C]35.9907149589762[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 43 )[/C][C]6.82761904761905[/C][C]0.181474905873272[/C][C]37.6229375337818[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 43 )[/C][C]6.84271844660194[/C][C]0.175142931713277[/C][C]39.0693382808278[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 43 )[/C][C]6.85346534653465[/C][C]0.169813901379872[/C][C]40.3586825980962[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 43 )[/C][C]6.85959595959596[/C][C]0.165087879072870[/C][C]41.5511786699261[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 43 )[/C][C]6.85979381443299[/C][C]0.161638011111865[/C][C]42.4392367070486[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 43 )[/C][C]6.8578947368421[/C][C]0.158178170392539[/C][C]43.3555067669792[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 43 )[/C][C]6.85698924731183[/C][C]0.154951000786828[/C][C]44.2526296215747[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 43 )[/C][C]6.85824175824176[/C][C]0.151750598151154[/C][C]45.1941662293184[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 43 )[/C][C]6.86404494382022[/C][C]0.149002875723866[/C][C]46.0665266389944[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 43 )[/C][C]6.87126436781609[/C][C]0.146069487680214[/C][C]47.0410657074335[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 43 )[/C][C]6.88235294117647[/C][C]0.143331474848757[/C][C]48.0170384658268[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 43 )[/C][C]6.89156626506024[/C][C]0.140767436261370[/C][C]48.9571057631846[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 43 )[/C][C]6.9[/C][C]0.138097746738754[/C][C]49.9646095823204[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 43 )[/C][C]6.91012658227848[/C][C]0.135221876845551[/C][C]51.102134828162[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 43 )[/C][C]6.91818181818182[/C][C]0.132535700096848[/C][C]52.1986288458619[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 43 )[/C][C]6.928[/C][C]0.129636498030538[/C][C]53.4417398283006[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 43 )[/C][C]6.93561643835616[/C][C]0.126950083417288[/C][C]54.6326260815333[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 43 )[/C][C]6.94225352112676[/C][C]0.124141510280698[/C][C]55.9220965286273[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 43 )[/C][C]6.94782608695652[/C][C]0.121857055295133[/C][C]57.0161987759278[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 43 )[/C][C]6.95522388059702[/C][C]0.119422770861819[/C][C]58.2403492265701[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 43 )[/C][C]6.96461538461538[/C][C]0.116796806817825[/C][C]59.6301865981536[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 43 )[/C][C]6.96984126984127[/C][C]0.114906291450133[/C][C]60.6567419579983[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 43 )[/C][C]6.97377049180328[/C][C]0.113004222546578[/C][C]61.7124770618975[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 43 )[/C][C]6.97796610169492[/C][C]0.110655762695442[/C][C]63.0601238626893[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 43 )[/C][C]6.98245614035088[/C][C]0.108623271362833[/C][C]64.281401699158[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 43 )[/C][C]6.98909090909091[/C][C]0.106479404033447[/C][C]65.6379604350107[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 43 )[/C][C]6.99433962264151[/C][C]0.104312494340870[/C][C]67.0517915120076[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 43 )[/C][C]7.00196078431373[/C][C]0.101999238600712[/C][C]68.6471867865968[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 43 )[/C][C]7.00816326530612[/C][C]0.0996523179795103[/C][C]70.3261440114929[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 43 )[/C][C]7.01276595744681[/C][C]0.0983497986679478[/C][C]71.3043244869628[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 43 )[/C][C]7.01777777777778[/C][C]0.0965719959036628[/C][C]72.6688696045849[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 43 )[/C][C]7.02558139534884[/C][C]0.0947160484059897[/C][C]74.1751953716911[/C][/ROW]
[ROW][C]Median[/C][C]7.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6.98636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6.98636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6.98636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6.98636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6.98636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6.89565217391304[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6.98636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6.98636363636364[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]129[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=101515&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=101515&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 Mean6.634883720930230.26479398887451725.0567762098045
Geometric MeanNaN
Harmonic Mean0
Quadratic Mean7.27987030295918
Winsorized Mean ( 1 / 43 )6.635658914728680.2646341779175725.0748371466803
Winsorized Mean ( 2 / 43 )6.629457364341080.26305175286626925.2021029782356
Winsorized Mean ( 3 / 43 )6.622480620155040.26198787323923125.2778135807370
Winsorized Mean ( 4 / 43 )6.625581395348840.26136075938763925.3503296013999
Winsorized Mean ( 5 / 43 )6.625581395348840.26136075938763925.3503296013999
Winsorized Mean ( 6 / 43 )6.620930232558140.25906686871229825.5568389175649
Winsorized Mean ( 7 / 43 )6.631782945736430.25692205899722825.8124310992229
Winsorized Mean ( 8 / 43 )6.606976744186050.25344330772532826.0688546226931
Winsorized Mean ( 9 / 43 )6.61395348837210.25207170720686726.2383809815841
Winsorized Mean ( 10 / 43 )6.644961240310080.23861417876671827.8481407712429
Winsorized Mean ( 11 / 43 )6.636434108527130.23481225487474228.2627246694057
Winsorized Mean ( 12 / 43 )6.682945736434110.2207916189329830.2681132949285
Winsorized Mean ( 13 / 43 )6.733333333333330.20937433713111932.1593057945618
Winsorized Mean ( 14 / 43 )6.78759689922480.20087926801860933.7894346498515
Winsorized Mean ( 15 / 43 )6.857364341085270.18762842886425836.5475764125612
Winsorized Mean ( 16 / 43 )6.882170542635660.18432535171902137.3370807566752
Winsorized Mean ( 17 / 43 )6.868992248062010.17907018691853338.3592175016103
Winsorized Mean ( 18 / 43 )6.841085271317830.1754479745318338.9921017302865
Winsorized Mean ( 19 / 43 )6.782170542635660.16824752787241240.3106698113199
Winsorized Mean ( 20 / 43 )6.766666666666670.16645577742990340.6514377040246
Winsorized Mean ( 21 / 43 )6.717829457364340.16107924531371841.7051212543284
Winsorized Mean ( 22 / 43 )6.751937984496120.15648954806032343.1462552495416
Winsorized Mean ( 23 / 43 )6.769767441860470.15414808964321543.9172970455197
Winsorized Mean ( 24 / 43 )6.751162790697680.15216507683873644.3673603099648
Winsorized Mean ( 25 / 43 )6.789922480620160.14716657295493746.1376679791223
Winsorized Mean ( 26 / 43 )6.769767441860460.14504328348216746.6741187825688
Winsorized Mean ( 27 / 43 )6.811627906976740.13978296744633048.7300279241253
Winsorized Mean ( 28 / 43 )6.833333333333330.13712216115604149.8339092362845
Winsorized Mean ( 29 / 43 )6.855813953488370.12935208142853253.0011877487743
Winsorized Mean ( 30 / 43 )6.832558139534880.12693350930036753.8278518981681
Winsorized Mean ( 31 / 43 )6.808527131782950.12450011970235654.6869123343829
Winsorized Mean ( 32 / 43 )6.882945736434110.11581111425439659.4325145798593
Winsorized Mean ( 33 / 43 )6.908527131782950.11293537100021161.1723950662899
Winsorized Mean ( 34 / 43 )6.908527131782940.11293537100021161.1723950662899
Winsorized Mean ( 35 / 43 )6.908527131782950.10715687424227164.4711520435304
Winsorized Mean ( 36 / 43 )6.880620155038760.10436266939291465.9298980666541
Winsorized Mean ( 37 / 43 )6.90930232558140.10121262026808968.2652252977963
Winsorized Mean ( 38 / 43 )6.879844961240310.098316619947734369.9764186858506
Winsorized Mean ( 39 / 43 )6.910077519379850.095030626446123372.7142162247815
Winsorized Mean ( 40 / 43 )6.941085271317830.085431051939787981.2478029207686
Winsorized Mean ( 41 / 43 )6.941085271317830.085431051939787981.2478029207686
Winsorized Mean ( 42 / 43 )6.908527131782950.08232209358806983.9206928622646
Winsorized Mean ( 43 / 43 )6.941860465116280.07884751310407388.041590556617
Trimmed Mean ( 1 / 43 )6.644881889763780.25919102671240525.6370059336076
Trimmed Mean ( 2 / 43 )6.65440.25319252906472926.2819761095668
Trimmed Mean ( 3 / 43 )6.667479674796750.24748904537826826.9405042336562
Trimmed Mean ( 4 / 43 )6.683471074380170.24160946537087827.6622899029259
Trimmed Mean ( 5 / 43 )6.699159663865550.23529081121651928.4718286669549
Trimmed Mean ( 6 / 43 )6.715384615384620.22825603700029129.4204030861013
Trimmed Mean ( 7 / 43 )6.733043478260870.22095321454839430.4727111213229
Trimmed Mean ( 8 / 43 )6.74955752212390.21325069637280231.6508111669863
Trimmed Mean ( 9 / 43 )6.770270270270270.20528079327143632.9805344298245
Trimmed Mean ( 10 / 43 )6.79082568807340.19654050655689634.5517868404778
Trimmed Mean ( 11 / 43 )6.808411214953270.18917132440169135.9907149589762
Trimmed Mean ( 12 / 43 )6.827619047619050.18147490587327237.6229375337818
Trimmed Mean ( 13 / 43 )6.842718446601940.17514293171327739.0693382808278
Trimmed Mean ( 14 / 43 )6.853465346534650.16981390137987240.3586825980962
Trimmed Mean ( 15 / 43 )6.859595959595960.16508787907287041.5511786699261
Trimmed Mean ( 16 / 43 )6.859793814432990.16163801111186542.4392367070486
Trimmed Mean ( 17 / 43 )6.85789473684210.15817817039253943.3555067669792
Trimmed Mean ( 18 / 43 )6.856989247311830.15495100078682844.2526296215747
Trimmed Mean ( 19 / 43 )6.858241758241760.15175059815115445.1941662293184
Trimmed Mean ( 20 / 43 )6.864044943820220.14900287572386646.0665266389944
Trimmed Mean ( 21 / 43 )6.871264367816090.14606948768021447.0410657074335
Trimmed Mean ( 22 / 43 )6.882352941176470.14333147484875748.0170384658268
Trimmed Mean ( 23 / 43 )6.891566265060240.14076743626137048.9571057631846
Trimmed Mean ( 24 / 43 )6.90.13809774673875449.9646095823204
Trimmed Mean ( 25 / 43 )6.910126582278480.13522187684555151.102134828162
Trimmed Mean ( 26 / 43 )6.918181818181820.13253570009684852.1986288458619
Trimmed Mean ( 27 / 43 )6.9280.12963649803053853.4417398283006
Trimmed Mean ( 28 / 43 )6.935616438356160.12695008341728854.6326260815333
Trimmed Mean ( 29 / 43 )6.942253521126760.12414151028069855.9220965286273
Trimmed Mean ( 30 / 43 )6.947826086956520.12185705529513357.0161987759278
Trimmed Mean ( 31 / 43 )6.955223880597020.11942277086181958.2403492265701
Trimmed Mean ( 32 / 43 )6.964615384615380.11679680681782559.6301865981536
Trimmed Mean ( 33 / 43 )6.969841269841270.11490629145013360.6567419579983
Trimmed Mean ( 34 / 43 )6.973770491803280.11300422254657861.7124770618975
Trimmed Mean ( 35 / 43 )6.977966101694920.11065576269544263.0601238626893
Trimmed Mean ( 36 / 43 )6.982456140350880.10862327136283364.281401699158
Trimmed Mean ( 37 / 43 )6.989090909090910.10647940403344765.6379604350107
Trimmed Mean ( 38 / 43 )6.994339622641510.10431249434087067.0517915120076
Trimmed Mean ( 39 / 43 )7.001960784313730.10199923860071268.6471867865968
Trimmed Mean ( 40 / 43 )7.008163265306120.099652317979510370.3261440114929
Trimmed Mean ( 41 / 43 )7.012765957446810.098349798667947871.3043244869628
Trimmed Mean ( 42 / 43 )7.017777777777780.096571995903662872.6688696045849
Trimmed Mean ( 43 / 43 )7.025581395348840.094716048405989774.1751953716911
Median7.1
Midrange6
Midmean - Weighted Average at Xnp6.98636363636364
Midmean - Weighted Average at X(n+1)p6.98636363636364
Midmean - Empirical Distribution Function6.98636363636364
Midmean - Empirical Distribution Function - Averaging6.98636363636364
Midmean - Empirical Distribution Function - Interpolation6.98636363636364
Midmean - Closest Observation6.89565217391304
Midmean - True Basic - Statistics Graphics Toolkit6.98636363636364
Midmean - MS Excel (old versions)6.98636363636364
Number of observations129



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')