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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 computationSun, 18 Oct 2009 10:56:27 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/18/t12558851195ym2kmjkl4dr0w5.htm/, Retrieved Mon, 29 Apr 2024 11:31:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=47394, Retrieved Mon, 29 Apr 2024 11:31:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact100
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Workshop 3: deel ...] [2009-10-18 16:56:27] [a5c6be3c0aa55fdb2a703a08e16947ef] [Current]
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Dataseries X:
7.7489
7.2189
6.8365
6.6674
7.1773
8.0057
7.4385
6.9834
7.4106
7.8803
7.9468
7.8612
6.8408
6.9622
7.5461
7.1024
6.6892
5.7357
6.1217
6.5577
6.0674
5.5326
5.6068
4.9369
4.8656
5.3659
5.5938
5.6525
5.8362
5.8747
5.8013
4.9516
4.9100
5.0551
4.7295
5.2889
6.3747
7.7545
8.0331
8.6451
8.7020
10.4179
9.7930
11.3237
12.3803
12.6329
12.0686
12.6772
11.9029
9.0336
8.2125
7.5105
6.6734
4.0605
3.9648
2.2108
0.9532
0.0000
1.5387




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=47394&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=47394&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47394&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 Mean6.875661016949150.34273473667751620.0611734999554
Geometric Mean0
Harmonic Mean0
Quadratic Mean7.35444125709546
Winsorized Mean ( 1 / 19 )6.891066101694920.33726613855401820.4321315244969
Winsorized Mean ( 2 / 19 )6.902350847457630.32897520733179920.9813709167938
Winsorized Mean ( 3 / 19 )6.920676271186440.31525474776248121.9526472489500
Winsorized Mean ( 4 / 19 )7.028357627118640.28549385566089724.6182447984687
Winsorized Mean ( 5 / 19 )6.987383050847460.26995193814448425.8838039796094
Winsorized Mean ( 6 / 19 )6.963301694915250.23333900142906029.8419966326643
Winsorized Mean ( 7 / 19 )6.905308474576270.21248542359039132.4977984743446
Winsorized Mean ( 8 / 19 )6.80835932203390.18884945069285736.0517825021739
Winsorized Mean ( 9 / 19 )6.761879661016950.17823578398255037.9378344231873
Winsorized Mean ( 10 / 19 )6.754727118644070.17599777798047638.3796159028405
Winsorized Mean ( 11 / 19 )6.693369491525420.15839520909207242.2573986289870
Winsorized Mean ( 12 / 19 )6.704433898305080.14420038424344346.4938698567300
Winsorized Mean ( 13 / 19 )6.71536271186440.14040057566678547.8300226332554
Winsorized Mean ( 14 / 19 )6.740942372881360.13178161100637451.1523749133352
Winsorized Mean ( 15 / 19 )6.739594915254240.12669194209053153.1967132561459
Winsorized Mean ( 16 / 19 )6.73794067796610.12534060245009253.757047167928
Winsorized Mean ( 17 / 19 )6.720364406779660.11860629721526556.6611096085607
Winsorized Mean ( 18 / 19 )6.744038983050850.11444983593075258.9257199733458
Winsorized Mean ( 19 / 19 )6.699855932203390.10158668409287965.9521077199232
Trimmed Mean ( 1 / 19 )6.89450526315790.31712781613973221.7404620858615
Trimmed Mean ( 2 / 19 )6.898194545454550.29174418840969123.6446682384896
Trimmed Mean ( 3 / 19 )6.895881132075470.26532330185443925.9904843784081
Trimmed Mean ( 4 / 19 )6.886319607843140.23870644894677928.8484858210868
Trimmed Mean ( 5 / 19 )6.843563265306120.21774004227358331.4299712347232
Trimmed Mean ( 6 / 19 )6.807455319148940.19667881121472534.6120422281629
Trimmed Mean ( 7 / 19 )6.77340.18288690124354137.0360039671743
Trimmed Mean ( 8 / 19 )6.747544186046510.17201794542166639.2258154781836
Trimmed Mean ( 9 / 19 )6.736604878048780.16533839504922640.7443466234392
Trimmed Mean ( 10 / 19 )6.732356410256410.15955806805753242.1937699059437
Trimmed Mean ( 11 / 19 )6.728789189189190.15230894440676544.1785557335287
Trimmed Mean ( 12 / 19 )6.734217142857140.14751752754345245.6502847830985
Trimmed Mean ( 13 / 19 )6.738654545454550.14472872613406246.5605876970998
Trimmed Mean ( 14 / 19 )6.742064516129030.14153225670924947.6362397723887
Trimmed Mean ( 15 / 19 )6.74222758620690.13911662868529548.4645699793295
Trimmed Mean ( 16 / 19 )6.742611111111110.13660980486197049.3567143143483
Trimmed Mean ( 17 / 19 )6.74330.13266230172886350.8305668763536
Trimmed Mean ( 18 / 19 )6.746760869565220.12843637183540552.5299864294782
Trimmed Mean ( 19 / 19 )6.747185714285710.12267257528841255.0015820440925
Median6.8365
Midrange6.3386
Midmean - Weighted Average at Xnp6.70190666666667
Midmean - Weighted Average at X(n+1)p6.74206451612903
Midmean - Empirical Distribution Function6.74206451612903
Midmean - Empirical Distribution Function - Averaging6.74206451612903
Midmean - Empirical Distribution Function - Interpolation6.7422275862069
Midmean - Closest Observation6.70190666666667
Midmean - True Basic - Statistics Graphics Toolkit6.74206451612903
Midmean - MS Excel (old versions)6.74206451612903
Number of observations59

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.87566101694915 & 0.342734736677516 & 20.0611734999554 \tabularnewline
Geometric Mean & 0 &  &  \tabularnewline
Harmonic Mean & 0 &  &  \tabularnewline
Quadratic Mean & 7.35444125709546 &  &  \tabularnewline
Winsorized Mean ( 1 / 19 ) & 6.89106610169492 & 0.337266138554018 & 20.4321315244969 \tabularnewline
Winsorized Mean ( 2 / 19 ) & 6.90235084745763 & 0.328975207331799 & 20.9813709167938 \tabularnewline
Winsorized Mean ( 3 / 19 ) & 6.92067627118644 & 0.315254747762481 & 21.9526472489500 \tabularnewline
Winsorized Mean ( 4 / 19 ) & 7.02835762711864 & 0.285493855660897 & 24.6182447984687 \tabularnewline
Winsorized Mean ( 5 / 19 ) & 6.98738305084746 & 0.269951938144484 & 25.8838039796094 \tabularnewline
Winsorized Mean ( 6 / 19 ) & 6.96330169491525 & 0.233339001429060 & 29.8419966326643 \tabularnewline
Winsorized Mean ( 7 / 19 ) & 6.90530847457627 & 0.212485423590391 & 32.4977984743446 \tabularnewline
Winsorized Mean ( 8 / 19 ) & 6.8083593220339 & 0.188849450692857 & 36.0517825021739 \tabularnewline
Winsorized Mean ( 9 / 19 ) & 6.76187966101695 & 0.178235783982550 & 37.9378344231873 \tabularnewline
Winsorized Mean ( 10 / 19 ) & 6.75472711864407 & 0.175997777980476 & 38.3796159028405 \tabularnewline
Winsorized Mean ( 11 / 19 ) & 6.69336949152542 & 0.158395209092072 & 42.2573986289870 \tabularnewline
Winsorized Mean ( 12 / 19 ) & 6.70443389830508 & 0.144200384243443 & 46.4938698567300 \tabularnewline
Winsorized Mean ( 13 / 19 ) & 6.7153627118644 & 0.140400575666785 & 47.8300226332554 \tabularnewline
Winsorized Mean ( 14 / 19 ) & 6.74094237288136 & 0.131781611006374 & 51.1523749133352 \tabularnewline
Winsorized Mean ( 15 / 19 ) & 6.73959491525424 & 0.126691942090531 & 53.1967132561459 \tabularnewline
Winsorized Mean ( 16 / 19 ) & 6.7379406779661 & 0.125340602450092 & 53.757047167928 \tabularnewline
Winsorized Mean ( 17 / 19 ) & 6.72036440677966 & 0.118606297215265 & 56.6611096085607 \tabularnewline
Winsorized Mean ( 18 / 19 ) & 6.74403898305085 & 0.114449835930752 & 58.9257199733458 \tabularnewline
Winsorized Mean ( 19 / 19 ) & 6.69985593220339 & 0.101586684092879 & 65.9521077199232 \tabularnewline
Trimmed Mean ( 1 / 19 ) & 6.8945052631579 & 0.317127816139732 & 21.7404620858615 \tabularnewline
Trimmed Mean ( 2 / 19 ) & 6.89819454545455 & 0.291744188409691 & 23.6446682384896 \tabularnewline
Trimmed Mean ( 3 / 19 ) & 6.89588113207547 & 0.265323301854439 & 25.9904843784081 \tabularnewline
Trimmed Mean ( 4 / 19 ) & 6.88631960784314 & 0.238706448946779 & 28.8484858210868 \tabularnewline
Trimmed Mean ( 5 / 19 ) & 6.84356326530612 & 0.217740042273583 & 31.4299712347232 \tabularnewline
Trimmed Mean ( 6 / 19 ) & 6.80745531914894 & 0.196678811214725 & 34.6120422281629 \tabularnewline
Trimmed Mean ( 7 / 19 ) & 6.7734 & 0.182886901243541 & 37.0360039671743 \tabularnewline
Trimmed Mean ( 8 / 19 ) & 6.74754418604651 & 0.172017945421666 & 39.2258154781836 \tabularnewline
Trimmed Mean ( 9 / 19 ) & 6.73660487804878 & 0.165338395049226 & 40.7443466234392 \tabularnewline
Trimmed Mean ( 10 / 19 ) & 6.73235641025641 & 0.159558068057532 & 42.1937699059437 \tabularnewline
Trimmed Mean ( 11 / 19 ) & 6.72878918918919 & 0.152308944406765 & 44.1785557335287 \tabularnewline
Trimmed Mean ( 12 / 19 ) & 6.73421714285714 & 0.147517527543452 & 45.6502847830985 \tabularnewline
Trimmed Mean ( 13 / 19 ) & 6.73865454545455 & 0.144728726134062 & 46.5605876970998 \tabularnewline
Trimmed Mean ( 14 / 19 ) & 6.74206451612903 & 0.141532256709249 & 47.6362397723887 \tabularnewline
Trimmed Mean ( 15 / 19 ) & 6.7422275862069 & 0.139116628685295 & 48.4645699793295 \tabularnewline
Trimmed Mean ( 16 / 19 ) & 6.74261111111111 & 0.136609804861970 & 49.3567143143483 \tabularnewline
Trimmed Mean ( 17 / 19 ) & 6.7433 & 0.132662301728863 & 50.8305668763536 \tabularnewline
Trimmed Mean ( 18 / 19 ) & 6.74676086956522 & 0.128436371835405 & 52.5299864294782 \tabularnewline
Trimmed Mean ( 19 / 19 ) & 6.74718571428571 & 0.122672575288412 & 55.0015820440925 \tabularnewline
Median & 6.8365 &  &  \tabularnewline
Midrange & 6.3386 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6.70190666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 6.74206451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 6.74206451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 6.74206451612903 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 6.7422275862069 &  &  \tabularnewline
Midmean - Closest Observation & 6.70190666666667 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 6.74206451612903 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 6.74206451612903 &  &  \tabularnewline
Number of observations & 59 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=47394&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]6.87566101694915[/C][C]0.342734736677516[/C][C]20.0611734999554[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0[/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]7.35444125709546[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 19 )[/C][C]6.89106610169492[/C][C]0.337266138554018[/C][C]20.4321315244969[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 19 )[/C][C]6.90235084745763[/C][C]0.328975207331799[/C][C]20.9813709167938[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 19 )[/C][C]6.92067627118644[/C][C]0.315254747762481[/C][C]21.9526472489500[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 19 )[/C][C]7.02835762711864[/C][C]0.285493855660897[/C][C]24.6182447984687[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 19 )[/C][C]6.98738305084746[/C][C]0.269951938144484[/C][C]25.8838039796094[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 19 )[/C][C]6.96330169491525[/C][C]0.233339001429060[/C][C]29.8419966326643[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 19 )[/C][C]6.90530847457627[/C][C]0.212485423590391[/C][C]32.4977984743446[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 19 )[/C][C]6.8083593220339[/C][C]0.188849450692857[/C][C]36.0517825021739[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 19 )[/C][C]6.76187966101695[/C][C]0.178235783982550[/C][C]37.9378344231873[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 19 )[/C][C]6.75472711864407[/C][C]0.175997777980476[/C][C]38.3796159028405[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 19 )[/C][C]6.69336949152542[/C][C]0.158395209092072[/C][C]42.2573986289870[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 19 )[/C][C]6.70443389830508[/C][C]0.144200384243443[/C][C]46.4938698567300[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 19 )[/C][C]6.7153627118644[/C][C]0.140400575666785[/C][C]47.8300226332554[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 19 )[/C][C]6.74094237288136[/C][C]0.131781611006374[/C][C]51.1523749133352[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 19 )[/C][C]6.73959491525424[/C][C]0.126691942090531[/C][C]53.1967132561459[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 19 )[/C][C]6.7379406779661[/C][C]0.125340602450092[/C][C]53.757047167928[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 19 )[/C][C]6.72036440677966[/C][C]0.118606297215265[/C][C]56.6611096085607[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 19 )[/C][C]6.74403898305085[/C][C]0.114449835930752[/C][C]58.9257199733458[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 19 )[/C][C]6.69985593220339[/C][C]0.101586684092879[/C][C]65.9521077199232[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 19 )[/C][C]6.8945052631579[/C][C]0.317127816139732[/C][C]21.7404620858615[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 19 )[/C][C]6.89819454545455[/C][C]0.291744188409691[/C][C]23.6446682384896[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 19 )[/C][C]6.89588113207547[/C][C]0.265323301854439[/C][C]25.9904843784081[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 19 )[/C][C]6.88631960784314[/C][C]0.238706448946779[/C][C]28.8484858210868[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 19 )[/C][C]6.84356326530612[/C][C]0.217740042273583[/C][C]31.4299712347232[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 19 )[/C][C]6.80745531914894[/C][C]0.196678811214725[/C][C]34.6120422281629[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 19 )[/C][C]6.7734[/C][C]0.182886901243541[/C][C]37.0360039671743[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 19 )[/C][C]6.74754418604651[/C][C]0.172017945421666[/C][C]39.2258154781836[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 19 )[/C][C]6.73660487804878[/C][C]0.165338395049226[/C][C]40.7443466234392[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 19 )[/C][C]6.73235641025641[/C][C]0.159558068057532[/C][C]42.1937699059437[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 19 )[/C][C]6.72878918918919[/C][C]0.152308944406765[/C][C]44.1785557335287[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 19 )[/C][C]6.73421714285714[/C][C]0.147517527543452[/C][C]45.6502847830985[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 19 )[/C][C]6.73865454545455[/C][C]0.144728726134062[/C][C]46.5605876970998[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 19 )[/C][C]6.74206451612903[/C][C]0.141532256709249[/C][C]47.6362397723887[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 19 )[/C][C]6.7422275862069[/C][C]0.139116628685295[/C][C]48.4645699793295[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 19 )[/C][C]6.74261111111111[/C][C]0.136609804861970[/C][C]49.3567143143483[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 19 )[/C][C]6.7433[/C][C]0.132662301728863[/C][C]50.8305668763536[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 19 )[/C][C]6.74676086956522[/C][C]0.128436371835405[/C][C]52.5299864294782[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 19 )[/C][C]6.74718571428571[/C][C]0.122672575288412[/C][C]55.0015820440925[/C][/ROW]
[ROW][C]Median[/C][C]6.8365[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]6.3386[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6.70190666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]6.74206451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]6.74206451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]6.74206451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]6.7422275862069[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6.70190666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]6.74206451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]6.74206451612903[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]59[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=47394&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=47394&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 Mean6.875661016949150.34273473667751620.0611734999554
Geometric Mean0
Harmonic Mean0
Quadratic Mean7.35444125709546
Winsorized Mean ( 1 / 19 )6.891066101694920.33726613855401820.4321315244969
Winsorized Mean ( 2 / 19 )6.902350847457630.32897520733179920.9813709167938
Winsorized Mean ( 3 / 19 )6.920676271186440.31525474776248121.9526472489500
Winsorized Mean ( 4 / 19 )7.028357627118640.28549385566089724.6182447984687
Winsorized Mean ( 5 / 19 )6.987383050847460.26995193814448425.8838039796094
Winsorized Mean ( 6 / 19 )6.963301694915250.23333900142906029.8419966326643
Winsorized Mean ( 7 / 19 )6.905308474576270.21248542359039132.4977984743446
Winsorized Mean ( 8 / 19 )6.80835932203390.18884945069285736.0517825021739
Winsorized Mean ( 9 / 19 )6.761879661016950.17823578398255037.9378344231873
Winsorized Mean ( 10 / 19 )6.754727118644070.17599777798047638.3796159028405
Winsorized Mean ( 11 / 19 )6.693369491525420.15839520909207242.2573986289870
Winsorized Mean ( 12 / 19 )6.704433898305080.14420038424344346.4938698567300
Winsorized Mean ( 13 / 19 )6.71536271186440.14040057566678547.8300226332554
Winsorized Mean ( 14 / 19 )6.740942372881360.13178161100637451.1523749133352
Winsorized Mean ( 15 / 19 )6.739594915254240.12669194209053153.1967132561459
Winsorized Mean ( 16 / 19 )6.73794067796610.12534060245009253.757047167928
Winsorized Mean ( 17 / 19 )6.720364406779660.11860629721526556.6611096085607
Winsorized Mean ( 18 / 19 )6.744038983050850.11444983593075258.9257199733458
Winsorized Mean ( 19 / 19 )6.699855932203390.10158668409287965.9521077199232
Trimmed Mean ( 1 / 19 )6.89450526315790.31712781613973221.7404620858615
Trimmed Mean ( 2 / 19 )6.898194545454550.29174418840969123.6446682384896
Trimmed Mean ( 3 / 19 )6.895881132075470.26532330185443925.9904843784081
Trimmed Mean ( 4 / 19 )6.886319607843140.23870644894677928.8484858210868
Trimmed Mean ( 5 / 19 )6.843563265306120.21774004227358331.4299712347232
Trimmed Mean ( 6 / 19 )6.807455319148940.19667881121472534.6120422281629
Trimmed Mean ( 7 / 19 )6.77340.18288690124354137.0360039671743
Trimmed Mean ( 8 / 19 )6.747544186046510.17201794542166639.2258154781836
Trimmed Mean ( 9 / 19 )6.736604878048780.16533839504922640.7443466234392
Trimmed Mean ( 10 / 19 )6.732356410256410.15955806805753242.1937699059437
Trimmed Mean ( 11 / 19 )6.728789189189190.15230894440676544.1785557335287
Trimmed Mean ( 12 / 19 )6.734217142857140.14751752754345245.6502847830985
Trimmed Mean ( 13 / 19 )6.738654545454550.14472872613406246.5605876970998
Trimmed Mean ( 14 / 19 )6.742064516129030.14153225670924947.6362397723887
Trimmed Mean ( 15 / 19 )6.74222758620690.13911662868529548.4645699793295
Trimmed Mean ( 16 / 19 )6.742611111111110.13660980486197049.3567143143483
Trimmed Mean ( 17 / 19 )6.74330.13266230172886350.8305668763536
Trimmed Mean ( 18 / 19 )6.746760869565220.12843637183540552.5299864294782
Trimmed Mean ( 19 / 19 )6.747185714285710.12267257528841255.0015820440925
Median6.8365
Midrange6.3386
Midmean - Weighted Average at Xnp6.70190666666667
Midmean - Weighted Average at X(n+1)p6.74206451612903
Midmean - Empirical Distribution Function6.74206451612903
Midmean - Empirical Distribution Function - Averaging6.74206451612903
Midmean - Empirical Distribution Function - Interpolation6.7422275862069
Midmean - Closest Observation6.70190666666667
Midmean - True Basic - Statistics Graphics Toolkit6.74206451612903
Midmean - MS Excel (old versions)6.74206451612903
Number of observations59



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')