Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 14:04:59 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/20/t12560692489wcfazzvgz887cf.htm/, Retrieved Fri, 03 May 2024 03:40:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49114, Retrieved Fri, 03 May 2024 03:40:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [Central Tendency ...] [2009-10-20 20:04:59] [557d56ec4b06cd0135c259898de8ce95] [Current]
Feedback Forum

Post a new message
Dataseries X:
10284,5
12792
12823,61538
13845,66667
15335,63636
11188,5
13633,25
12298,46667
15353,63636
12696,15385
12213,93333
13683,72727
11214,14286
13950,23077
11179,13333
11801,875
11188,82353
16456,27273
11110,0625
16530,69231
10038,41176
11681,25
11148,88235
8631
9386,444444
9764,736842
12043,75
12948,06667
10987,125
11648,3125
10633,35294
10219,3
9037,6
10296,31579
11705,41176
10681,94444
9362,947368
11306,35294
10984,45
10062,61905
8118,583333
8867,48
8346,72
8529,307692
10697,18182
8591,84
8695,607143
8125,571429
7009,758621
7883,466667
7527,645161
6763,758621
6682,333333
7855,681818
6738,88
7895,434783
6361,884615
6935,956522
8344,454545
9107,944444




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=49114&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=49114&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49114&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 Mean10520.46805535319.34850996905232.9435326201131
Geometric Mean10237.6539583325
Harmonic Mean9958.9177986642
Quadratic Mean10802.6511969047
Winsorized Mean ( 1 / 20 )10524.5685409833317.81782496459133.1150983811431
Winsorized Mean ( 2 / 20 )10489.6988842167306.66000203678434.2062832275023
Winsorized Mean ( 3 / 20 )10490.0428152667306.16107081024834.2631503982692
Winsorized Mean ( 4 / 20 )10409.1623026667281.43389232411936.9861718384605
Winsorized Mean ( 5 / 20 )10406.5988025833278.31278847038337.3917377630341
Winsorized Mean ( 6 / 20 )10442.1935165833264.73456185909439.4440130644567
Winsorized Mean ( 7 / 20 )10474.5754450667256.62469926811340.8167081147679
Winsorized Mean ( 8 / 20 )10386.9223142667238.07104424203843.6295070966576
Winsorized Mean ( 9 / 20 )10370.0498381667234.39217165228344.2423045320407
Winsorized Mean ( 10 / 20 )10401.9720331667226.95339511654545.8330752347858
Winsorized Mean ( 11 / 20 )10385.6813899333223.62747611000746.4418843810784
Winsorized Mean ( 12 / 20 )10349.9205771333202.73810891805151.0506911224908
Winsorized Mean ( 13 / 20 )10332.0958687167199.70092894385051.7378458045218
Winsorized Mean ( 14 / 20 )10334.99021985186.3500036313455.4601020577168
Winsorized Mean ( 15 / 20 )10290.15454685174.63455485266458.9239314952966
Winsorized Mean ( 16 / 20 )10274.87368285169.18297195706460.7323158116504
Winsorized Mean ( 17 / 20 )10286.3332080333165.20130036657262.2654493954258
Winsorized Mean ( 18 / 20 )10328.0138151333155.46749401805666.4319823276617
Winsorized Mean ( 19 / 20 )10273.5979544667131.86838706857277.9079670484204
Winsorized Mean ( 20 / 20 )10266.3094091333124.12042426626982.712490469011
Trimmed Mean ( 1 / 20 )10488.5432137241305.00253464557634.3883804962874
Trimmed Mean ( 2 / 20 )10449.9446488036289.0655010187836.1507845521997
Trimmed Mean ( 3 / 20 )10427.8589624630276.94851114398437.6526991222624
Trimmed Mean ( 4 / 20 )10403.942096261.95050392875639.7172058841682
Trimmed Mean ( 5 / 20 )10402.376034253.44314860016641.0442187585464
Trimmed Mean ( 6 / 20 )10401.3203418542243.72055708885742.6772384984415
Trimmed Mean ( 7 / 20 )10392.4348690870235.67142194350744.0971365275597
Trimmed Mean ( 8 / 20 )10376.4334581818227.61360200447145.5879322096841
Trimmed Mean ( 9 / 20 )10374.5604481667222.42502122798446.6429558639126
Trimmed Mean ( 10 / 20 )10375.3122165216.39286442645347.9466466881876
Trimmed Mean ( 11 / 20 )10371.1027717632210.18599352304649.3425018381445
Trimmed Mean ( 12 / 20 )10368.8938902222202.49638906519951.2053273546705
Trimmed Mean ( 13 / 20 )10371.6840833235197.67850951547752.4674336565224
Trimmed Mean ( 14 / 20 )10377.3939219688191.42071968033754.2124903683283
Trimmed Mean ( 15 / 20 )10383.4515937186.17594765994655.7722505200594
Trimmed Mean ( 16 / 20 )10396.77974325181.58881273217357.2545168770079
Trimmed Mean ( 17 / 20 )10414.3623481154175.80665060839159.2375903418658
Trimmed Mean ( 18 / 20 )10433.1901628333167.69188934206462.2164268276048
Trimmed Mean ( 19 / 20 )10449.1259730909158.38058301549765.9747916956997
Trimmed Mean ( 20 / 20 )10476.8409234152.57777118178868.6655784931962
Median10657.64869
Midrange11446.2884625
Midmean - Weighted Average at Xnp10323.6405000968
Midmean - Weighted Average at X(n+1)p10383.4515937
Midmean - Empirical Distribution Function10323.6405000968
Midmean - Empirical Distribution Function - Averaging10383.4515937
Midmean - Empirical Distribution Function - Interpolation10383.4515937
Midmean - Closest Observation10323.6405000968
Midmean - True Basic - Statistics Graphics Toolkit10383.4515937
Midmean - MS Excel (old versions)10377.3939219687
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 10520.46805535 & 319.348509969052 & 32.9435326201131 \tabularnewline
Geometric Mean & 10237.6539583325 &  &  \tabularnewline
Harmonic Mean & 9958.9177986642 &  &  \tabularnewline
Quadratic Mean & 10802.6511969047 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 10524.5685409833 & 317.817824964591 & 33.1150983811431 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 10489.6988842167 & 306.660002036784 & 34.2062832275023 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 10490.0428152667 & 306.161070810248 & 34.2631503982692 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 10409.1623026667 & 281.433892324119 & 36.9861718384605 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 10406.5988025833 & 278.312788470383 & 37.3917377630341 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 10442.1935165833 & 264.734561859094 & 39.4440130644567 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 10474.5754450667 & 256.624699268113 & 40.8167081147679 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 10386.9223142667 & 238.071044242038 & 43.6295070966576 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 10370.0498381667 & 234.392171652283 & 44.2423045320407 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 10401.9720331667 & 226.953395116545 & 45.8330752347858 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 10385.6813899333 & 223.627476110007 & 46.4418843810784 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 10349.9205771333 & 202.738108918051 & 51.0506911224908 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 10332.0958687167 & 199.700928943850 & 51.7378458045218 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 10334.99021985 & 186.35000363134 & 55.4601020577168 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 10290.15454685 & 174.634554852664 & 58.9239314952966 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 10274.87368285 & 169.182971957064 & 60.7323158116504 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 10286.3332080333 & 165.201300366572 & 62.2654493954258 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 10328.0138151333 & 155.467494018056 & 66.4319823276617 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 10273.5979544667 & 131.868387068572 & 77.9079670484204 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 10266.3094091333 & 124.120424266269 & 82.712490469011 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 10488.5432137241 & 305.002534645576 & 34.3883804962874 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 10449.9446488036 & 289.06550101878 & 36.1507845521997 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 10427.8589624630 & 276.948511143984 & 37.6526991222624 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 10403.942096 & 261.950503928756 & 39.7172058841682 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 10402.376034 & 253.443148600166 & 41.0442187585464 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 10401.3203418542 & 243.720557088857 & 42.6772384984415 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 10392.4348690870 & 235.671421943507 & 44.0971365275597 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 10376.4334581818 & 227.613602004471 & 45.5879322096841 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 10374.5604481667 & 222.425021227984 & 46.6429558639126 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 10375.3122165 & 216.392864426453 & 47.9466466881876 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 10371.1027717632 & 210.185993523046 & 49.3425018381445 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 10368.8938902222 & 202.496389065199 & 51.2053273546705 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 10371.6840833235 & 197.678509515477 & 52.4674336565224 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 10377.3939219688 & 191.420719680337 & 54.2124903683283 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 10383.4515937 & 186.175947659946 & 55.7722505200594 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 10396.77974325 & 181.588812732173 & 57.2545168770079 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 10414.3623481154 & 175.806650608391 & 59.2375903418658 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 10433.1901628333 & 167.691889342064 & 62.2164268276048 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 10449.1259730909 & 158.380583015497 & 65.9747916956997 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 10476.8409234 & 152.577771181788 & 68.6655784931962 \tabularnewline
Median & 10657.64869 &  &  \tabularnewline
Midrange & 11446.2884625 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 10323.6405000968 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 10383.4515937 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 10323.6405000968 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 10383.4515937 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 10383.4515937 &  &  \tabularnewline
Midmean - Closest Observation & 10323.6405000968 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 10383.4515937 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 10377.3939219687 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49114&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]10520.46805535[/C][C]319.348509969052[/C][C]32.9435326201131[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]10237.6539583325[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]9958.9177986642[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]10802.6511969047[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]10524.5685409833[/C][C]317.817824964591[/C][C]33.1150983811431[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]10489.6988842167[/C][C]306.660002036784[/C][C]34.2062832275023[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]10490.0428152667[/C][C]306.161070810248[/C][C]34.2631503982692[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]10409.1623026667[/C][C]281.433892324119[/C][C]36.9861718384605[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]10406.5988025833[/C][C]278.312788470383[/C][C]37.3917377630341[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]10442.1935165833[/C][C]264.734561859094[/C][C]39.4440130644567[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]10474.5754450667[/C][C]256.624699268113[/C][C]40.8167081147679[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]10386.9223142667[/C][C]238.071044242038[/C][C]43.6295070966576[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]10370.0498381667[/C][C]234.392171652283[/C][C]44.2423045320407[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]10401.9720331667[/C][C]226.953395116545[/C][C]45.8330752347858[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]10385.6813899333[/C][C]223.627476110007[/C][C]46.4418843810784[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]10349.9205771333[/C][C]202.738108918051[/C][C]51.0506911224908[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]10332.0958687167[/C][C]199.700928943850[/C][C]51.7378458045218[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]10334.99021985[/C][C]186.35000363134[/C][C]55.4601020577168[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]10290.15454685[/C][C]174.634554852664[/C][C]58.9239314952966[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]10274.87368285[/C][C]169.182971957064[/C][C]60.7323158116504[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]10286.3332080333[/C][C]165.201300366572[/C][C]62.2654493954258[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]10328.0138151333[/C][C]155.467494018056[/C][C]66.4319823276617[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]10273.5979544667[/C][C]131.868387068572[/C][C]77.9079670484204[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]10266.3094091333[/C][C]124.120424266269[/C][C]82.712490469011[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]10488.5432137241[/C][C]305.002534645576[/C][C]34.3883804962874[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]10449.9446488036[/C][C]289.06550101878[/C][C]36.1507845521997[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]10427.8589624630[/C][C]276.948511143984[/C][C]37.6526991222624[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]10403.942096[/C][C]261.950503928756[/C][C]39.7172058841682[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]10402.376034[/C][C]253.443148600166[/C][C]41.0442187585464[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]10401.3203418542[/C][C]243.720557088857[/C][C]42.6772384984415[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]10392.4348690870[/C][C]235.671421943507[/C][C]44.0971365275597[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]10376.4334581818[/C][C]227.613602004471[/C][C]45.5879322096841[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]10374.5604481667[/C][C]222.425021227984[/C][C]46.6429558639126[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]10375.3122165[/C][C]216.392864426453[/C][C]47.9466466881876[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]10371.1027717632[/C][C]210.185993523046[/C][C]49.3425018381445[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]10368.8938902222[/C][C]202.496389065199[/C][C]51.2053273546705[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]10371.6840833235[/C][C]197.678509515477[/C][C]52.4674336565224[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]10377.3939219688[/C][C]191.420719680337[/C][C]54.2124903683283[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]10383.4515937[/C][C]186.175947659946[/C][C]55.7722505200594[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]10396.77974325[/C][C]181.588812732173[/C][C]57.2545168770079[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]10414.3623481154[/C][C]175.806650608391[/C][C]59.2375903418658[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]10433.1901628333[/C][C]167.691889342064[/C][C]62.2164268276048[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]10449.1259730909[/C][C]158.380583015497[/C][C]65.9747916956997[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]10476.8409234[/C][C]152.577771181788[/C][C]68.6655784931962[/C][/ROW]
[ROW][C]Median[/C][C]10657.64869[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]11446.2884625[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]10323.6405000968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]10383.4515937[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]10323.6405000968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]10383.4515937[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]10383.4515937[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]10323.6405000968[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]10383.4515937[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]10377.3939219687[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49114&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49114&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 Mean10520.46805535319.34850996905232.9435326201131
Geometric Mean10237.6539583325
Harmonic Mean9958.9177986642
Quadratic Mean10802.6511969047
Winsorized Mean ( 1 / 20 )10524.5685409833317.81782496459133.1150983811431
Winsorized Mean ( 2 / 20 )10489.6988842167306.66000203678434.2062832275023
Winsorized Mean ( 3 / 20 )10490.0428152667306.16107081024834.2631503982692
Winsorized Mean ( 4 / 20 )10409.1623026667281.43389232411936.9861718384605
Winsorized Mean ( 5 / 20 )10406.5988025833278.31278847038337.3917377630341
Winsorized Mean ( 6 / 20 )10442.1935165833264.73456185909439.4440130644567
Winsorized Mean ( 7 / 20 )10474.5754450667256.62469926811340.8167081147679
Winsorized Mean ( 8 / 20 )10386.9223142667238.07104424203843.6295070966576
Winsorized Mean ( 9 / 20 )10370.0498381667234.39217165228344.2423045320407
Winsorized Mean ( 10 / 20 )10401.9720331667226.95339511654545.8330752347858
Winsorized Mean ( 11 / 20 )10385.6813899333223.62747611000746.4418843810784
Winsorized Mean ( 12 / 20 )10349.9205771333202.73810891805151.0506911224908
Winsorized Mean ( 13 / 20 )10332.0958687167199.70092894385051.7378458045218
Winsorized Mean ( 14 / 20 )10334.99021985186.3500036313455.4601020577168
Winsorized Mean ( 15 / 20 )10290.15454685174.63455485266458.9239314952966
Winsorized Mean ( 16 / 20 )10274.87368285169.18297195706460.7323158116504
Winsorized Mean ( 17 / 20 )10286.3332080333165.20130036657262.2654493954258
Winsorized Mean ( 18 / 20 )10328.0138151333155.46749401805666.4319823276617
Winsorized Mean ( 19 / 20 )10273.5979544667131.86838706857277.9079670484204
Winsorized Mean ( 20 / 20 )10266.3094091333124.12042426626982.712490469011
Trimmed Mean ( 1 / 20 )10488.5432137241305.00253464557634.3883804962874
Trimmed Mean ( 2 / 20 )10449.9446488036289.0655010187836.1507845521997
Trimmed Mean ( 3 / 20 )10427.8589624630276.94851114398437.6526991222624
Trimmed Mean ( 4 / 20 )10403.942096261.95050392875639.7172058841682
Trimmed Mean ( 5 / 20 )10402.376034253.44314860016641.0442187585464
Trimmed Mean ( 6 / 20 )10401.3203418542243.72055708885742.6772384984415
Trimmed Mean ( 7 / 20 )10392.4348690870235.67142194350744.0971365275597
Trimmed Mean ( 8 / 20 )10376.4334581818227.61360200447145.5879322096841
Trimmed Mean ( 9 / 20 )10374.5604481667222.42502122798446.6429558639126
Trimmed Mean ( 10 / 20 )10375.3122165216.39286442645347.9466466881876
Trimmed Mean ( 11 / 20 )10371.1027717632210.18599352304649.3425018381445
Trimmed Mean ( 12 / 20 )10368.8938902222202.49638906519951.2053273546705
Trimmed Mean ( 13 / 20 )10371.6840833235197.67850951547752.4674336565224
Trimmed Mean ( 14 / 20 )10377.3939219688191.42071968033754.2124903683283
Trimmed Mean ( 15 / 20 )10383.4515937186.17594765994655.7722505200594
Trimmed Mean ( 16 / 20 )10396.77974325181.58881273217357.2545168770079
Trimmed Mean ( 17 / 20 )10414.3623481154175.80665060839159.2375903418658
Trimmed Mean ( 18 / 20 )10433.1901628333167.69188934206462.2164268276048
Trimmed Mean ( 19 / 20 )10449.1259730909158.38058301549765.9747916956997
Trimmed Mean ( 20 / 20 )10476.8409234152.57777118178868.6655784931962
Median10657.64869
Midrange11446.2884625
Midmean - Weighted Average at Xnp10323.6405000968
Midmean - Weighted Average at X(n+1)p10383.4515937
Midmean - Empirical Distribution Function10323.6405000968
Midmean - Empirical Distribution Function - Averaging10383.4515937
Midmean - Empirical Distribution Function - Interpolation10383.4515937
Midmean - Closest Observation10323.6405000968
Midmean - True Basic - Statistics Graphics Toolkit10383.4515937
Midmean - MS Excel (old versions)10377.3939219687
Number of observations60



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')