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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationWed, 05 Aug 2009 15:26:17 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Aug/05/t12495076775km8f6b59rjqe4i.htm/, Retrieved Mon, 29 Apr 2024 04:25:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42504, Retrieved Mon, 29 Apr 2024 04:25:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact206
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [datareeks-diesel-...] [2009-08-05 21:26:17] [dd4d1946c4ef9dfd99dff91c071853fb] [Current]
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Dataseries X:
0,9
0,92
0,92
0,95
1,06
1,17
1,23
1,26
1,37
1,37
1,31
1,21
1,2
1,11
1,11
1,11
1,17
1,08
1,05
1,03
1,04
1,02
1,01
1,01
0,98
0,96
0,94
0,99
0,99
0,98
1,02
1,06
1,06
1,06
1,06
1,06
1,04
1,02
1,01
1
1,04
1,09
1,08
1,06
1,06
1,03
0,97
0,98
0,93
0,88
0,86
0,9
0,91
0,93
0,89
0,88
0,83
0,81
0,83
0,8
0,76
0,73
0,74
0,74
0,75
0,74
0,74
0,73
0,71
0,71
0,7
0,75
0,81
0,78
0,75




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42504&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42504&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42504&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.9698666666666670.018599131369171252.1458044150524
Geometric Mean0.956636030074306
Harmonic Mean0.94338655231831
Quadratic Mean0.982975075981075
Winsorized Mean ( 1 / 25 )0.970.018573448063646552.2250901758283
Winsorized Mean ( 2 / 25 )0.96840.018136658412683953.3946208813608
Winsorized Mean ( 3 / 25 )0.96720.017505273336757555.2519221718792
Winsorized Mean ( 4 / 25 )0.96560.017157710424967256.2779051565587
Winsorized Mean ( 5 / 25 )0.9649333333333330.016764799387362257.5571058763
Winsorized Mean ( 6 / 25 )0.9641333333333330.016609010181802558.0488134319814
Winsorized Mean ( 7 / 25 )0.9613333333333330.016094689777657759.729845471631
Winsorized Mean ( 8 / 25 )0.9613333333333330.016094689777657759.729845471631
Winsorized Mean ( 9 / 25 )0.9553333333333330.014723069271343164.8868327470812
Winsorized Mean ( 10 / 25 )0.9553333333333330.014723069271343164.8868327470812
Winsorized Mean ( 11 / 25 )0.9553333333333330.014723069271343164.8868327470812
Winsorized Mean ( 12 / 25 )0.9537333333333330.013984255410975668.2005087367608
Winsorized Mean ( 13 / 25 )0.9554666666666670.013120774165982572.8209063413232
Winsorized Mean ( 14 / 25 )0.95920.012460763645564976.9776257124825
Winsorized Mean ( 15 / 25 )0.95720.011614777787933182.4122525180348
Winsorized Mean ( 16 / 25 )0.95720.011614777787933182.4122525180347
Winsorized Mean ( 17 / 25 )0.9617333333333330.010854273594085288.6041175392344
Winsorized Mean ( 18 / 25 )0.9617333333333330.010854273594085288.6041175392344
Winsorized Mean ( 19 / 25 )0.9693333333333330.00964660857799554100.484364582226
Winsorized Mean ( 20 / 25 )0.9746666666666670.0088517994980882110.109437846754
Winsorized Mean ( 21 / 25 )0.9746666666666670.0088517994980882110.109437846754
Winsorized Mean ( 22 / 25 )0.97760.00843382293917589115.914219097363
Winsorized Mean ( 23 / 25 )0.97760.00760710905062548128.511369232918
Winsorized Mean ( 24 / 25 )0.97440.00720420297746673135.254379012879
Winsorized Mean ( 25 / 25 )0.9777333333333330.00674523076982086144.951798789132
Trimmed Mean ( 1 / 25 )0.9680821917808220.017914112629095654.040197905672
Trimmed Mean ( 2 / 25 )0.9660563380281690.017129497160377556.397238575267
Trimmed Mean ( 3 / 25 )0.9647826086956520.016480126624428958.5421842126825
Trimmed Mean ( 4 / 25 )0.9638805970149250.015999710569352760.2436270854317
Trimmed Mean ( 5 / 25 )0.9633846153846150.015554304566021161.936849140087
Trimmed Mean ( 6 / 25 )0.9630158730158730.015143341258345763.5933547680664
Trimmed Mean ( 7 / 25 )0.9627868852459020.014690116277928965.5397729351155
Trimmed Mean ( 8 / 25 )0.9630508474576270.014274290231680367.4675119972157
Trimmed Mean ( 9 / 25 )0.9633333333333330.013763426648771969.9922597705196
Trimmed Mean ( 10 / 25 )0.9645454545454550.013453544416305171.6945233686127
Trimmed Mean ( 11 / 25 )0.9658490566037740.013062965638853673.9379619686835
Trimmed Mean ( 12 / 25 )0.9672549019607840.012568489797661776.9587211775228
Trimmed Mean ( 13 / 25 )0.9689795918367350.012105140647616280.0469503035101
Trimmed Mean ( 14 / 25 )0.970638297872340.011710366286667382.8870996953742
Trimmed Mean ( 15 / 25 )0.9720.011355593113065385.5965857812974
Trimmed Mean ( 16 / 25 )0.9737209302325580.011067212636871087.98249045912
Trimmed Mean ( 17 / 25 )0.975609756097560.010672787258461091.4109625228534
Trimmed Mean ( 18 / 25 )0.9771794871794870.010338068989827094.5224381981838
Trimmed Mean ( 19 / 25 )0.9789189189189190.0098699028642696299.1822242205379
Trimmed Mean ( 20 / 25 )0.980.00957061328523215102.396781772823
Trimmed Mean ( 21 / 25 )0.980606060606060.00936364862213574104.724781992342
Trimmed Mean ( 22 / 25 )0.9812903225806450.0090487560540421108.444775913956
Trimmed Mean ( 23 / 25 )0.9817241379310350.00871085848502423112.701192381764
Trimmed Mean ( 24 / 25 )0.9822222222222220.00846197011762657116.074886647995
Trimmed Mean ( 25 / 25 )0.98320.00817964954424495120.200748782906
Median0.99
Midrange1.035
Midmean - Weighted Average at Xnp0.97953488372093
Midmean - Weighted Average at X(n+1)p0.97953488372093
Midmean - Empirical Distribution Function0.97953488372093
Midmean - Empirical Distribution Function - Averaging0.97953488372093
Midmean - Empirical Distribution Function - Interpolation0.986829268292683
Midmean - Closest Observation0.97953488372093
Midmean - True Basic - Statistics Graphics Toolkit0.97953488372093
Midmean - MS Excel (old versions)0.97953488372093
Number of observations75

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.969866666666667 & 0.0185991313691712 & 52.1458044150524 \tabularnewline
Geometric Mean & 0.956636030074306 &  &  \tabularnewline
Harmonic Mean & 0.94338655231831 &  &  \tabularnewline
Quadratic Mean & 0.982975075981075 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 0.97 & 0.0185734480636465 & 52.2250901758283 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 0.9684 & 0.0181366584126839 & 53.3946208813608 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 0.9672 & 0.0175052733367575 & 55.2519221718792 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 0.9656 & 0.0171577104249672 & 56.2779051565587 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 0.964933333333333 & 0.0167647993873622 & 57.5571058763 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 0.964133333333333 & 0.0166090101818025 & 58.0488134319814 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 0.961333333333333 & 0.0160946897776577 & 59.729845471631 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 0.961333333333333 & 0.0160946897776577 & 59.729845471631 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 0.955333333333333 & 0.0147230692713431 & 64.8868327470812 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 0.955333333333333 & 0.0147230692713431 & 64.8868327470812 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 0.955333333333333 & 0.0147230692713431 & 64.8868327470812 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 0.953733333333333 & 0.0139842554109756 & 68.2005087367608 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 0.955466666666667 & 0.0131207741659825 & 72.8209063413232 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 0.9592 & 0.0124607636455649 & 76.9776257124825 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 0.9572 & 0.0116147777879331 & 82.4122525180348 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 0.9572 & 0.0116147777879331 & 82.4122525180347 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 0.961733333333333 & 0.0108542735940852 & 88.6041175392344 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 0.961733333333333 & 0.0108542735940852 & 88.6041175392344 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 0.969333333333333 & 0.00964660857799554 & 100.484364582226 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 0.974666666666667 & 0.0088517994980882 & 110.109437846754 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 0.974666666666667 & 0.0088517994980882 & 110.109437846754 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 0.9776 & 0.00843382293917589 & 115.914219097363 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 0.9776 & 0.00760710905062548 & 128.511369232918 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 0.9744 & 0.00720420297746673 & 135.254379012879 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 0.977733333333333 & 0.00674523076982086 & 144.951798789132 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 0.968082191780822 & 0.0179141126290956 & 54.040197905672 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 0.966056338028169 & 0.0171294971603775 & 56.397238575267 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 0.964782608695652 & 0.0164801266244289 & 58.5421842126825 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 0.963880597014925 & 0.0159997105693527 & 60.2436270854317 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 0.963384615384615 & 0.0155543045660211 & 61.936849140087 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 0.963015873015873 & 0.0151433412583457 & 63.5933547680664 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 0.962786885245902 & 0.0146901162779289 & 65.5397729351155 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 0.963050847457627 & 0.0142742902316803 & 67.4675119972157 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 0.963333333333333 & 0.0137634266487719 & 69.9922597705196 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 0.964545454545455 & 0.0134535444163051 & 71.6945233686127 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 0.965849056603774 & 0.0130629656388536 & 73.9379619686835 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 0.967254901960784 & 0.0125684897976617 & 76.9587211775228 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 0.968979591836735 & 0.0121051406476162 & 80.0469503035101 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 0.97063829787234 & 0.0117103662866673 & 82.8870996953742 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 0.972 & 0.0113555931130653 & 85.5965857812974 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 0.973720930232558 & 0.0110672126368710 & 87.98249045912 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 0.97560975609756 & 0.0106727872584610 & 91.4109625228534 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 0.977179487179487 & 0.0103380689898270 & 94.5224381981838 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 0.978918918918919 & 0.00986990286426962 & 99.1822242205379 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 0.98 & 0.00957061328523215 & 102.396781772823 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 0.98060606060606 & 0.00936364862213574 & 104.724781992342 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 0.981290322580645 & 0.0090487560540421 & 108.444775913956 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 0.981724137931035 & 0.00871085848502423 & 112.701192381764 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 0.982222222222222 & 0.00846197011762657 & 116.074886647995 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 0.9832 & 0.00817964954424495 & 120.200748782906 \tabularnewline
Median & 0.99 &  &  \tabularnewline
Midrange & 1.035 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.97953488372093 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.97953488372093 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.97953488372093 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.97953488372093 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.986829268292683 &  &  \tabularnewline
Midmean - Closest Observation & 0.97953488372093 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.97953488372093 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.97953488372093 &  &  \tabularnewline
Number of observations & 75 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42504&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]0.969866666666667[/C][C]0.0185991313691712[/C][C]52.1458044150524[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.956636030074306[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.94338655231831[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.982975075981075[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]0.97[/C][C]0.0185734480636465[/C][C]52.2250901758283[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]0.9684[/C][C]0.0181366584126839[/C][C]53.3946208813608[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]0.9672[/C][C]0.0175052733367575[/C][C]55.2519221718792[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]0.9656[/C][C]0.0171577104249672[/C][C]56.2779051565587[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]0.964933333333333[/C][C]0.0167647993873622[/C][C]57.5571058763[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]0.964133333333333[/C][C]0.0166090101818025[/C][C]58.0488134319814[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]0.961333333333333[/C][C]0.0160946897776577[/C][C]59.729845471631[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]0.961333333333333[/C][C]0.0160946897776577[/C][C]59.729845471631[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]0.955333333333333[/C][C]0.0147230692713431[/C][C]64.8868327470812[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]0.955333333333333[/C][C]0.0147230692713431[/C][C]64.8868327470812[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]0.955333333333333[/C][C]0.0147230692713431[/C][C]64.8868327470812[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]0.953733333333333[/C][C]0.0139842554109756[/C][C]68.2005087367608[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]0.955466666666667[/C][C]0.0131207741659825[/C][C]72.8209063413232[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]0.9592[/C][C]0.0124607636455649[/C][C]76.9776257124825[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]0.9572[/C][C]0.0116147777879331[/C][C]82.4122525180348[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]0.9572[/C][C]0.0116147777879331[/C][C]82.4122525180347[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]0.961733333333333[/C][C]0.0108542735940852[/C][C]88.6041175392344[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]0.961733333333333[/C][C]0.0108542735940852[/C][C]88.6041175392344[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]0.969333333333333[/C][C]0.00964660857799554[/C][C]100.484364582226[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]0.974666666666667[/C][C]0.0088517994980882[/C][C]110.109437846754[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]0.974666666666667[/C][C]0.0088517994980882[/C][C]110.109437846754[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]0.9776[/C][C]0.00843382293917589[/C][C]115.914219097363[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]0.9776[/C][C]0.00760710905062548[/C][C]128.511369232918[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]0.9744[/C][C]0.00720420297746673[/C][C]135.254379012879[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]0.977733333333333[/C][C]0.00674523076982086[/C][C]144.951798789132[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]0.968082191780822[/C][C]0.0179141126290956[/C][C]54.040197905672[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]0.966056338028169[/C][C]0.0171294971603775[/C][C]56.397238575267[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]0.964782608695652[/C][C]0.0164801266244289[/C][C]58.5421842126825[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]0.963880597014925[/C][C]0.0159997105693527[/C][C]60.2436270854317[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]0.963384615384615[/C][C]0.0155543045660211[/C][C]61.936849140087[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]0.963015873015873[/C][C]0.0151433412583457[/C][C]63.5933547680664[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]0.962786885245902[/C][C]0.0146901162779289[/C][C]65.5397729351155[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]0.963050847457627[/C][C]0.0142742902316803[/C][C]67.4675119972157[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]0.963333333333333[/C][C]0.0137634266487719[/C][C]69.9922597705196[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]0.964545454545455[/C][C]0.0134535444163051[/C][C]71.6945233686127[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]0.965849056603774[/C][C]0.0130629656388536[/C][C]73.9379619686835[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]0.967254901960784[/C][C]0.0125684897976617[/C][C]76.9587211775228[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]0.968979591836735[/C][C]0.0121051406476162[/C][C]80.0469503035101[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]0.97063829787234[/C][C]0.0117103662866673[/C][C]82.8870996953742[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]0.972[/C][C]0.0113555931130653[/C][C]85.5965857812974[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]0.973720930232558[/C][C]0.0110672126368710[/C][C]87.98249045912[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]0.97560975609756[/C][C]0.0106727872584610[/C][C]91.4109625228534[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]0.977179487179487[/C][C]0.0103380689898270[/C][C]94.5224381981838[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]0.978918918918919[/C][C]0.00986990286426962[/C][C]99.1822242205379[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]0.98[/C][C]0.00957061328523215[/C][C]102.396781772823[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]0.98060606060606[/C][C]0.00936364862213574[/C][C]104.724781992342[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]0.981290322580645[/C][C]0.0090487560540421[/C][C]108.444775913956[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]0.981724137931035[/C][C]0.00871085848502423[/C][C]112.701192381764[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]0.982222222222222[/C][C]0.00846197011762657[/C][C]116.074886647995[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]0.9832[/C][C]0.00817964954424495[/C][C]120.200748782906[/C][/ROW]
[ROW][C]Median[/C][C]0.99[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.035[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.97953488372093[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.97953488372093[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.97953488372093[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.97953488372093[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.986829268292683[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.97953488372093[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.97953488372093[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.97953488372093[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]75[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42504&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42504&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 Mean0.9698666666666670.018599131369171252.1458044150524
Geometric Mean0.956636030074306
Harmonic Mean0.94338655231831
Quadratic Mean0.982975075981075
Winsorized Mean ( 1 / 25 )0.970.018573448063646552.2250901758283
Winsorized Mean ( 2 / 25 )0.96840.018136658412683953.3946208813608
Winsorized Mean ( 3 / 25 )0.96720.017505273336757555.2519221718792
Winsorized Mean ( 4 / 25 )0.96560.017157710424967256.2779051565587
Winsorized Mean ( 5 / 25 )0.9649333333333330.016764799387362257.5571058763
Winsorized Mean ( 6 / 25 )0.9641333333333330.016609010181802558.0488134319814
Winsorized Mean ( 7 / 25 )0.9613333333333330.016094689777657759.729845471631
Winsorized Mean ( 8 / 25 )0.9613333333333330.016094689777657759.729845471631
Winsorized Mean ( 9 / 25 )0.9553333333333330.014723069271343164.8868327470812
Winsorized Mean ( 10 / 25 )0.9553333333333330.014723069271343164.8868327470812
Winsorized Mean ( 11 / 25 )0.9553333333333330.014723069271343164.8868327470812
Winsorized Mean ( 12 / 25 )0.9537333333333330.013984255410975668.2005087367608
Winsorized Mean ( 13 / 25 )0.9554666666666670.013120774165982572.8209063413232
Winsorized Mean ( 14 / 25 )0.95920.012460763645564976.9776257124825
Winsorized Mean ( 15 / 25 )0.95720.011614777787933182.4122525180348
Winsorized Mean ( 16 / 25 )0.95720.011614777787933182.4122525180347
Winsorized Mean ( 17 / 25 )0.9617333333333330.010854273594085288.6041175392344
Winsorized Mean ( 18 / 25 )0.9617333333333330.010854273594085288.6041175392344
Winsorized Mean ( 19 / 25 )0.9693333333333330.00964660857799554100.484364582226
Winsorized Mean ( 20 / 25 )0.9746666666666670.0088517994980882110.109437846754
Winsorized Mean ( 21 / 25 )0.9746666666666670.0088517994980882110.109437846754
Winsorized Mean ( 22 / 25 )0.97760.00843382293917589115.914219097363
Winsorized Mean ( 23 / 25 )0.97760.00760710905062548128.511369232918
Winsorized Mean ( 24 / 25 )0.97440.00720420297746673135.254379012879
Winsorized Mean ( 25 / 25 )0.9777333333333330.00674523076982086144.951798789132
Trimmed Mean ( 1 / 25 )0.9680821917808220.017914112629095654.040197905672
Trimmed Mean ( 2 / 25 )0.9660563380281690.017129497160377556.397238575267
Trimmed Mean ( 3 / 25 )0.9647826086956520.016480126624428958.5421842126825
Trimmed Mean ( 4 / 25 )0.9638805970149250.015999710569352760.2436270854317
Trimmed Mean ( 5 / 25 )0.9633846153846150.015554304566021161.936849140087
Trimmed Mean ( 6 / 25 )0.9630158730158730.015143341258345763.5933547680664
Trimmed Mean ( 7 / 25 )0.9627868852459020.014690116277928965.5397729351155
Trimmed Mean ( 8 / 25 )0.9630508474576270.014274290231680367.4675119972157
Trimmed Mean ( 9 / 25 )0.9633333333333330.013763426648771969.9922597705196
Trimmed Mean ( 10 / 25 )0.9645454545454550.013453544416305171.6945233686127
Trimmed Mean ( 11 / 25 )0.9658490566037740.013062965638853673.9379619686835
Trimmed Mean ( 12 / 25 )0.9672549019607840.012568489797661776.9587211775228
Trimmed Mean ( 13 / 25 )0.9689795918367350.012105140647616280.0469503035101
Trimmed Mean ( 14 / 25 )0.970638297872340.011710366286667382.8870996953742
Trimmed Mean ( 15 / 25 )0.9720.011355593113065385.5965857812974
Trimmed Mean ( 16 / 25 )0.9737209302325580.011067212636871087.98249045912
Trimmed Mean ( 17 / 25 )0.975609756097560.010672787258461091.4109625228534
Trimmed Mean ( 18 / 25 )0.9771794871794870.010338068989827094.5224381981838
Trimmed Mean ( 19 / 25 )0.9789189189189190.0098699028642696299.1822242205379
Trimmed Mean ( 20 / 25 )0.980.00957061328523215102.396781772823
Trimmed Mean ( 21 / 25 )0.980606060606060.00936364862213574104.724781992342
Trimmed Mean ( 22 / 25 )0.9812903225806450.0090487560540421108.444775913956
Trimmed Mean ( 23 / 25 )0.9817241379310350.00871085848502423112.701192381764
Trimmed Mean ( 24 / 25 )0.9822222222222220.00846197011762657116.074886647995
Trimmed Mean ( 25 / 25 )0.98320.00817964954424495120.200748782906
Median0.99
Midrange1.035
Midmean - Weighted Average at Xnp0.97953488372093
Midmean - Weighted Average at X(n+1)p0.97953488372093
Midmean - Empirical Distribution Function0.97953488372093
Midmean - Empirical Distribution Function - Averaging0.97953488372093
Midmean - Empirical Distribution Function - Interpolation0.986829268292683
Midmean - Closest Observation0.97953488372093
Midmean - True Basic - Statistics Graphics Toolkit0.97953488372093
Midmean - MS Excel (old versions)0.97953488372093
Number of observations75



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')