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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 computationThu, 18 Oct 2012 14:25:29 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/18/t1350584797vxm9dirr40wo5i8.htm/, Retrieved Sun, 28 Apr 2024 19:01:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=179772, Retrieved Sun, 28 Apr 2024 19:01:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten DVD-...] [2012-10-18 18:25:29] [b1f6fc9a787b52224ca67a81ef5dc78d] [Current]
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Dataseries X:
126,81
125,8
123,07
119,52
118,03
117,27
117,27
116,69
115,38
114,31
113,33
111,79
111,79
110,92
109,37
107,04
104,72
104,14
104,14
102,95
102,13
101,01
100,07
99,4
99,4
99,34
97,72
96,26
95,77
95,04
95,04
94,55
94
93,14
91,21
90,3
90,3
89,74
89,07
89,06
88,97
88,78
88,78
88,23
87,91
87,79
87,89
88
88
87,08
85,75
84,29
84,39
83,72
83,72
81,76
81,53
80,55
79,83
78,98
78,98
78,27
77,41
76,75
76,38
74,96
74,96
74,46
74,04
73,22
72,97
72,91




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net

\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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179772&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=179772&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179772&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean94.27986111111111.7126513445689555.0490684575618
Geometric Mean93.2073526208236
Harmonic Mean92.1711651041897
Quadratic Mean95.3779199276343
Winsorized Mean ( 1 / 24 )94.26666666666671.7088055914280555.1652377189893
Winsorized Mean ( 2 / 24 )94.19777777777781.6885982512360855.7845998649018
Winsorized Mean ( 3 / 24 )94.08402777777781.648781805481357.0627523090078
Winsorized Mean ( 4 / 24 )94.02458333333331.6272128299023857.7825970920929
Winsorized Mean ( 5 / 24 )94.00652777777781.6105284001496758.369990724188
Winsorized Mean ( 6 / 24 )94.00652777777781.6105284001496758.369990724188
Winsorized Mean ( 7 / 24 )94.08819444444441.5766761124689659.6750300840856
Winsorized Mean ( 8 / 24 )93.983751.5412578247062760.9786036401217
Winsorized Mean ( 9 / 24 )93.93251.5025173418886262.5167493121439
Winsorized Mean ( 10 / 24 )93.91583333333331.4584780176383464.3930400030352
Winsorized Mean ( 11 / 24 )93.78902777777781.3988011460931567.0495788766905
Winsorized Mean ( 12 / 24 )93.78902777777781.3988011460931567.0495788766905
Winsorized Mean ( 13 / 24 )93.78541666666671.3478622432069169.5808619458969
Winsorized Mean ( 14 / 24 )93.62402777777781.2743076560770473.470505596741
Winsorized Mean ( 15 / 24 )93.34277777777781.1623239635207580.3070234352194
Winsorized Mean ( 16 / 24 )92.87833333333331.0719341221028186.6455609707937
Winsorized Mean ( 17 / 24 )93.20416666666670.98530330542306794.5943915479375
Winsorized Mean ( 18 / 24 )93.20416666666670.98530330542306794.5943915479375
Winsorized Mean ( 19 / 24 )93.04055555555560.916512084466835101.515907026671
Winsorized Mean ( 20 / 24 )92.84055555555560.878448645201869105.686947168347
Winsorized Mean ( 21 / 24 )92.91055555555560.777463696924028119.504686743765
Winsorized Mean ( 22 / 24 )93.02972222222220.684224655500606135.963709396233
Winsorized Mean ( 23 / 24 )93.04250.62609202720193148.608345031667
Winsorized Mean ( 24 / 24 )93.07583333333330.622166055444791149.599664782086
Trimmed Mean ( 1 / 24 )94.12042857142861.6704550208353856.3441861034724
Trimmed Mean ( 2 / 24 )93.96558823529411.6246268077223757.838260324553
Trimmed Mean ( 3 / 24 )93.83893939393941.5827344537200359.2891240684008
Trimmed Mean ( 4 / 24 )93.747031251.5506176713435660.4578633292445
Trimmed Mean ( 5 / 24 )93.66645161290321.5195315056478761.6416647267655
Trimmed Mean ( 6 / 24 )93.58483333333331.48676730977962.9451782520319
Trimmed Mean ( 7 / 24 )93.49758620689661.446439990291364.639796213092
Trimmed Mean ( 8 / 24 )93.38910714285711.4056029874160266.4406009228384
Trimmed Mean ( 9 / 24 )93.291.3639343756691868.3977188816211
Trimmed Mean ( 10 / 24 )93.19115384615391.3212648098987570.5317761798977
Trimmed Mean ( 11 / 24 )93.08681.2779041974886872.8433322176522
Trimmed Mean ( 12 / 24 )92.99104166666671.2369342405988775.1786462161841
Trimmed Mean ( 13 / 24 )92.88695652173911.1839273409927978.4566360667438
Trimmed Mean ( 14 / 24 )92.77386363636361.1275073639690182.2822684809654
Trimmed Mean ( 15 / 24 )92.66976190476191.0722826438508486.4228871335279
Trimmed Mean ( 16 / 24 )92.5891.0281547947907990.0535604843826
Trimmed Mean ( 17 / 24 )92.55473684210530.99236292408209293.2670241864545
Trimmed Mean ( 18 / 24 )92.47833333333330.96449900639312995.8822484215595
Trimmed Mean ( 19 / 24 )92.39294117647060.92459689433149499.9278082620782
Trimmed Mean ( 20 / 24 )92.316250.887796605366342103.983558218165
Trimmed Mean ( 21 / 24 )92.25333333333330.845966404231352109.050823852934
Trimmed Mean ( 22 / 24 )92.17285714285710.816066811953644112.947684910991
Trimmed Mean ( 23 / 24 )92.0650.798907956573799115.238556885615
Trimmed Mean ( 24 / 24 )91.93750.787581431262549116.733960896739
Median90.3
Midrange99.86
Midmean - Weighted Average at Xnp92.5547368421053
Midmean - Weighted Average at X(n+1)p92.5547368421053
Midmean - Empirical Distribution Function92.5547368421053
Midmean - Empirical Distribution Function - Averaging92.5547368421053
Midmean - Empirical Distribution Function - Interpolation92.5547368421053
Midmean - Closest Observation92.5547368421053
Midmean - True Basic - Statistics Graphics Toolkit92.5547368421053
Midmean - MS Excel (old versions)92.5547368421053
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 94.2798611111111 & 1.71265134456895 & 55.0490684575618 \tabularnewline
Geometric Mean & 93.2073526208236 &  &  \tabularnewline
Harmonic Mean & 92.1711651041897 &  &  \tabularnewline
Quadratic Mean & 95.3779199276343 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 94.2666666666667 & 1.70880559142805 & 55.1652377189893 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 94.1977777777778 & 1.68859825123608 & 55.7845998649018 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 94.0840277777778 & 1.6487818054813 & 57.0627523090078 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 94.0245833333333 & 1.62721282990238 & 57.7825970920929 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 94.0065277777778 & 1.61052840014967 & 58.369990724188 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 94.0065277777778 & 1.61052840014967 & 58.369990724188 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 94.0881944444444 & 1.57667611246896 & 59.6750300840856 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 93.98375 & 1.54125782470627 & 60.9786036401217 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 93.9325 & 1.50251734188862 & 62.5167493121439 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 93.9158333333333 & 1.45847801763834 & 64.3930400030352 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 93.7890277777778 & 1.39880114609315 & 67.0495788766905 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 93.7890277777778 & 1.39880114609315 & 67.0495788766905 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 93.7854166666667 & 1.34786224320691 & 69.5808619458969 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 93.6240277777778 & 1.27430765607704 & 73.470505596741 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 93.3427777777778 & 1.16232396352075 & 80.3070234352194 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 92.8783333333333 & 1.07193412210281 & 86.6455609707937 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 93.2041666666667 & 0.985303305423067 & 94.5943915479375 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 93.2041666666667 & 0.985303305423067 & 94.5943915479375 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 93.0405555555556 & 0.916512084466835 & 101.515907026671 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 92.8405555555556 & 0.878448645201869 & 105.686947168347 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 92.9105555555556 & 0.777463696924028 & 119.504686743765 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 93.0297222222222 & 0.684224655500606 & 135.963709396233 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 93.0425 & 0.62609202720193 & 148.608345031667 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 93.0758333333333 & 0.622166055444791 & 149.599664782086 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 94.1204285714286 & 1.67045502083538 & 56.3441861034724 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 93.9655882352941 & 1.62462680772237 & 57.838260324553 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 93.8389393939394 & 1.58273445372003 & 59.2891240684008 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 93.74703125 & 1.55061767134356 & 60.4578633292445 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 93.6664516129032 & 1.51953150564787 & 61.6416647267655 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 93.5848333333333 & 1.486767309779 & 62.9451782520319 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 93.4975862068966 & 1.4464399902913 & 64.639796213092 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 93.3891071428571 & 1.40560298741602 & 66.4406009228384 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 93.29 & 1.36393437566918 & 68.3977188816211 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 93.1911538461539 & 1.32126480989875 & 70.5317761798977 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 93.0868 & 1.27790419748868 & 72.8433322176522 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 92.9910416666667 & 1.23693424059887 & 75.1786462161841 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 92.8869565217391 & 1.18392734099279 & 78.4566360667438 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 92.7738636363636 & 1.12750736396901 & 82.2822684809654 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 92.6697619047619 & 1.07228264385084 & 86.4228871335279 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 92.589 & 1.02815479479079 & 90.0535604843826 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 92.5547368421053 & 0.992362924082092 & 93.2670241864545 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 92.4783333333333 & 0.964499006393129 & 95.8822484215595 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 92.3929411764706 & 0.924596894331494 & 99.9278082620782 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 92.31625 & 0.887796605366342 & 103.983558218165 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 92.2533333333333 & 0.845966404231352 & 109.050823852934 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 92.1728571428571 & 0.816066811953644 & 112.947684910991 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 92.065 & 0.798907956573799 & 115.238556885615 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 91.9375 & 0.787581431262549 & 116.733960896739 \tabularnewline
Median & 90.3 &  &  \tabularnewline
Midrange & 99.86 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 92.5547368421053 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 92.5547368421053 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 92.5547368421053 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 92.5547368421053 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 92.5547368421053 &  &  \tabularnewline
Midmean - Closest Observation & 92.5547368421053 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 92.5547368421053 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 92.5547368421053 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=179772&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]94.2798611111111[/C][C]1.71265134456895[/C][C]55.0490684575618[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]93.2073526208236[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]92.1711651041897[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]95.3779199276343[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]94.2666666666667[/C][C]1.70880559142805[/C][C]55.1652377189893[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]94.1977777777778[/C][C]1.68859825123608[/C][C]55.7845998649018[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]94.0840277777778[/C][C]1.6487818054813[/C][C]57.0627523090078[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]94.0245833333333[/C][C]1.62721282990238[/C][C]57.7825970920929[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]94.0065277777778[/C][C]1.61052840014967[/C][C]58.369990724188[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]94.0065277777778[/C][C]1.61052840014967[/C][C]58.369990724188[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]94.0881944444444[/C][C]1.57667611246896[/C][C]59.6750300840856[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]93.98375[/C][C]1.54125782470627[/C][C]60.9786036401217[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]93.9325[/C][C]1.50251734188862[/C][C]62.5167493121439[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]93.9158333333333[/C][C]1.45847801763834[/C][C]64.3930400030352[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]93.7890277777778[/C][C]1.39880114609315[/C][C]67.0495788766905[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]93.7890277777778[/C][C]1.39880114609315[/C][C]67.0495788766905[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]93.7854166666667[/C][C]1.34786224320691[/C][C]69.5808619458969[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]93.6240277777778[/C][C]1.27430765607704[/C][C]73.470505596741[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]93.3427777777778[/C][C]1.16232396352075[/C][C]80.3070234352194[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]92.8783333333333[/C][C]1.07193412210281[/C][C]86.6455609707937[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]93.2041666666667[/C][C]0.985303305423067[/C][C]94.5943915479375[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]93.2041666666667[/C][C]0.985303305423067[/C][C]94.5943915479375[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]93.0405555555556[/C][C]0.916512084466835[/C][C]101.515907026671[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]92.8405555555556[/C][C]0.878448645201869[/C][C]105.686947168347[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]92.9105555555556[/C][C]0.777463696924028[/C][C]119.504686743765[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]93.0297222222222[/C][C]0.684224655500606[/C][C]135.963709396233[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]93.0425[/C][C]0.62609202720193[/C][C]148.608345031667[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]93.0758333333333[/C][C]0.622166055444791[/C][C]149.599664782086[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]94.1204285714286[/C][C]1.67045502083538[/C][C]56.3441861034724[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]93.9655882352941[/C][C]1.62462680772237[/C][C]57.838260324553[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]93.8389393939394[/C][C]1.58273445372003[/C][C]59.2891240684008[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]93.74703125[/C][C]1.55061767134356[/C][C]60.4578633292445[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]93.6664516129032[/C][C]1.51953150564787[/C][C]61.6416647267655[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]93.5848333333333[/C][C]1.486767309779[/C][C]62.9451782520319[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]93.4975862068966[/C][C]1.4464399902913[/C][C]64.639796213092[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]93.3891071428571[/C][C]1.40560298741602[/C][C]66.4406009228384[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]93.29[/C][C]1.36393437566918[/C][C]68.3977188816211[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]93.1911538461539[/C][C]1.32126480989875[/C][C]70.5317761798977[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]93.0868[/C][C]1.27790419748868[/C][C]72.8433322176522[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]92.9910416666667[/C][C]1.23693424059887[/C][C]75.1786462161841[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]92.8869565217391[/C][C]1.18392734099279[/C][C]78.4566360667438[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]92.7738636363636[/C][C]1.12750736396901[/C][C]82.2822684809654[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]92.6697619047619[/C][C]1.07228264385084[/C][C]86.4228871335279[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]92.589[/C][C]1.02815479479079[/C][C]90.0535604843826[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]92.5547368421053[/C][C]0.992362924082092[/C][C]93.2670241864545[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]92.4783333333333[/C][C]0.964499006393129[/C][C]95.8822484215595[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]92.3929411764706[/C][C]0.924596894331494[/C][C]99.9278082620782[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]92.31625[/C][C]0.887796605366342[/C][C]103.983558218165[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]92.2533333333333[/C][C]0.845966404231352[/C][C]109.050823852934[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]92.1728571428571[/C][C]0.816066811953644[/C][C]112.947684910991[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]92.065[/C][C]0.798907956573799[/C][C]115.238556885615[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]91.9375[/C][C]0.787581431262549[/C][C]116.733960896739[/C][/ROW]
[ROW][C]Median[/C][C]90.3[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]99.86[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]92.5547368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]92.5547368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]92.5547368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]92.5547368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]92.5547368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]92.5547368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]92.5547368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]92.5547368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=179772&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=179772&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 Mean94.27986111111111.7126513445689555.0490684575618
Geometric Mean93.2073526208236
Harmonic Mean92.1711651041897
Quadratic Mean95.3779199276343
Winsorized Mean ( 1 / 24 )94.26666666666671.7088055914280555.1652377189893
Winsorized Mean ( 2 / 24 )94.19777777777781.6885982512360855.7845998649018
Winsorized Mean ( 3 / 24 )94.08402777777781.648781805481357.0627523090078
Winsorized Mean ( 4 / 24 )94.02458333333331.6272128299023857.7825970920929
Winsorized Mean ( 5 / 24 )94.00652777777781.6105284001496758.369990724188
Winsorized Mean ( 6 / 24 )94.00652777777781.6105284001496758.369990724188
Winsorized Mean ( 7 / 24 )94.08819444444441.5766761124689659.6750300840856
Winsorized Mean ( 8 / 24 )93.983751.5412578247062760.9786036401217
Winsorized Mean ( 9 / 24 )93.93251.5025173418886262.5167493121439
Winsorized Mean ( 10 / 24 )93.91583333333331.4584780176383464.3930400030352
Winsorized Mean ( 11 / 24 )93.78902777777781.3988011460931567.0495788766905
Winsorized Mean ( 12 / 24 )93.78902777777781.3988011460931567.0495788766905
Winsorized Mean ( 13 / 24 )93.78541666666671.3478622432069169.5808619458969
Winsorized Mean ( 14 / 24 )93.62402777777781.2743076560770473.470505596741
Winsorized Mean ( 15 / 24 )93.34277777777781.1623239635207580.3070234352194
Winsorized Mean ( 16 / 24 )92.87833333333331.0719341221028186.6455609707937
Winsorized Mean ( 17 / 24 )93.20416666666670.98530330542306794.5943915479375
Winsorized Mean ( 18 / 24 )93.20416666666670.98530330542306794.5943915479375
Winsorized Mean ( 19 / 24 )93.04055555555560.916512084466835101.515907026671
Winsorized Mean ( 20 / 24 )92.84055555555560.878448645201869105.686947168347
Winsorized Mean ( 21 / 24 )92.91055555555560.777463696924028119.504686743765
Winsorized Mean ( 22 / 24 )93.02972222222220.684224655500606135.963709396233
Winsorized Mean ( 23 / 24 )93.04250.62609202720193148.608345031667
Winsorized Mean ( 24 / 24 )93.07583333333330.622166055444791149.599664782086
Trimmed Mean ( 1 / 24 )94.12042857142861.6704550208353856.3441861034724
Trimmed Mean ( 2 / 24 )93.96558823529411.6246268077223757.838260324553
Trimmed Mean ( 3 / 24 )93.83893939393941.5827344537200359.2891240684008
Trimmed Mean ( 4 / 24 )93.747031251.5506176713435660.4578633292445
Trimmed Mean ( 5 / 24 )93.66645161290321.5195315056478761.6416647267655
Trimmed Mean ( 6 / 24 )93.58483333333331.48676730977962.9451782520319
Trimmed Mean ( 7 / 24 )93.49758620689661.446439990291364.639796213092
Trimmed Mean ( 8 / 24 )93.38910714285711.4056029874160266.4406009228384
Trimmed Mean ( 9 / 24 )93.291.3639343756691868.3977188816211
Trimmed Mean ( 10 / 24 )93.19115384615391.3212648098987570.5317761798977
Trimmed Mean ( 11 / 24 )93.08681.2779041974886872.8433322176522
Trimmed Mean ( 12 / 24 )92.99104166666671.2369342405988775.1786462161841
Trimmed Mean ( 13 / 24 )92.88695652173911.1839273409927978.4566360667438
Trimmed Mean ( 14 / 24 )92.77386363636361.1275073639690182.2822684809654
Trimmed Mean ( 15 / 24 )92.66976190476191.0722826438508486.4228871335279
Trimmed Mean ( 16 / 24 )92.5891.0281547947907990.0535604843826
Trimmed Mean ( 17 / 24 )92.55473684210530.99236292408209293.2670241864545
Trimmed Mean ( 18 / 24 )92.47833333333330.96449900639312995.8822484215595
Trimmed Mean ( 19 / 24 )92.39294117647060.92459689433149499.9278082620782
Trimmed Mean ( 20 / 24 )92.316250.887796605366342103.983558218165
Trimmed Mean ( 21 / 24 )92.25333333333330.845966404231352109.050823852934
Trimmed Mean ( 22 / 24 )92.17285714285710.816066811953644112.947684910991
Trimmed Mean ( 23 / 24 )92.0650.798907956573799115.238556885615
Trimmed Mean ( 24 / 24 )91.93750.787581431262549116.733960896739
Median90.3
Midrange99.86
Midmean - Weighted Average at Xnp92.5547368421053
Midmean - Weighted Average at X(n+1)p92.5547368421053
Midmean - Empirical Distribution Function92.5547368421053
Midmean - Empirical Distribution Function - Averaging92.5547368421053
Midmean - Empirical Distribution Function - Interpolation92.5547368421053
Midmean - Closest Observation92.5547368421053
Midmean - True Basic - Statistics Graphics Toolkit92.5547368421053
Midmean - MS Excel (old versions)92.5547368421053
Number of observations72



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')