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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 computationMon, 18 Oct 2010 13:48:50 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Oct/18/t1287409787qywrwnozw3xbgll.htm/, Retrieved Sat, 04 May 2024 17:56:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=84895, Retrieved Sat, 04 May 2024 17:56:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [index eletricitei...] [2010-10-18 13:48:50] [bc974f2989c3f1048b8acb0f98df66e5] [Current]
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Dataseries X:
132,1
125
127,1
101,5
85,7
79,3
70,9
77,1
83,9
96,2
111,7
127,2
143,6
134,9
135,6
105,3
86,4
74,6
67,6
73,4
78,5
98,2
118,6
136,9
137,9
115,6
119,3
98,5
84,3
73,5
60,7
69,5
77,9
113,9
126,3
135,1
130,5
113,1
110
90,8
85,4
72,5
64,7
67,2
77,9
105,2
107,2
120,7
121,3
107,9
105,6
81,3
71,7
64,8
57,3
61,9
70,1
88,8
106,8
110,7
114,1
108
111,5
86,8
78,4
68
57,3
65,3
73,3
88,6
101,3
122,9
126,6
114,1
124,7




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=84895&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=84895&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=84895&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 Mean97.57466666666672.7932396466690334.9324365286830
Geometric Mean94.5373778483119
Harmonic Mean91.4932199499188
Quadratic Mean100.489688359884
Winsorized Mean ( 1 / 25 )97.49866666666672.7773053849372135.1054900895859
Winsorized Mean ( 2 / 25 )97.56266666666672.7550450190617735.4123674900571
Winsorized Mean ( 3 / 25 )97.55866666666672.7365777887708635.6498788621995
Winsorized Mean ( 4 / 25 )97.68133333333332.7061316384175536.0962977360754
Winsorized Mean ( 5 / 25 )97.67466666666672.7025480758169936.1416944033972
Winsorized Mean ( 6 / 25 )97.49066666666672.6554001909644836.7141145046227
Winsorized Mean ( 7 / 25 )97.51866666666672.6009524889643537.4934440672912
Winsorized Mean ( 8 / 25 )97.20933333333332.5359136977196838.3330605535769
Winsorized Mean ( 9 / 25 )97.24533333333332.5264555475277338.4908150980503
Winsorized Mean ( 10 / 25 )97.37866666666672.485028535615439.1861362036841
Winsorized Mean ( 11 / 25 )97.42266666666672.4647873824816739.5257892664870
Winsorized Mean ( 12 / 25 )97.34266666666672.4131450625880540.3385060333955
Winsorized Mean ( 13 / 25 )97.42933333333332.3847237347943040.8556060024023
Winsorized Mean ( 14 / 25 )97.24266666666672.3118676770429942.0623842931381
Winsorized Mean ( 15 / 25 )97.08266666666672.2414589628816143.3122659278392
Winsorized Mean ( 16 / 25 )96.9762.2198107540472443.6866069880911
Winsorized Mean ( 17 / 25 )96.68133333333332.1712915518195644.5271079566968
Winsorized Mean ( 18 / 25 )96.77733333333332.1099272634517745.8676159172469
Winsorized Mean ( 19 / 25 )96.65066666666671.9172694297010250.4105814078194
Winsorized Mean ( 20 / 25 )96.4641.8352883662758252.5606775330599
Winsorized Mean ( 21 / 25 )96.4641.8352883662758252.5606775330599
Winsorized Mean ( 22 / 25 )96.5521.8076996083071653.4115289710202
Winsorized Mean ( 23 / 25 )96.33733333333331.7719412404929754.3682437835983
Winsorized Mean ( 24 / 25 )96.14533333333331.6805182526820757.2117161952198
Winsorized Mean ( 25 / 25 )96.74533333333331.5830126294458361.1146945600817
Trimmed Mean ( 1 / 25 )97.49589041095892.7435169453943235.5368282213931
Trimmed Mean ( 2 / 25 )97.49295774647892.7030464398732336.0678071631841
Trimmed Mean ( 3 / 25 )97.45507246376812.6683060840526136.5231983865036
Trimmed Mean ( 4 / 25 )97.41641791044782.6343189537592736.9797354156492
Trimmed Mean ( 5 / 25 )97.342.6034498192856537.3888520066459
Trimmed Mean ( 6 / 25 )97.26031746031752.5663878992414537.8977462795334
Trimmed Mean ( 7 / 25 )97.21311475409842.5334305511363038.3721253817263
Trimmed Mean ( 8 / 25 )97.1576271186442.5055102376722138.7775813715733
Trimmed Mean ( 9 / 25 )97.14912280701752.4846447263309239.0998044016046
Trimmed Mean ( 10 / 25 )97.13454545454552.4590206615681339.5013132555796
Trimmed Mean ( 11 / 25 )97.12.4339608577757239.8938215007841
Trimmed Mean ( 12 / 25 )97.0568627450982.4046739698328940.3617554656871
Trimmed Mean ( 13 / 25 )97.02040816326532.3762035611193340.8300070544307
Trimmed Mean ( 14 / 25 )96.97021276595742.3434122730213441.3799201627183
Trimmed Mean ( 15 / 25 )96.93777777777782.3139460565045641.8928425341996
Trimmed Mean ( 16 / 25 )96.92093023255812.2873976037803342.3717022665316
Trimmed Mean ( 17 / 25 )96.91463414634152.2538113003868243.0003319841852
Trimmed Mean ( 18 / 25 )96.94102564102562.2165605322436243.7348875570302
Trimmed Mean ( 19 / 25 )96.95945945945952.1770418928663744.5372501912672
Trimmed Mean ( 20 / 25 )96.99428571428572.1637034189079644.8279024133721
Trimmed Mean ( 21 / 25 )97.05454545454552.1571326845451144.992385563437
Trimmed Mean ( 22 / 25 )97.12258064516132.1392929677033345.3993829323099
Trimmed Mean ( 23 / 25 )97.18965517241382.1126136826471746.0044616631623
Trimmed Mean ( 24 / 25 )97.29259259259262.0745845423917246.8973862498885
Trimmed Mean ( 25 / 25 )97.4362.0369575351489347.8340850600384
Median98.5
Midrange100.45
Midmean - Weighted Average at Xnp96.371052631579
Midmean - Weighted Average at X(n+1)p96.9410256410256
Midmean - Empirical Distribution Function96.9410256410256
Midmean - Empirical Distribution Function - Averaging96.9410256410256
Midmean - Empirical Distribution Function - Interpolation96.9594594594594
Midmean - Closest Observation96.371052631579
Midmean - True Basic - Statistics Graphics Toolkit96.9410256410256
Midmean - MS Excel (old versions)96.9410256410256
Number of observations75

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 97.5746666666667 & 2.79323964666903 & 34.9324365286830 \tabularnewline
Geometric Mean & 94.5373778483119 &  &  \tabularnewline
Harmonic Mean & 91.4932199499188 &  &  \tabularnewline
Quadratic Mean & 100.489688359884 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 97.4986666666667 & 2.77730538493721 & 35.1054900895859 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 97.5626666666667 & 2.75504501906177 & 35.4123674900571 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 97.5586666666667 & 2.73657778877086 & 35.6498788621995 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 97.6813333333333 & 2.70613163841755 & 36.0962977360754 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 97.6746666666667 & 2.70254807581699 & 36.1416944033972 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 97.4906666666667 & 2.65540019096448 & 36.7141145046227 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 97.5186666666667 & 2.60095248896435 & 37.4934440672912 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 97.2093333333333 & 2.53591369771968 & 38.3330605535769 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 97.2453333333333 & 2.52645554752773 & 38.4908150980503 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 97.3786666666667 & 2.4850285356154 & 39.1861362036841 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 97.4226666666667 & 2.46478738248167 & 39.5257892664870 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 97.3426666666667 & 2.41314506258805 & 40.3385060333955 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 97.4293333333333 & 2.38472373479430 & 40.8556060024023 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 97.2426666666667 & 2.31186767704299 & 42.0623842931381 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 97.0826666666667 & 2.24145896288161 & 43.3122659278392 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 96.976 & 2.21981075404724 & 43.6866069880911 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 96.6813333333333 & 2.17129155181956 & 44.5271079566968 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 96.7773333333333 & 2.10992726345177 & 45.8676159172469 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 96.6506666666667 & 1.91726942970102 & 50.4105814078194 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 96.464 & 1.83528836627582 & 52.5606775330599 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 96.464 & 1.83528836627582 & 52.5606775330599 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 96.552 & 1.80769960830716 & 53.4115289710202 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 96.3373333333333 & 1.77194124049297 & 54.3682437835983 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 96.1453333333333 & 1.68051825268207 & 57.2117161952198 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 96.7453333333333 & 1.58301262944583 & 61.1146945600817 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 97.4958904109589 & 2.74351694539432 & 35.5368282213931 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 97.4929577464789 & 2.70304643987323 & 36.0678071631841 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 97.4550724637681 & 2.66830608405261 & 36.5231983865036 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 97.4164179104478 & 2.63431895375927 & 36.9797354156492 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 97.34 & 2.60344981928565 & 37.3888520066459 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 97.2603174603175 & 2.56638789924145 & 37.8977462795334 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 97.2131147540984 & 2.53343055113630 & 38.3721253817263 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 97.157627118644 & 2.50551023767221 & 38.7775813715733 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 97.1491228070175 & 2.48464472633092 & 39.0998044016046 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 97.1345454545455 & 2.45902066156813 & 39.5013132555796 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 97.1 & 2.43396085777572 & 39.8938215007841 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 97.056862745098 & 2.40467396983289 & 40.3617554656871 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 97.0204081632653 & 2.37620356111933 & 40.8300070544307 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 96.9702127659574 & 2.34341227302134 & 41.3799201627183 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 96.9377777777778 & 2.31394605650456 & 41.8928425341996 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 96.9209302325581 & 2.28739760378033 & 42.3717022665316 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 96.9146341463415 & 2.25381130038682 & 43.0003319841852 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 96.9410256410256 & 2.21656053224362 & 43.7348875570302 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 96.9594594594595 & 2.17704189286637 & 44.5372501912672 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 96.9942857142857 & 2.16370341890796 & 44.8279024133721 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 97.0545454545455 & 2.15713268454511 & 44.992385563437 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 97.1225806451613 & 2.13929296770333 & 45.3993829323099 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 97.1896551724138 & 2.11261368264717 & 46.0044616631623 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 97.2925925925926 & 2.07458454239172 & 46.8973862498885 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 97.436 & 2.03695753514893 & 47.8340850600384 \tabularnewline
Median & 98.5 &  &  \tabularnewline
Midrange & 100.45 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 96.371052631579 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 96.9410256410256 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 96.9410256410256 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 96.9410256410256 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 96.9594594594594 &  &  \tabularnewline
Midmean - Closest Observation & 96.371052631579 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 96.9410256410256 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 96.9410256410256 &  &  \tabularnewline
Number of observations & 75 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=84895&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]97.5746666666667[/C][C]2.79323964666903[/C][C]34.9324365286830[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]94.5373778483119[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]91.4932199499188[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]100.489688359884[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]97.4986666666667[/C][C]2.77730538493721[/C][C]35.1054900895859[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]97.5626666666667[/C][C]2.75504501906177[/C][C]35.4123674900571[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]97.5586666666667[/C][C]2.73657778877086[/C][C]35.6498788621995[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]97.6813333333333[/C][C]2.70613163841755[/C][C]36.0962977360754[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]97.6746666666667[/C][C]2.70254807581699[/C][C]36.1416944033972[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]97.4906666666667[/C][C]2.65540019096448[/C][C]36.7141145046227[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]97.5186666666667[/C][C]2.60095248896435[/C][C]37.4934440672912[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]97.2093333333333[/C][C]2.53591369771968[/C][C]38.3330605535769[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]97.2453333333333[/C][C]2.52645554752773[/C][C]38.4908150980503[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]97.3786666666667[/C][C]2.4850285356154[/C][C]39.1861362036841[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]97.4226666666667[/C][C]2.46478738248167[/C][C]39.5257892664870[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]97.3426666666667[/C][C]2.41314506258805[/C][C]40.3385060333955[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]97.4293333333333[/C][C]2.38472373479430[/C][C]40.8556060024023[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]97.2426666666667[/C][C]2.31186767704299[/C][C]42.0623842931381[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]97.0826666666667[/C][C]2.24145896288161[/C][C]43.3122659278392[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]96.976[/C][C]2.21981075404724[/C][C]43.6866069880911[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]96.6813333333333[/C][C]2.17129155181956[/C][C]44.5271079566968[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]96.7773333333333[/C][C]2.10992726345177[/C][C]45.8676159172469[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]96.6506666666667[/C][C]1.91726942970102[/C][C]50.4105814078194[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]96.464[/C][C]1.83528836627582[/C][C]52.5606775330599[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]96.464[/C][C]1.83528836627582[/C][C]52.5606775330599[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]96.552[/C][C]1.80769960830716[/C][C]53.4115289710202[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]96.3373333333333[/C][C]1.77194124049297[/C][C]54.3682437835983[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]96.1453333333333[/C][C]1.68051825268207[/C][C]57.2117161952198[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]96.7453333333333[/C][C]1.58301262944583[/C][C]61.1146945600817[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]97.4958904109589[/C][C]2.74351694539432[/C][C]35.5368282213931[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]97.4929577464789[/C][C]2.70304643987323[/C][C]36.0678071631841[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]97.4550724637681[/C][C]2.66830608405261[/C][C]36.5231983865036[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]97.4164179104478[/C][C]2.63431895375927[/C][C]36.9797354156492[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]97.34[/C][C]2.60344981928565[/C][C]37.3888520066459[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]97.2603174603175[/C][C]2.56638789924145[/C][C]37.8977462795334[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]97.2131147540984[/C][C]2.53343055113630[/C][C]38.3721253817263[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]97.157627118644[/C][C]2.50551023767221[/C][C]38.7775813715733[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]97.1491228070175[/C][C]2.48464472633092[/C][C]39.0998044016046[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]97.1345454545455[/C][C]2.45902066156813[/C][C]39.5013132555796[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]97.1[/C][C]2.43396085777572[/C][C]39.8938215007841[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]97.056862745098[/C][C]2.40467396983289[/C][C]40.3617554656871[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]97.0204081632653[/C][C]2.37620356111933[/C][C]40.8300070544307[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]96.9702127659574[/C][C]2.34341227302134[/C][C]41.3799201627183[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]96.9377777777778[/C][C]2.31394605650456[/C][C]41.8928425341996[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]96.9209302325581[/C][C]2.28739760378033[/C][C]42.3717022665316[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]96.9146341463415[/C][C]2.25381130038682[/C][C]43.0003319841852[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]96.9410256410256[/C][C]2.21656053224362[/C][C]43.7348875570302[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]96.9594594594595[/C][C]2.17704189286637[/C][C]44.5372501912672[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]96.9942857142857[/C][C]2.16370341890796[/C][C]44.8279024133721[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]97.0545454545455[/C][C]2.15713268454511[/C][C]44.992385563437[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]97.1225806451613[/C][C]2.13929296770333[/C][C]45.3993829323099[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]97.1896551724138[/C][C]2.11261368264717[/C][C]46.0044616631623[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]97.2925925925926[/C][C]2.07458454239172[/C][C]46.8973862498885[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]97.436[/C][C]2.03695753514893[/C][C]47.8340850600384[/C][/ROW]
[ROW][C]Median[/C][C]98.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]100.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]96.371052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]96.9410256410256[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]96.9410256410256[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]96.9410256410256[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]96.9594594594594[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]96.371052631579[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]96.9410256410256[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]96.9410256410256[/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=84895&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=84895&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 Mean97.57466666666672.7932396466690334.9324365286830
Geometric Mean94.5373778483119
Harmonic Mean91.4932199499188
Quadratic Mean100.489688359884
Winsorized Mean ( 1 / 25 )97.49866666666672.7773053849372135.1054900895859
Winsorized Mean ( 2 / 25 )97.56266666666672.7550450190617735.4123674900571
Winsorized Mean ( 3 / 25 )97.55866666666672.7365777887708635.6498788621995
Winsorized Mean ( 4 / 25 )97.68133333333332.7061316384175536.0962977360754
Winsorized Mean ( 5 / 25 )97.67466666666672.7025480758169936.1416944033972
Winsorized Mean ( 6 / 25 )97.49066666666672.6554001909644836.7141145046227
Winsorized Mean ( 7 / 25 )97.51866666666672.6009524889643537.4934440672912
Winsorized Mean ( 8 / 25 )97.20933333333332.5359136977196838.3330605535769
Winsorized Mean ( 9 / 25 )97.24533333333332.5264555475277338.4908150980503
Winsorized Mean ( 10 / 25 )97.37866666666672.485028535615439.1861362036841
Winsorized Mean ( 11 / 25 )97.42266666666672.4647873824816739.5257892664870
Winsorized Mean ( 12 / 25 )97.34266666666672.4131450625880540.3385060333955
Winsorized Mean ( 13 / 25 )97.42933333333332.3847237347943040.8556060024023
Winsorized Mean ( 14 / 25 )97.24266666666672.3118676770429942.0623842931381
Winsorized Mean ( 15 / 25 )97.08266666666672.2414589628816143.3122659278392
Winsorized Mean ( 16 / 25 )96.9762.2198107540472443.6866069880911
Winsorized Mean ( 17 / 25 )96.68133333333332.1712915518195644.5271079566968
Winsorized Mean ( 18 / 25 )96.77733333333332.1099272634517745.8676159172469
Winsorized Mean ( 19 / 25 )96.65066666666671.9172694297010250.4105814078194
Winsorized Mean ( 20 / 25 )96.4641.8352883662758252.5606775330599
Winsorized Mean ( 21 / 25 )96.4641.8352883662758252.5606775330599
Winsorized Mean ( 22 / 25 )96.5521.8076996083071653.4115289710202
Winsorized Mean ( 23 / 25 )96.33733333333331.7719412404929754.3682437835983
Winsorized Mean ( 24 / 25 )96.14533333333331.6805182526820757.2117161952198
Winsorized Mean ( 25 / 25 )96.74533333333331.5830126294458361.1146945600817
Trimmed Mean ( 1 / 25 )97.49589041095892.7435169453943235.5368282213931
Trimmed Mean ( 2 / 25 )97.49295774647892.7030464398732336.0678071631841
Trimmed Mean ( 3 / 25 )97.45507246376812.6683060840526136.5231983865036
Trimmed Mean ( 4 / 25 )97.41641791044782.6343189537592736.9797354156492
Trimmed Mean ( 5 / 25 )97.342.6034498192856537.3888520066459
Trimmed Mean ( 6 / 25 )97.26031746031752.5663878992414537.8977462795334
Trimmed Mean ( 7 / 25 )97.21311475409842.5334305511363038.3721253817263
Trimmed Mean ( 8 / 25 )97.1576271186442.5055102376722138.7775813715733
Trimmed Mean ( 9 / 25 )97.14912280701752.4846447263309239.0998044016046
Trimmed Mean ( 10 / 25 )97.13454545454552.4590206615681339.5013132555796
Trimmed Mean ( 11 / 25 )97.12.4339608577757239.8938215007841
Trimmed Mean ( 12 / 25 )97.0568627450982.4046739698328940.3617554656871
Trimmed Mean ( 13 / 25 )97.02040816326532.3762035611193340.8300070544307
Trimmed Mean ( 14 / 25 )96.97021276595742.3434122730213441.3799201627183
Trimmed Mean ( 15 / 25 )96.93777777777782.3139460565045641.8928425341996
Trimmed Mean ( 16 / 25 )96.92093023255812.2873976037803342.3717022665316
Trimmed Mean ( 17 / 25 )96.91463414634152.2538113003868243.0003319841852
Trimmed Mean ( 18 / 25 )96.94102564102562.2165605322436243.7348875570302
Trimmed Mean ( 19 / 25 )96.95945945945952.1770418928663744.5372501912672
Trimmed Mean ( 20 / 25 )96.99428571428572.1637034189079644.8279024133721
Trimmed Mean ( 21 / 25 )97.05454545454552.1571326845451144.992385563437
Trimmed Mean ( 22 / 25 )97.12258064516132.1392929677033345.3993829323099
Trimmed Mean ( 23 / 25 )97.18965517241382.1126136826471746.0044616631623
Trimmed Mean ( 24 / 25 )97.29259259259262.0745845423917246.8973862498885
Trimmed Mean ( 25 / 25 )97.4362.0369575351489347.8340850600384
Median98.5
Midrange100.45
Midmean - Weighted Average at Xnp96.371052631579
Midmean - Weighted Average at X(n+1)p96.9410256410256
Midmean - Empirical Distribution Function96.9410256410256
Midmean - Empirical Distribution Function - Averaging96.9410256410256
Midmean - Empirical Distribution Function - Interpolation96.9594594594594
Midmean - Closest Observation96.371052631579
Midmean - True Basic - Statistics Graphics Toolkit96.9410256410256
Midmean - MS Excel (old versions)96.9410256410256
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')