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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, 16 Apr 2008 08:44:29 -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/2008/Apr/16/t1208357172hvakoiy9ghg1eld.htm/, Retrieved Fri, 10 May 2024 18:49:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=10145, Retrieved Fri, 10 May 2024 18:49:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact286
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Plantaardige stof...] [2008-04-16 14:44:29] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
79,2
81,5
81,5
82
85,8
88,2
88
88,8
89
90,4
90,9
94,6
97,9
101,7
102,3
103,5
103,6
102,3
101,6
104,3
110,8
112,1
111,1
114,4
115
115,3
114,1
114,8
114,5
114,1
112,3
113
112,2
113,7
113,6
115,8
117,9
120,1
118,8
114,7
110,9
112,9
113,3
114,3
116,5
114,3
115,9
120,1
122,6
122,4
123,1
127,9
130,9
135
134,9
130,2
130,8
132,6
138,6
146,2
149,3
149,9
156,8
158,8
156,7
159,9
158,2
157,5
159,1
160,6
161,6
161,3




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of compuational 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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10145&T=0

[TABLE]
[ROW][C]Summary of compuational 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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=10145&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10145&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean118.4513888888892.6567229459696144.5855255884268
Geometric Mean116.375124707461
Harmonic Mean114.339822234113
Quadratic Mean120.548173289077
Winsorized Mean ( 1 / 24 )118.4791666666672.6493081872978244.7207943699107
Winsorized Mean ( 2 / 24 )118.4597222222222.6449132237853444.7877537746533
Winsorized Mean ( 3 / 24 )118.4513888888892.634328564128944.9645463750485
Winsorized Mean ( 4 / 24 )118.6180555555562.5850405735267945.8863418896843
Winsorized Mean ( 5 / 24 )118.752.5538243438699446.4988910788015
Winsorized Mean ( 6 / 24 )118.7166666666672.5400054218516946.7387453764256
Winsorized Mean ( 7 / 24 )118.7069444444442.5153436238658247.1931323092964
Winsorized Mean ( 8 / 24 )118.6513888888892.4947997503661647.5594840313233
Winsorized Mean ( 9 / 24 )118.8138888888892.4632338007707748.2349214482648
Winsorized Mean ( 10 / 24 )117.9388888888892.254811023692452.3054427398338
Winsorized Mean ( 11 / 24 )118.41252.144334108659855.2211054806228
Winsorized Mean ( 12 / 24 )118.4458333333331.9564796816023160.5402828596353
Winsorized Mean ( 13 / 24 )117.7416666666671.5947018966816773.8330260418382
Winsorized Mean ( 14 / 24 )117.0611111111111.4669488038964979.7990432932457
Winsorized Mean ( 15 / 24 )117.1652777777781.445079828578181.0787580455425
Winsorized Mean ( 16 / 24 )116.6541666666671.3586014417565785.8634203389637
Winsorized Mean ( 17 / 24 )116.5361111111111.2510563698389893.1501680664556
Winsorized Mean ( 18 / 24 )116.5361111111111.2433489809389993.7275961115133
Winsorized Mean ( 19 / 24 )116.56251.1908549510648897.8813581752907
Winsorized Mean ( 20 / 24 )117.7291666666670.846077290843678139.147058951637
Winsorized Mean ( 21 / 24 )116.3583333333330.614224799931857189.439327989105
Winsorized Mean ( 22 / 24 )116.2666666666670.58308847979862199.397982801549
Winsorized Mean ( 23 / 24 )116.5222222222220.53466025594654217.936943930751
Winsorized Mean ( 24 / 24 )115.7888888888890.414824828480371279.127190416877
Trimmed Mean ( 1 / 24 )118.3957142857142.6011109552872745.5173640497925
Trimmed Mean ( 2 / 24 )118.3073529411762.5435671033419046.5123773560904
Trimmed Mean ( 3 / 24 )118.2242424242422.4775072634782947.719029593585
Trimmed Mean ( 4 / 24 )118.13906252.4030131725560149.1628859338875
Trimmed Mean ( 5 / 24 )1182.3314611864411450.6120370719621
Trimmed Mean ( 6 / 24 )117.822.2543915711189652.262438127162
Trimmed Mean ( 7 / 24 )117.6344827586212.1639816091789554.3602044766236
Trimmed Mean ( 8 / 24 )117.43752.059073304517557.0341520830502
Trimmed Mean ( 9 / 24 )117.2351851851851.9333968713035960.6368960895957
Trimmed Mean ( 10 / 24 )116.9923076923081.7815838661287165.6675837251074
Trimmed Mean ( 11 / 24 )116.8561.6478685305198270.9134241207566
Trimmed Mean ( 12 / 24 )116.643751.5039543216158877.558040376303
Trimmed Mean ( 13 / 24 )116.4086956521741.3682663881908185.0775087781667
Trimmed Mean ( 14 / 24 )116.2409090909091.2928422160416589.9111335076984
Trimmed Mean ( 15 / 24 )116.1404761904761.2284380020102494.5432134144509
Trimmed Mean ( 16 / 24 )116.01751.14760557583706101.095273883954
Trimmed Mean ( 17 / 24 )115.9421052631581.06380802059356108.987808907914
Trimmed Mean ( 18 / 24 )115.8722222222220.980942299737585118.123382234836
Trimmed Mean ( 19 / 24 )115.7941176470590.864624027556484133.924242163735
Trimmed Mean ( 20 / 24 )115.7031250.709149370824743163.157622018950
Trimmed Mean ( 21 / 24 )115.460.610532083749377189.113730585527
Trimmed Mean ( 22 / 24 )115.350.569031015232295202.713027782696
Trimmed Mean ( 23 / 24 )115.2346153846150.517120498015168222.839001406661
Trimmed Mean ( 24 / 24 )115.0666666666670.450388989148151255.482859126506
Median114.45
Midrange120.4
Midmean - Weighted Average at Xnp115.537837837838
Midmean - Weighted Average at X(n+1)p115.872222222222
Midmean - Empirical Distribution Function115.537837837838
Midmean - Empirical Distribution Function - Averaging115.872222222222
Midmean - Empirical Distribution Function - Interpolation115.872222222222
Midmean - Closest Observation115.537837837838
Midmean - True Basic - Statistics Graphics Toolkit115.872222222222
Midmean - MS Excel (old versions)115.942105263158
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 118.451388888889 & 2.65672294596961 & 44.5855255884268 \tabularnewline
Geometric Mean & 116.375124707461 &  &  \tabularnewline
Harmonic Mean & 114.339822234113 &  &  \tabularnewline
Quadratic Mean & 120.548173289077 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 118.479166666667 & 2.64930818729782 & 44.7207943699107 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 118.459722222222 & 2.64491322378534 & 44.7877537746533 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 118.451388888889 & 2.6343285641289 & 44.9645463750485 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 118.618055555556 & 2.58504057352679 & 45.8863418896843 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 118.75 & 2.55382434386994 & 46.4988910788015 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 118.716666666667 & 2.54000542185169 & 46.7387453764256 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 118.706944444444 & 2.51534362386582 & 47.1931323092964 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 118.651388888889 & 2.49479975036616 & 47.5594840313233 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 118.813888888889 & 2.46323380077077 & 48.2349214482648 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 117.938888888889 & 2.2548110236924 & 52.3054427398338 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 118.4125 & 2.1443341086598 & 55.2211054806228 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 118.445833333333 & 1.95647968160231 & 60.5402828596353 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 117.741666666667 & 1.59470189668167 & 73.8330260418382 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 117.061111111111 & 1.46694880389649 & 79.7990432932457 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 117.165277777778 & 1.4450798285781 & 81.0787580455425 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 116.654166666667 & 1.35860144175657 & 85.8634203389637 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 116.536111111111 & 1.25105636983898 & 93.1501680664556 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 116.536111111111 & 1.24334898093899 & 93.7275961115133 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 116.5625 & 1.19085495106488 & 97.8813581752907 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 117.729166666667 & 0.846077290843678 & 139.147058951637 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 116.358333333333 & 0.614224799931857 & 189.439327989105 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 116.266666666667 & 0.58308847979862 & 199.397982801549 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 116.522222222222 & 0.53466025594654 & 217.936943930751 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 115.788888888889 & 0.414824828480371 & 279.127190416877 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 118.395714285714 & 2.60111095528727 & 45.5173640497925 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 118.307352941176 & 2.54356710334190 & 46.5123773560904 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 118.224242424242 & 2.47750726347829 & 47.719029593585 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 118.1390625 & 2.40301317255601 & 49.1628859338875 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 118 & 2.33146118644114 & 50.6120370719621 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 117.82 & 2.25439157111896 & 52.262438127162 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 117.634482758621 & 2.16398160917895 & 54.3602044766236 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 117.4375 & 2.0590733045175 & 57.0341520830502 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 117.235185185185 & 1.93339687130359 & 60.6368960895957 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 116.992307692308 & 1.78158386612871 & 65.6675837251074 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 116.856 & 1.64786853051982 & 70.9134241207566 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 116.64375 & 1.50395432161588 & 77.558040376303 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 116.408695652174 & 1.36826638819081 & 85.0775087781667 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 116.240909090909 & 1.29284221604165 & 89.9111335076984 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 116.140476190476 & 1.22843800201024 & 94.5432134144509 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 116.0175 & 1.14760557583706 & 101.095273883954 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 115.942105263158 & 1.06380802059356 & 108.987808907914 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 115.872222222222 & 0.980942299737585 & 118.123382234836 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 115.794117647059 & 0.864624027556484 & 133.924242163735 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 115.703125 & 0.709149370824743 & 163.157622018950 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 115.46 & 0.610532083749377 & 189.113730585527 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 115.35 & 0.569031015232295 & 202.713027782696 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 115.234615384615 & 0.517120498015168 & 222.839001406661 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 115.066666666667 & 0.450388989148151 & 255.482859126506 \tabularnewline
Median & 114.45 &  &  \tabularnewline
Midrange & 120.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 115.537837837838 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 115.872222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 115.537837837838 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 115.872222222222 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 115.872222222222 &  &  \tabularnewline
Midmean - Closest Observation & 115.537837837838 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 115.872222222222 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 115.942105263158 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=10145&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]118.451388888889[/C][C]2.65672294596961[/C][C]44.5855255884268[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]116.375124707461[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]114.339822234113[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]120.548173289077[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]118.479166666667[/C][C]2.64930818729782[/C][C]44.7207943699107[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]118.459722222222[/C][C]2.64491322378534[/C][C]44.7877537746533[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]118.451388888889[/C][C]2.6343285641289[/C][C]44.9645463750485[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]118.618055555556[/C][C]2.58504057352679[/C][C]45.8863418896843[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]118.75[/C][C]2.55382434386994[/C][C]46.4988910788015[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]118.716666666667[/C][C]2.54000542185169[/C][C]46.7387453764256[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]118.706944444444[/C][C]2.51534362386582[/C][C]47.1931323092964[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]118.651388888889[/C][C]2.49479975036616[/C][C]47.5594840313233[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]118.813888888889[/C][C]2.46323380077077[/C][C]48.2349214482648[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]117.938888888889[/C][C]2.2548110236924[/C][C]52.3054427398338[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]118.4125[/C][C]2.1443341086598[/C][C]55.2211054806228[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]118.445833333333[/C][C]1.95647968160231[/C][C]60.5402828596353[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]117.741666666667[/C][C]1.59470189668167[/C][C]73.8330260418382[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]117.061111111111[/C][C]1.46694880389649[/C][C]79.7990432932457[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]117.165277777778[/C][C]1.4450798285781[/C][C]81.0787580455425[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]116.654166666667[/C][C]1.35860144175657[/C][C]85.8634203389637[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]116.536111111111[/C][C]1.25105636983898[/C][C]93.1501680664556[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]116.536111111111[/C][C]1.24334898093899[/C][C]93.7275961115133[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]116.5625[/C][C]1.19085495106488[/C][C]97.8813581752907[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]117.729166666667[/C][C]0.846077290843678[/C][C]139.147058951637[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]116.358333333333[/C][C]0.614224799931857[/C][C]189.439327989105[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]116.266666666667[/C][C]0.58308847979862[/C][C]199.397982801549[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]116.522222222222[/C][C]0.53466025594654[/C][C]217.936943930751[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]115.788888888889[/C][C]0.414824828480371[/C][C]279.127190416877[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]118.395714285714[/C][C]2.60111095528727[/C][C]45.5173640497925[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]118.307352941176[/C][C]2.54356710334190[/C][C]46.5123773560904[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]118.224242424242[/C][C]2.47750726347829[/C][C]47.719029593585[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]118.1390625[/C][C]2.40301317255601[/C][C]49.1628859338875[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]118[/C][C]2.33146118644114[/C][C]50.6120370719621[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]117.82[/C][C]2.25439157111896[/C][C]52.262438127162[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]117.634482758621[/C][C]2.16398160917895[/C][C]54.3602044766236[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]117.4375[/C][C]2.0590733045175[/C][C]57.0341520830502[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]117.235185185185[/C][C]1.93339687130359[/C][C]60.6368960895957[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]116.992307692308[/C][C]1.78158386612871[/C][C]65.6675837251074[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]116.856[/C][C]1.64786853051982[/C][C]70.9134241207566[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]116.64375[/C][C]1.50395432161588[/C][C]77.558040376303[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]116.408695652174[/C][C]1.36826638819081[/C][C]85.0775087781667[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]116.240909090909[/C][C]1.29284221604165[/C][C]89.9111335076984[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]116.140476190476[/C][C]1.22843800201024[/C][C]94.5432134144509[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]116.0175[/C][C]1.14760557583706[/C][C]101.095273883954[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]115.942105263158[/C][C]1.06380802059356[/C][C]108.987808907914[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]115.872222222222[/C][C]0.980942299737585[/C][C]118.123382234836[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]115.794117647059[/C][C]0.864624027556484[/C][C]133.924242163735[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]115.703125[/C][C]0.709149370824743[/C][C]163.157622018950[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]115.46[/C][C]0.610532083749377[/C][C]189.113730585527[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]115.35[/C][C]0.569031015232295[/C][C]202.713027782696[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]115.234615384615[/C][C]0.517120498015168[/C][C]222.839001406661[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]115.066666666667[/C][C]0.450388989148151[/C][C]255.482859126506[/C][/ROW]
[ROW][C]Median[/C][C]114.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]120.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]115.537837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]115.872222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]115.537837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]115.872222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]115.872222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]115.537837837838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]115.872222222222[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]115.942105263158[/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=10145&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=10145&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 Mean118.4513888888892.6567229459696144.5855255884268
Geometric Mean116.375124707461
Harmonic Mean114.339822234113
Quadratic Mean120.548173289077
Winsorized Mean ( 1 / 24 )118.4791666666672.6493081872978244.7207943699107
Winsorized Mean ( 2 / 24 )118.4597222222222.6449132237853444.7877537746533
Winsorized Mean ( 3 / 24 )118.4513888888892.634328564128944.9645463750485
Winsorized Mean ( 4 / 24 )118.6180555555562.5850405735267945.8863418896843
Winsorized Mean ( 5 / 24 )118.752.5538243438699446.4988910788015
Winsorized Mean ( 6 / 24 )118.7166666666672.5400054218516946.7387453764256
Winsorized Mean ( 7 / 24 )118.7069444444442.5153436238658247.1931323092964
Winsorized Mean ( 8 / 24 )118.6513888888892.4947997503661647.5594840313233
Winsorized Mean ( 9 / 24 )118.8138888888892.4632338007707748.2349214482648
Winsorized Mean ( 10 / 24 )117.9388888888892.254811023692452.3054427398338
Winsorized Mean ( 11 / 24 )118.41252.144334108659855.2211054806228
Winsorized Mean ( 12 / 24 )118.4458333333331.9564796816023160.5402828596353
Winsorized Mean ( 13 / 24 )117.7416666666671.5947018966816773.8330260418382
Winsorized Mean ( 14 / 24 )117.0611111111111.4669488038964979.7990432932457
Winsorized Mean ( 15 / 24 )117.1652777777781.445079828578181.0787580455425
Winsorized Mean ( 16 / 24 )116.6541666666671.3586014417565785.8634203389637
Winsorized Mean ( 17 / 24 )116.5361111111111.2510563698389893.1501680664556
Winsorized Mean ( 18 / 24 )116.5361111111111.2433489809389993.7275961115133
Winsorized Mean ( 19 / 24 )116.56251.1908549510648897.8813581752907
Winsorized Mean ( 20 / 24 )117.7291666666670.846077290843678139.147058951637
Winsorized Mean ( 21 / 24 )116.3583333333330.614224799931857189.439327989105
Winsorized Mean ( 22 / 24 )116.2666666666670.58308847979862199.397982801549
Winsorized Mean ( 23 / 24 )116.5222222222220.53466025594654217.936943930751
Winsorized Mean ( 24 / 24 )115.7888888888890.414824828480371279.127190416877
Trimmed Mean ( 1 / 24 )118.3957142857142.6011109552872745.5173640497925
Trimmed Mean ( 2 / 24 )118.3073529411762.5435671033419046.5123773560904
Trimmed Mean ( 3 / 24 )118.2242424242422.4775072634782947.719029593585
Trimmed Mean ( 4 / 24 )118.13906252.4030131725560149.1628859338875
Trimmed Mean ( 5 / 24 )1182.3314611864411450.6120370719621
Trimmed Mean ( 6 / 24 )117.822.2543915711189652.262438127162
Trimmed Mean ( 7 / 24 )117.6344827586212.1639816091789554.3602044766236
Trimmed Mean ( 8 / 24 )117.43752.059073304517557.0341520830502
Trimmed Mean ( 9 / 24 )117.2351851851851.9333968713035960.6368960895957
Trimmed Mean ( 10 / 24 )116.9923076923081.7815838661287165.6675837251074
Trimmed Mean ( 11 / 24 )116.8561.6478685305198270.9134241207566
Trimmed Mean ( 12 / 24 )116.643751.5039543216158877.558040376303
Trimmed Mean ( 13 / 24 )116.4086956521741.3682663881908185.0775087781667
Trimmed Mean ( 14 / 24 )116.2409090909091.2928422160416589.9111335076984
Trimmed Mean ( 15 / 24 )116.1404761904761.2284380020102494.5432134144509
Trimmed Mean ( 16 / 24 )116.01751.14760557583706101.095273883954
Trimmed Mean ( 17 / 24 )115.9421052631581.06380802059356108.987808907914
Trimmed Mean ( 18 / 24 )115.8722222222220.980942299737585118.123382234836
Trimmed Mean ( 19 / 24 )115.7941176470590.864624027556484133.924242163735
Trimmed Mean ( 20 / 24 )115.7031250.709149370824743163.157622018950
Trimmed Mean ( 21 / 24 )115.460.610532083749377189.113730585527
Trimmed Mean ( 22 / 24 )115.350.569031015232295202.713027782696
Trimmed Mean ( 23 / 24 )115.2346153846150.517120498015168222.839001406661
Trimmed Mean ( 24 / 24 )115.0666666666670.450388989148151255.482859126506
Median114.45
Midrange120.4
Midmean - Weighted Average at Xnp115.537837837838
Midmean - Weighted Average at X(n+1)p115.872222222222
Midmean - Empirical Distribution Function115.537837837838
Midmean - Empirical Distribution Function - Averaging115.872222222222
Midmean - Empirical Distribution Function - Interpolation115.872222222222
Midmean - Closest Observation115.537837837838
Midmean - True Basic - Statistics Graphics Toolkit115.872222222222
Midmean - MS Excel (old versions)115.942105263158
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')