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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, 01 Jun 2009 20:08:58 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/02/t1243908567nccf5bz87g2gnwz.htm/, Retrieved Fri, 10 May 2024 01:52:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41133, Retrieved Fri, 10 May 2024 01:52:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Duncan Huysmans O...] [2009-06-02 02:08:58] [7ecc19fd9fa5f5e7f58eda40682a000b] [Current]
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Dataseries X:
49.1
52.7
55.1
60.4
57.5
55.9
62.6
61.3
67.1
68.6
74.8
76.9
85.7
86.5
90.8
89.7
96.3
107.5
109.2
100.2
116.8
120.1
123.3
130.2
131.4
125.6
124.5
134.3
135.2
151.8
146.4
140.0
127.8
148.0
165.9
165.5
179.9
190.0
189.8
190.9
203.6
183.5
169.3
144.2
141.5
154.3
169.5
194.0
203.2
192.9
209.4
227.2
263.7
297.8
337.1
361.3
355.2
312.6
309.9
323.7
324.1
355.3
383.4
395.1
412.8
407.0
438.0
446.1
452.5
447.3
475.9
487.7




Summary of computational 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 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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41133&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41133&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41133&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean197.56111111111114.801446255356913.3474194144786
Geometric Mean161.837605668408
Harmonic Mean132.671663985153
Quadratic Mean233.634912250336
Winsorized Mean ( 1 / 24 )197.44722222222214.750045750999613.3862108331997
Winsorized Mean ( 2 / 24 )196.86388888888914.574130470570913.5077622151394
Winsorized Mean ( 3 / 24 )196.68055555555614.51646367678913.5487925940280
Winsorized Mean ( 4 / 24 )196.70277777777814.488191453632613.5767654925942
Winsorized Mean ( 5 / 24 )196.34166666666714.326089821358813.7051818824939
Winsorized Mean ( 6 / 24 )194.31666666666713.832675616470114.0476558588059
Winsorized Mean ( 7 / 24 )193.87916666666713.691040605802014.1610248810821
Winsorized Mean ( 8 / 24 )193.05694444444413.337973492231014.4742336275368
Winsorized Mean ( 9 / 24 )191.78194444444413.005181092021114.7465800812344
Winsorized Mean ( 10 / 24 )189.57361111111112.269505564446815.4507946644921
Winsorized Mean ( 11 / 24 )188.97777777777812.047871100427415.6855743394428
Winsorized Mean ( 12 / 24 )190.42777777777811.857270509552616.0600011296329
Winsorized Mean ( 13 / 24 )187.30416666666711.211489020741516.7064487437976
Winsorized Mean ( 14 / 24 )185.39861111111110.663215861457717.3867446293793
Winsorized Mean ( 15 / 24 )185.54444444444410.619064463582717.4727675004475
Winsorized Mean ( 16 / 24 )184.310.018061349789118.3967729448852
Winsorized Mean ( 17 / 24 )184.5833333333339.7902317897817218.8538266812015
Winsorized Mean ( 18 / 24 )183.3833333333339.028572277547120.3114432377513
Winsorized Mean ( 19 / 24 )174.8333333333337.406525218072723.6053112877712
Winsorized Mean ( 20 / 24 )166.8055555555565.4866693224458930.4019698933114
Winsorized Mean ( 21 / 24 )162.5763888888894.5836468066320535.4687862628635
Winsorized Mean ( 22 / 24 )161.7819444444444.2050356979000638.4733819323428
Winsorized Mean ( 23 / 24 )162.03754.1379406197260439.1589717908345
Winsorized Mean ( 24 / 24 )159.33753.6714295983150043.3993069275053
Trimmed Mean ( 1 / 24 )195.53714285714314.485255610773213.499046762538
Trimmed Mean ( 2 / 24 )193.51470588235314.165082343235113.6613894076493
Trimmed Mean ( 3 / 24 )191.68787878787913.890238311503413.8001864683005
Trimmed Mean ( 4 / 24 )189.81562513.581277820435913.9762714164040
Trimmed Mean ( 5 / 24 )187.81612903225813.212955797918914.2145430518915
Trimmed Mean ( 6 / 24 )185.7712.813215348639914.4983124801472
Trimmed Mean ( 7 / 24 )184.00172413793112.468655071598214.7571428579383
Trimmed Mean ( 8 / 24 )182.187512.078264276720915.0839140315170
Trimmed Mean ( 9 / 24 )180.37592592592611.681931892484115.4405904422346
Trimmed Mean ( 10 / 24 )178.62115384615411.267642889870715.8525749876870
Trimmed Mean ( 11 / 24 )177.04410.925023947108716.2053649362348
Trimmed Mean ( 12 / 24 )175.41666666666710.537240331611816.6473062344811
Trimmed Mean ( 13 / 24 )173.45869565217410.070858891016817.2238234622569
Trimmed Mean ( 14 / 24 )171.7159090909099.6303239267570217.8307511145925
Trimmed Mean ( 15 / 24 )170.0404761904769.189089917594318.5046046687279
Trimmed Mean ( 16 / 24 )168.188.5999345555053119.5559627709421
Trimmed Mean ( 17 / 24 )166.2710526315797.9656757500525320.8734397242422
Trimmed Mean ( 18 / 24 )164.1166666666677.1298472790251423.0182583502835
Trimmed Mean ( 19 / 24 )161.856.1762861571649326.2050682046593
Trimmed Mean ( 20 / 24 )160.31255.460571188219529.358192481009
Trimmed Mean ( 21 / 24 )159.5333333333335.1632884766125830.8976215557099
Trimmed Mean ( 22 / 24 )159.1607142857145.0327297527457531.6251263439845
Trimmed Mean ( 23 / 24 )158.8307692307694.9434611644093732.1294663694897
Trimmed Mean ( 24 / 24 )158.41254.8028422763150832.9830735398498
Median153.05
Midrange268.4
Midmean - Weighted Average at Xnp162.389189189189
Midmean - Weighted Average at X(n+1)p164.116666666667
Midmean - Empirical Distribution Function162.389189189189
Midmean - Empirical Distribution Function - Averaging164.116666666667
Midmean - Empirical Distribution Function - Interpolation164.116666666667
Midmean - Closest Observation162.389189189189
Midmean - True Basic - Statistics Graphics Toolkit164.116666666667
Midmean - MS Excel (old versions)166.271052631579
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 197.561111111111 & 14.8014462553569 & 13.3474194144786 \tabularnewline
Geometric Mean & 161.837605668408 &  &  \tabularnewline
Harmonic Mean & 132.671663985153 &  &  \tabularnewline
Quadratic Mean & 233.634912250336 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 197.447222222222 & 14.7500457509996 & 13.3862108331997 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 196.863888888889 & 14.5741304705709 & 13.5077622151394 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 196.680555555556 & 14.516463676789 & 13.5487925940280 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 196.702777777778 & 14.4881914536326 & 13.5767654925942 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 196.341666666667 & 14.3260898213588 & 13.7051818824939 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 194.316666666667 & 13.8326756164701 & 14.0476558588059 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 193.879166666667 & 13.6910406058020 & 14.1610248810821 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 193.056944444444 & 13.3379734922310 & 14.4742336275368 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 191.781944444444 & 13.0051810920211 & 14.7465800812344 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 189.573611111111 & 12.2695055644468 & 15.4507946644921 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 188.977777777778 & 12.0478711004274 & 15.6855743394428 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 190.427777777778 & 11.8572705095526 & 16.0600011296329 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 187.304166666667 & 11.2114890207415 & 16.7064487437976 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 185.398611111111 & 10.6632158614577 & 17.3867446293793 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 185.544444444444 & 10.6190644635827 & 17.4727675004475 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 184.3 & 10.0180613497891 & 18.3967729448852 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 184.583333333333 & 9.79023178978172 & 18.8538266812015 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 183.383333333333 & 9.0285722775471 & 20.3114432377513 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 174.833333333333 & 7.4065252180727 & 23.6053112877712 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 166.805555555556 & 5.48666932244589 & 30.4019698933114 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 162.576388888889 & 4.58364680663205 & 35.4687862628635 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 161.781944444444 & 4.20503569790006 & 38.4733819323428 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 162.0375 & 4.13794061972604 & 39.1589717908345 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 159.3375 & 3.67142959831500 & 43.3993069275053 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 195.537142857143 & 14.4852556107732 & 13.499046762538 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 193.514705882353 & 14.1650823432351 & 13.6613894076493 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 191.687878787879 & 13.8902383115034 & 13.8001864683005 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 189.815625 & 13.5812778204359 & 13.9762714164040 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 187.816129032258 & 13.2129557979189 & 14.2145430518915 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 185.77 & 12.8132153486399 & 14.4983124801472 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 184.001724137931 & 12.4686550715982 & 14.7571428579383 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 182.1875 & 12.0782642767209 & 15.0839140315170 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 180.375925925926 & 11.6819318924841 & 15.4405904422346 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 178.621153846154 & 11.2676428898707 & 15.8525749876870 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 177.044 & 10.9250239471087 & 16.2053649362348 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 175.416666666667 & 10.5372403316118 & 16.6473062344811 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 173.458695652174 & 10.0708588910168 & 17.2238234622569 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 171.715909090909 & 9.63032392675702 & 17.8307511145925 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 170.040476190476 & 9.1890899175943 & 18.5046046687279 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 168.18 & 8.59993455550531 & 19.5559627709421 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 166.271052631579 & 7.96567575005253 & 20.8734397242422 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 164.116666666667 & 7.12984727902514 & 23.0182583502835 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 161.85 & 6.17628615716493 & 26.2050682046593 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 160.3125 & 5.4605711882195 & 29.358192481009 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 159.533333333333 & 5.16328847661258 & 30.8976215557099 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 159.160714285714 & 5.03272975274575 & 31.6251263439845 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 158.830769230769 & 4.94346116440937 & 32.1294663694897 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 158.4125 & 4.80284227631508 & 32.9830735398498 \tabularnewline
Median & 153.05 &  &  \tabularnewline
Midrange & 268.4 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 162.389189189189 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 164.116666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 162.389189189189 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 164.116666666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 164.116666666667 &  &  \tabularnewline
Midmean - Closest Observation & 162.389189189189 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 164.116666666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 166.271052631579 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41133&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]197.561111111111[/C][C]14.8014462553569[/C][C]13.3474194144786[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]161.837605668408[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]132.671663985153[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]233.634912250336[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]197.447222222222[/C][C]14.7500457509996[/C][C]13.3862108331997[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]196.863888888889[/C][C]14.5741304705709[/C][C]13.5077622151394[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]196.680555555556[/C][C]14.516463676789[/C][C]13.5487925940280[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]196.702777777778[/C][C]14.4881914536326[/C][C]13.5767654925942[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]196.341666666667[/C][C]14.3260898213588[/C][C]13.7051818824939[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]194.316666666667[/C][C]13.8326756164701[/C][C]14.0476558588059[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]193.879166666667[/C][C]13.6910406058020[/C][C]14.1610248810821[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]193.056944444444[/C][C]13.3379734922310[/C][C]14.4742336275368[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]191.781944444444[/C][C]13.0051810920211[/C][C]14.7465800812344[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]189.573611111111[/C][C]12.2695055644468[/C][C]15.4507946644921[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]188.977777777778[/C][C]12.0478711004274[/C][C]15.6855743394428[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]190.427777777778[/C][C]11.8572705095526[/C][C]16.0600011296329[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]187.304166666667[/C][C]11.2114890207415[/C][C]16.7064487437976[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]185.398611111111[/C][C]10.6632158614577[/C][C]17.3867446293793[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]185.544444444444[/C][C]10.6190644635827[/C][C]17.4727675004475[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]184.3[/C][C]10.0180613497891[/C][C]18.3967729448852[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]184.583333333333[/C][C]9.79023178978172[/C][C]18.8538266812015[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]183.383333333333[/C][C]9.0285722775471[/C][C]20.3114432377513[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]174.833333333333[/C][C]7.4065252180727[/C][C]23.6053112877712[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]166.805555555556[/C][C]5.48666932244589[/C][C]30.4019698933114[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]162.576388888889[/C][C]4.58364680663205[/C][C]35.4687862628635[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]161.781944444444[/C][C]4.20503569790006[/C][C]38.4733819323428[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]162.0375[/C][C]4.13794061972604[/C][C]39.1589717908345[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]159.3375[/C][C]3.67142959831500[/C][C]43.3993069275053[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]195.537142857143[/C][C]14.4852556107732[/C][C]13.499046762538[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]193.514705882353[/C][C]14.1650823432351[/C][C]13.6613894076493[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]191.687878787879[/C][C]13.8902383115034[/C][C]13.8001864683005[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]189.815625[/C][C]13.5812778204359[/C][C]13.9762714164040[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]187.816129032258[/C][C]13.2129557979189[/C][C]14.2145430518915[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]185.77[/C][C]12.8132153486399[/C][C]14.4983124801472[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]184.001724137931[/C][C]12.4686550715982[/C][C]14.7571428579383[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]182.1875[/C][C]12.0782642767209[/C][C]15.0839140315170[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]180.375925925926[/C][C]11.6819318924841[/C][C]15.4405904422346[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]178.621153846154[/C][C]11.2676428898707[/C][C]15.8525749876870[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]177.044[/C][C]10.9250239471087[/C][C]16.2053649362348[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]175.416666666667[/C][C]10.5372403316118[/C][C]16.6473062344811[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]173.458695652174[/C][C]10.0708588910168[/C][C]17.2238234622569[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]171.715909090909[/C][C]9.63032392675702[/C][C]17.8307511145925[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]170.040476190476[/C][C]9.1890899175943[/C][C]18.5046046687279[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]168.18[/C][C]8.59993455550531[/C][C]19.5559627709421[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]166.271052631579[/C][C]7.96567575005253[/C][C]20.8734397242422[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]164.116666666667[/C][C]7.12984727902514[/C][C]23.0182583502835[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]161.85[/C][C]6.17628615716493[/C][C]26.2050682046593[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]160.3125[/C][C]5.4605711882195[/C][C]29.358192481009[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]159.533333333333[/C][C]5.16328847661258[/C][C]30.8976215557099[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]159.160714285714[/C][C]5.03272975274575[/C][C]31.6251263439845[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]158.830769230769[/C][C]4.94346116440937[/C][C]32.1294663694897[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]158.4125[/C][C]4.80284227631508[/C][C]32.9830735398498[/C][/ROW]
[ROW][C]Median[/C][C]153.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]268.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]162.389189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]164.116666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]162.389189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]164.116666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]164.116666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]162.389189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]164.116666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]166.271052631579[/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=41133&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41133&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 Mean197.56111111111114.801446255356913.3474194144786
Geometric Mean161.837605668408
Harmonic Mean132.671663985153
Quadratic Mean233.634912250336
Winsorized Mean ( 1 / 24 )197.44722222222214.750045750999613.3862108331997
Winsorized Mean ( 2 / 24 )196.86388888888914.574130470570913.5077622151394
Winsorized Mean ( 3 / 24 )196.68055555555614.51646367678913.5487925940280
Winsorized Mean ( 4 / 24 )196.70277777777814.488191453632613.5767654925942
Winsorized Mean ( 5 / 24 )196.34166666666714.326089821358813.7051818824939
Winsorized Mean ( 6 / 24 )194.31666666666713.832675616470114.0476558588059
Winsorized Mean ( 7 / 24 )193.87916666666713.691040605802014.1610248810821
Winsorized Mean ( 8 / 24 )193.05694444444413.337973492231014.4742336275368
Winsorized Mean ( 9 / 24 )191.78194444444413.005181092021114.7465800812344
Winsorized Mean ( 10 / 24 )189.57361111111112.269505564446815.4507946644921
Winsorized Mean ( 11 / 24 )188.97777777777812.047871100427415.6855743394428
Winsorized Mean ( 12 / 24 )190.42777777777811.857270509552616.0600011296329
Winsorized Mean ( 13 / 24 )187.30416666666711.211489020741516.7064487437976
Winsorized Mean ( 14 / 24 )185.39861111111110.663215861457717.3867446293793
Winsorized Mean ( 15 / 24 )185.54444444444410.619064463582717.4727675004475
Winsorized Mean ( 16 / 24 )184.310.018061349789118.3967729448852
Winsorized Mean ( 17 / 24 )184.5833333333339.7902317897817218.8538266812015
Winsorized Mean ( 18 / 24 )183.3833333333339.028572277547120.3114432377513
Winsorized Mean ( 19 / 24 )174.8333333333337.406525218072723.6053112877712
Winsorized Mean ( 20 / 24 )166.8055555555565.4866693224458930.4019698933114
Winsorized Mean ( 21 / 24 )162.5763888888894.5836468066320535.4687862628635
Winsorized Mean ( 22 / 24 )161.7819444444444.2050356979000638.4733819323428
Winsorized Mean ( 23 / 24 )162.03754.1379406197260439.1589717908345
Winsorized Mean ( 24 / 24 )159.33753.6714295983150043.3993069275053
Trimmed Mean ( 1 / 24 )195.53714285714314.485255610773213.499046762538
Trimmed Mean ( 2 / 24 )193.51470588235314.165082343235113.6613894076493
Trimmed Mean ( 3 / 24 )191.68787878787913.890238311503413.8001864683005
Trimmed Mean ( 4 / 24 )189.81562513.581277820435913.9762714164040
Trimmed Mean ( 5 / 24 )187.81612903225813.212955797918914.2145430518915
Trimmed Mean ( 6 / 24 )185.7712.813215348639914.4983124801472
Trimmed Mean ( 7 / 24 )184.00172413793112.468655071598214.7571428579383
Trimmed Mean ( 8 / 24 )182.187512.078264276720915.0839140315170
Trimmed Mean ( 9 / 24 )180.37592592592611.681931892484115.4405904422346
Trimmed Mean ( 10 / 24 )178.62115384615411.267642889870715.8525749876870
Trimmed Mean ( 11 / 24 )177.04410.925023947108716.2053649362348
Trimmed Mean ( 12 / 24 )175.41666666666710.537240331611816.6473062344811
Trimmed Mean ( 13 / 24 )173.45869565217410.070858891016817.2238234622569
Trimmed Mean ( 14 / 24 )171.7159090909099.6303239267570217.8307511145925
Trimmed Mean ( 15 / 24 )170.0404761904769.189089917594318.5046046687279
Trimmed Mean ( 16 / 24 )168.188.5999345555053119.5559627709421
Trimmed Mean ( 17 / 24 )166.2710526315797.9656757500525320.8734397242422
Trimmed Mean ( 18 / 24 )164.1166666666677.1298472790251423.0182583502835
Trimmed Mean ( 19 / 24 )161.856.1762861571649326.2050682046593
Trimmed Mean ( 20 / 24 )160.31255.460571188219529.358192481009
Trimmed Mean ( 21 / 24 )159.5333333333335.1632884766125830.8976215557099
Trimmed Mean ( 22 / 24 )159.1607142857145.0327297527457531.6251263439845
Trimmed Mean ( 23 / 24 )158.8307692307694.9434611644093732.1294663694897
Trimmed Mean ( 24 / 24 )158.41254.8028422763150832.9830735398498
Median153.05
Midrange268.4
Midmean - Weighted Average at Xnp162.389189189189
Midmean - Weighted Average at X(n+1)p164.116666666667
Midmean - Empirical Distribution Function162.389189189189
Midmean - Empirical Distribution Function - Averaging164.116666666667
Midmean - Empirical Distribution Function - Interpolation164.116666666667
Midmean - Closest Observation162.389189189189
Midmean - True Basic - Statistics Graphics Toolkit164.116666666667
Midmean - MS Excel (old versions)166.271052631579
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')