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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationTue, 20 Oct 2009 12:14:10 -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/Oct/20/t1256062528lbb3du5l0y78cz1.htm/, Retrieved Thu, 02 May 2024 16:34:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=48933, Retrieved Thu, 02 May 2024 16:34:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsshwws3vr2opl5
Estimated Impact139
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [] [2009-10-20 18:14:10] [4407d6264e55b051ec65750e6dca2820] [Current]
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Post a new message
Dataseries X:
200.1
172
136.1
182.6
208.7
142.3
188.8
143.9
149.7
196.9
231.5
219.2
220.7
244.2
182.5
229.8
238.1
206.5
249.3
181.8
218
246.4
214.3
242.3
220.7
204.5
180.7
233
236.5
239.4
208.7
209
247.2
284.3
245.8
249.1
251.4
251.2
207.2
228.3
254.3
217.9
244.4
233.2
212.6
239.5
335.5
248.8
264.6
275.4
180.7
256.1
247.4
227.8
248.1
153.7
225.5
274.4
400.3
301.8
345.2




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=48933&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=48933&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48933&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 Mean228.3590163934435.9898189473578138.124527368924
Geometric Mean223.801435939396
Harmonic Mean219.25413993834
Quadratic Mean233.02471162842
Winsorized Mean ( 1 / 20 )227.5573770491805.5872749934604640.7277925850296
Winsorized Mean ( 2 / 20 )227.2918032786895.4656249649311441.5856932623536
Winsorized Mean ( 3 / 20 )225.9196721311484.9019566850871646.0876516551942
Winsorized Mean ( 4 / 20 )225.0344262295084.5606333356353949.3428016830817
Winsorized Mean ( 5 / 20 )225.8049180327874.0431811491117855.8483307339303
Winsorized Mean ( 6 / 20 )226.5622950819673.8426689580229558.9596183165707
Winsorized Mean ( 7 / 20 )225.4377049180333.6242859963375262.2019634062672
Winsorized Mean ( 8 / 20 )224.4672131147543.4073415765356465.8775200762165
Winsorized Mean ( 9 / 20 )224.3049180327873.3454139772007067.0484787716694
Winsorized Mean ( 10 / 20 )223.8459016393443.2730891257305268.3897972345572
Winsorized Mean ( 11 / 20 )224.9278688524593.0395697595565473.9999034880762
Winsorized Mean ( 12 / 20 )226.1475409836072.6823299619740584.3101125475161
Winsorized Mean ( 13 / 20 )226.7868852459022.5547678296553288.7700567595214
Winsorized Mean ( 14 / 20 )227.7278688524592.3742276640638895.916609977775
Winsorized Mean ( 15 / 20 )228.0475409836072.26979405743232100.470586852088
Winsorized Mean ( 16 / 20 )228.0475409836072.21396660391804103.004056420740
Winsorized Mean ( 17 / 20 )228.4098360655742.14094446361259106.686483441125
Winsorized Mean ( 18 / 20 )228.1737704918032.10665728750335108.310816308531
Winsorized Mean ( 19 / 20 )228.0803278688522.06542949882145110.427554171661
Winsorized Mean ( 20 / 20 )228.8016393442621.82127303673416125.627313823600
Trimmed Mean ( 1 / 20 )227.0084745762715.2168125504051143.5147846281429
Trimmed Mean ( 2 / 20 )226.4210526315794.7482273020088347.6853861936616
Trimmed Mean ( 3 / 20 )225.9381818181824.2341003766311253.3615554003352
Trimmed Mean ( 4 / 20 )225.9452830188683.8887705979781258.1019829599471
Trimmed Mean ( 5 / 20 )226.2176470588243.6000693957171562.8370240106886
Trimmed Mean ( 6 / 20 )226.3204081632653.4311931687322865.9596813801316
Trimmed Mean ( 7 / 20 )226.2680851063833.2826529545207968.9284210792896
Trimmed Mean ( 8 / 20 )226.4288888888893.1583105415699971.6930415513641
Trimmed Mean ( 9 / 20 )226.7767441860463.0565939780258574.1926293830212
Trimmed Mean ( 10 / 20 )227.1853658536592.9371704505867877.3483764989779
Trimmed Mean ( 11 / 20 )227.7076923076922.7933055324791281.519078260514
Trimmed Mean ( 12 / 20 )228.1243243243242.6693775787135985.4597439281185
Trimmed Mean ( 13 / 20 )228.4114285714292.6033293855284387.7381978020677
Trimmed Mean ( 14 / 20 )228.6424242424242.5438764498502889.8795317893215
Trimmed Mean ( 15 / 20 )228.7709677419352.5067658706135491.261401961701
Trimmed Mean ( 16 / 20 )228.8724137931032.4750224985379692.4728619349128
Trimmed Mean ( 17 / 20 )228.9888888888892.4345467840410794.0581180817538
Trimmed Mean ( 18 / 20 )229.0722.3865283013895695.9854529555013
Trimmed Mean ( 19 / 20 )229.2043478260872.3106684885690599.193955757811
Trimmed Mean ( 20 / 20 )229.3761904761902.19163892535662104.659662603349
Median229.8
Midrange268.2
Midmean - Weighted Average at Xnp228.126666666667
Midmean - Weighted Average at X(n+1)p228.770967741935
Midmean - Empirical Distribution Function228.770967741935
Midmean - Empirical Distribution Function - Averaging228.770967741935
Midmean - Empirical Distribution Function - Interpolation228.770967741935
Midmean - Closest Observation228.0125
Midmean - True Basic - Statistics Graphics Toolkit228.770967741935
Midmean - MS Excel (old versions)228.770967741935
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 228.359016393443 & 5.98981894735781 & 38.124527368924 \tabularnewline
Geometric Mean & 223.801435939396 &  &  \tabularnewline
Harmonic Mean & 219.25413993834 &  &  \tabularnewline
Quadratic Mean & 233.02471162842 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 227.557377049180 & 5.58727499346046 & 40.7277925850296 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 227.291803278689 & 5.46562496493114 & 41.5856932623536 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 225.919672131148 & 4.90195668508716 & 46.0876516551942 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 225.034426229508 & 4.56063333563539 & 49.3428016830817 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 225.804918032787 & 4.04318114911178 & 55.8483307339303 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 226.562295081967 & 3.84266895802295 & 58.9596183165707 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 225.437704918033 & 3.62428599633752 & 62.2019634062672 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 224.467213114754 & 3.40734157653564 & 65.8775200762165 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 224.304918032787 & 3.34541397720070 & 67.0484787716694 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 223.845901639344 & 3.27308912573052 & 68.3897972345572 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 224.927868852459 & 3.03956975955654 & 73.9999034880762 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 226.147540983607 & 2.68232996197405 & 84.3101125475161 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 226.786885245902 & 2.55476782965532 & 88.7700567595214 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 227.727868852459 & 2.37422766406388 & 95.916609977775 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 228.047540983607 & 2.26979405743232 & 100.470586852088 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 228.047540983607 & 2.21396660391804 & 103.004056420740 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 228.409836065574 & 2.14094446361259 & 106.686483441125 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 228.173770491803 & 2.10665728750335 & 108.310816308531 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 228.080327868852 & 2.06542949882145 & 110.427554171661 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 228.801639344262 & 1.82127303673416 & 125.627313823600 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 227.008474576271 & 5.21681255040511 & 43.5147846281429 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 226.421052631579 & 4.74822730200883 & 47.6853861936616 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 225.938181818182 & 4.23410037663112 & 53.3615554003352 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 225.945283018868 & 3.88877059797812 & 58.1019829599471 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 226.217647058824 & 3.60006939571715 & 62.8370240106886 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 226.320408163265 & 3.43119316873228 & 65.9596813801316 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 226.268085106383 & 3.28265295452079 & 68.9284210792896 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 226.428888888889 & 3.15831054156999 & 71.6930415513641 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 226.776744186046 & 3.05659397802585 & 74.1926293830212 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 227.185365853659 & 2.93717045058678 & 77.3483764989779 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 227.707692307692 & 2.79330553247912 & 81.519078260514 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 228.124324324324 & 2.66937757871359 & 85.4597439281185 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 228.411428571429 & 2.60332938552843 & 87.7381978020677 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 228.642424242424 & 2.54387644985028 & 89.8795317893215 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 228.770967741935 & 2.50676587061354 & 91.261401961701 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 228.872413793103 & 2.47502249853796 & 92.4728619349128 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 228.988888888889 & 2.43454678404107 & 94.0581180817538 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 229.072 & 2.38652830138956 & 95.9854529555013 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 229.204347826087 & 2.31066848856905 & 99.193955757811 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 229.376190476190 & 2.19163892535662 & 104.659662603349 \tabularnewline
Median & 229.8 &  &  \tabularnewline
Midrange & 268.2 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 228.126666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 228.770967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 228.770967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 228.770967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 228.770967741935 &  &  \tabularnewline
Midmean - Closest Observation & 228.0125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 228.770967741935 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 228.770967741935 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=48933&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]228.359016393443[/C][C]5.98981894735781[/C][C]38.124527368924[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]223.801435939396[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]219.25413993834[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]233.02471162842[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]227.557377049180[/C][C]5.58727499346046[/C][C]40.7277925850296[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]227.291803278689[/C][C]5.46562496493114[/C][C]41.5856932623536[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]225.919672131148[/C][C]4.90195668508716[/C][C]46.0876516551942[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]225.034426229508[/C][C]4.56063333563539[/C][C]49.3428016830817[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]225.804918032787[/C][C]4.04318114911178[/C][C]55.8483307339303[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]226.562295081967[/C][C]3.84266895802295[/C][C]58.9596183165707[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]225.437704918033[/C][C]3.62428599633752[/C][C]62.2019634062672[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]224.467213114754[/C][C]3.40734157653564[/C][C]65.8775200762165[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]224.304918032787[/C][C]3.34541397720070[/C][C]67.0484787716694[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]223.845901639344[/C][C]3.27308912573052[/C][C]68.3897972345572[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]224.927868852459[/C][C]3.03956975955654[/C][C]73.9999034880762[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]226.147540983607[/C][C]2.68232996197405[/C][C]84.3101125475161[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]226.786885245902[/C][C]2.55476782965532[/C][C]88.7700567595214[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]227.727868852459[/C][C]2.37422766406388[/C][C]95.916609977775[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]228.047540983607[/C][C]2.26979405743232[/C][C]100.470586852088[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]228.047540983607[/C][C]2.21396660391804[/C][C]103.004056420740[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]228.409836065574[/C][C]2.14094446361259[/C][C]106.686483441125[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]228.173770491803[/C][C]2.10665728750335[/C][C]108.310816308531[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]228.080327868852[/C][C]2.06542949882145[/C][C]110.427554171661[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]228.801639344262[/C][C]1.82127303673416[/C][C]125.627313823600[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]227.008474576271[/C][C]5.21681255040511[/C][C]43.5147846281429[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]226.421052631579[/C][C]4.74822730200883[/C][C]47.6853861936616[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]225.938181818182[/C][C]4.23410037663112[/C][C]53.3615554003352[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]225.945283018868[/C][C]3.88877059797812[/C][C]58.1019829599471[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]226.217647058824[/C][C]3.60006939571715[/C][C]62.8370240106886[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]226.320408163265[/C][C]3.43119316873228[/C][C]65.9596813801316[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]226.268085106383[/C][C]3.28265295452079[/C][C]68.9284210792896[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]226.428888888889[/C][C]3.15831054156999[/C][C]71.6930415513641[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]226.776744186046[/C][C]3.05659397802585[/C][C]74.1926293830212[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]227.185365853659[/C][C]2.93717045058678[/C][C]77.3483764989779[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]227.707692307692[/C][C]2.79330553247912[/C][C]81.519078260514[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]228.124324324324[/C][C]2.66937757871359[/C][C]85.4597439281185[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]228.411428571429[/C][C]2.60332938552843[/C][C]87.7381978020677[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]228.642424242424[/C][C]2.54387644985028[/C][C]89.8795317893215[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]228.770967741935[/C][C]2.50676587061354[/C][C]91.261401961701[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]228.872413793103[/C][C]2.47502249853796[/C][C]92.4728619349128[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]228.988888888889[/C][C]2.43454678404107[/C][C]94.0581180817538[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]229.072[/C][C]2.38652830138956[/C][C]95.9854529555013[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]229.204347826087[/C][C]2.31066848856905[/C][C]99.193955757811[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]229.376190476190[/C][C]2.19163892535662[/C][C]104.659662603349[/C][/ROW]
[ROW][C]Median[/C][C]229.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]268.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]228.126666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]228.770967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]228.770967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]228.770967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]228.770967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]228.0125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]228.770967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]228.770967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]61[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=48933&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=48933&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 Mean228.3590163934435.9898189473578138.124527368924
Geometric Mean223.801435939396
Harmonic Mean219.25413993834
Quadratic Mean233.02471162842
Winsorized Mean ( 1 / 20 )227.5573770491805.5872749934604640.7277925850296
Winsorized Mean ( 2 / 20 )227.2918032786895.4656249649311441.5856932623536
Winsorized Mean ( 3 / 20 )225.9196721311484.9019566850871646.0876516551942
Winsorized Mean ( 4 / 20 )225.0344262295084.5606333356353949.3428016830817
Winsorized Mean ( 5 / 20 )225.8049180327874.0431811491117855.8483307339303
Winsorized Mean ( 6 / 20 )226.5622950819673.8426689580229558.9596183165707
Winsorized Mean ( 7 / 20 )225.4377049180333.6242859963375262.2019634062672
Winsorized Mean ( 8 / 20 )224.4672131147543.4073415765356465.8775200762165
Winsorized Mean ( 9 / 20 )224.3049180327873.3454139772007067.0484787716694
Winsorized Mean ( 10 / 20 )223.8459016393443.2730891257305268.3897972345572
Winsorized Mean ( 11 / 20 )224.9278688524593.0395697595565473.9999034880762
Winsorized Mean ( 12 / 20 )226.1475409836072.6823299619740584.3101125475161
Winsorized Mean ( 13 / 20 )226.7868852459022.5547678296553288.7700567595214
Winsorized Mean ( 14 / 20 )227.7278688524592.3742276640638895.916609977775
Winsorized Mean ( 15 / 20 )228.0475409836072.26979405743232100.470586852088
Winsorized Mean ( 16 / 20 )228.0475409836072.21396660391804103.004056420740
Winsorized Mean ( 17 / 20 )228.4098360655742.14094446361259106.686483441125
Winsorized Mean ( 18 / 20 )228.1737704918032.10665728750335108.310816308531
Winsorized Mean ( 19 / 20 )228.0803278688522.06542949882145110.427554171661
Winsorized Mean ( 20 / 20 )228.8016393442621.82127303673416125.627313823600
Trimmed Mean ( 1 / 20 )227.0084745762715.2168125504051143.5147846281429
Trimmed Mean ( 2 / 20 )226.4210526315794.7482273020088347.6853861936616
Trimmed Mean ( 3 / 20 )225.9381818181824.2341003766311253.3615554003352
Trimmed Mean ( 4 / 20 )225.9452830188683.8887705979781258.1019829599471
Trimmed Mean ( 5 / 20 )226.2176470588243.6000693957171562.8370240106886
Trimmed Mean ( 6 / 20 )226.3204081632653.4311931687322865.9596813801316
Trimmed Mean ( 7 / 20 )226.2680851063833.2826529545207968.9284210792896
Trimmed Mean ( 8 / 20 )226.4288888888893.1583105415699971.6930415513641
Trimmed Mean ( 9 / 20 )226.7767441860463.0565939780258574.1926293830212
Trimmed Mean ( 10 / 20 )227.1853658536592.9371704505867877.3483764989779
Trimmed Mean ( 11 / 20 )227.7076923076922.7933055324791281.519078260514
Trimmed Mean ( 12 / 20 )228.1243243243242.6693775787135985.4597439281185
Trimmed Mean ( 13 / 20 )228.4114285714292.6033293855284387.7381978020677
Trimmed Mean ( 14 / 20 )228.6424242424242.5438764498502889.8795317893215
Trimmed Mean ( 15 / 20 )228.7709677419352.5067658706135491.261401961701
Trimmed Mean ( 16 / 20 )228.8724137931032.4750224985379692.4728619349128
Trimmed Mean ( 17 / 20 )228.9888888888892.4345467840410794.0581180817538
Trimmed Mean ( 18 / 20 )229.0722.3865283013895695.9854529555013
Trimmed Mean ( 19 / 20 )229.2043478260872.3106684885690599.193955757811
Trimmed Mean ( 20 / 20 )229.3761904761902.19163892535662104.659662603349
Median229.8
Midrange268.2
Midmean - Weighted Average at Xnp228.126666666667
Midmean - Weighted Average at X(n+1)p228.770967741935
Midmean - Empirical Distribution Function228.770967741935
Midmean - Empirical Distribution Function - Averaging228.770967741935
Midmean - Empirical Distribution Function - Interpolation228.770967741935
Midmean - Closest Observation228.0125
Midmean - True Basic - Statistics Graphics Toolkit228.770967741935
Midmean - MS Excel (old versions)228.770967741935
Number of observations61



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')