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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 computationSat, 27 Nov 2010 00:29:17 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/27/t1290817645nilsjz9cvhl6ndr.htm/, Retrieved Mon, 29 Apr 2024 11:44:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=102291, Retrieved Mon, 29 Apr 2024 11:44:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact151
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [minitut w6 - yt1] [2010-11-27 00:29:17] [54d0a09f418287eaabab8ba43e4b06f8] [Current]
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Dataseries X:
288186
281477
282656
280190
280408
276836
275216
274352
271311
289802
290726
292300
278506
269826
265861
269034
264176
255198
253353
246057
235372
258556
260993
254663
250643
243422
247105
248541
245039
237080
237085
225554
226839
247934
248333
246969
245098
246263
255765
264319
268347
273046
273963
267430
271993
292710
295881
293299
288576
286445
297584
300431
298522
292213
285383
277537
277891
302686
300653
296369
287224




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102291&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102291&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102291&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean269495.5245901642634.59278534535102.291149542808
Geometric Mean268709.481506259
Harmonic Mean267911.004030331
Quadratic Mean270267.094783666
Winsorized Mean ( 1 / 20 )269483.2622950822622.00871042449102.777409252563
Winsorized Mean ( 2 / 20 )269755.7540983612551.12871833563105.739766151177
Winsorized Mean ( 3 / 20 )269745.8688524592514.23178714588107.287589883935
Winsorized Mean ( 4 / 20 )269684.688524592502.57962228365107.762680604942
Winsorized Mean ( 5 / 20 )270104.5245901642379.03120724191113.535511332491
Winsorized Mean ( 6 / 20 )270215.5737704922341.10581683230115.422195710963
Winsorized Mean ( 7 / 20 )269926.0491803282287.56858148275117.996920995203
Winsorized Mean ( 8 / 20 )269974.5737704922251.98341012668119.883020699209
Winsorized Mean ( 9 / 20 )269944.4754098362236.48319493033120.700426464973
Winsorized Mean ( 10 / 20 )270045.9508196722213.83798658213121.980900344287
Winsorized Mean ( 11 / 20 )269802.3278688522165.59249577828124.585917431289
Winsorized Mean ( 12 / 20 )269783.6393442622108.24014676017127.966275454365
Winsorized Mean ( 13 / 20 )269607.3934426232052.75088045322131.339558058354
Winsorized Mean ( 14 / 20 )269565.6229508202030.77731640689132.740119151897
Winsorized Mean ( 15 / 20 )269845.9508196721906.71907510793141.523706529446
Winsorized Mean ( 16 / 20 )270352.4426229511758.60885711079153.730854663789
Winsorized Mean ( 17 / 20 )270421.5573770491655.35487544956163.361682372553
Winsorized Mean ( 18 / 20 )269774.7377049181512.27357784998178.390168059710
Winsorized Mean ( 19 / 20 )269584.1147540981432.39653897323188.204947037460
Winsorized Mean ( 20 / 20 )270148.7049180331238.86732627053218.061045916261
Trimmed Mean ( 1 / 20 )269677.7457627122556.77355029512105.475803960653
Trimmed Mean ( 2 / 20 )269885.8771929822476.25513604532108.989527478175
Trimmed Mean ( 3 / 20 )269958.0363636362423.81096899975111.377512444810
Trimmed Mean ( 4 / 20 )270039.4339622642375.42423092326113.680508284328
Trimmed Mean ( 5 / 20 )270145.5098039222318.37036330882116.523879911217
Trimmed Mean ( 6 / 20 )270155.7142857142287.20397828119118.116143925534
Trimmed Mean ( 7 / 20 )270142.7659574472256.79925003553119.701726218313
Trimmed Mean ( 8 / 20 )270184.7333333332230.17009348134121.149832527603
Trimmed Mean ( 9 / 20 )2702222202.16460082464122.707448797792
Trimmed Mean ( 10 / 20 )270267.8780487802166.35739912087124.756828286255
Trimmed Mean ( 11 / 20 )270302.589743592121.83209886167127.391130470975
Trimmed Mean ( 12 / 20 )270377.5675675682071.68205713538130.511130622733
Trimmed Mean ( 13 / 20 )270463.8285714292015.79550470347134.172255042912
Trimmed Mean ( 14 / 20 )270585.6060606061950.41997125726138.731970574617
Trimmed Mean ( 15 / 20 )270728.9677419351860.97273181728145.477127694162
Trimmed Mean ( 16 / 20 )270852.7931034481770.31394364456152.997039918153
Trimmed Mean ( 17 / 20 )270923.4444444441685.92415359112160.697291077634
Trimmed Mean ( 18 / 20 )270995.481592.54111838073170.16545247858
Trimmed Mean ( 19 / 20 )271175.3478260871497.98291336384181.026996641197
Trimmed Mean ( 20 / 20 )271418.6190476191371.99408661122197.827834461018
Median271993
Midrange264120
Midmean - Weighted Average at Xnp270179.133333333
Midmean - Weighted Average at X(n+1)p270728.967741935
Midmean - Empirical Distribution Function270728.967741935
Midmean - Empirical Distribution Function - Averaging270728.967741935
Midmean - Empirical Distribution Function - Interpolation270728.967741935
Midmean - Closest Observation270035.59375
Midmean - True Basic - Statistics Graphics Toolkit270728.967741935
Midmean - MS Excel (old versions)270728.967741935
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 269495.524590164 & 2634.59278534535 & 102.291149542808 \tabularnewline
Geometric Mean & 268709.481506259 &  &  \tabularnewline
Harmonic Mean & 267911.004030331 &  &  \tabularnewline
Quadratic Mean & 270267.094783666 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 269483.262295082 & 2622.00871042449 & 102.777409252563 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 269755.754098361 & 2551.12871833563 & 105.739766151177 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 269745.868852459 & 2514.23178714588 & 107.287589883935 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 269684.68852459 & 2502.57962228365 & 107.762680604942 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 270104.524590164 & 2379.03120724191 & 113.535511332491 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 270215.573770492 & 2341.10581683230 & 115.422195710963 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 269926.049180328 & 2287.56858148275 & 117.996920995203 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 269974.573770492 & 2251.98341012668 & 119.883020699209 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 269944.475409836 & 2236.48319493033 & 120.700426464973 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 270045.950819672 & 2213.83798658213 & 121.980900344287 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 269802.327868852 & 2165.59249577828 & 124.585917431289 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 269783.639344262 & 2108.24014676017 & 127.966275454365 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 269607.393442623 & 2052.75088045322 & 131.339558058354 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 269565.622950820 & 2030.77731640689 & 132.740119151897 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 269845.950819672 & 1906.71907510793 & 141.523706529446 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 270352.442622951 & 1758.60885711079 & 153.730854663789 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 270421.557377049 & 1655.35487544956 & 163.361682372553 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 269774.737704918 & 1512.27357784998 & 178.390168059710 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 269584.114754098 & 1432.39653897323 & 188.204947037460 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 270148.704918033 & 1238.86732627053 & 218.061045916261 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 269677.745762712 & 2556.77355029512 & 105.475803960653 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 269885.877192982 & 2476.25513604532 & 108.989527478175 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 269958.036363636 & 2423.81096899975 & 111.377512444810 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 270039.433962264 & 2375.42423092326 & 113.680508284328 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 270145.509803922 & 2318.37036330882 & 116.523879911217 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 270155.714285714 & 2287.20397828119 & 118.116143925534 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 270142.765957447 & 2256.79925003553 & 119.701726218313 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 270184.733333333 & 2230.17009348134 & 121.149832527603 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 270222 & 2202.16460082464 & 122.707448797792 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 270267.878048780 & 2166.35739912087 & 124.756828286255 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 270302.58974359 & 2121.83209886167 & 127.391130470975 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 270377.567567568 & 2071.68205713538 & 130.511130622733 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 270463.828571429 & 2015.79550470347 & 134.172255042912 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 270585.606060606 & 1950.41997125726 & 138.731970574617 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 270728.967741935 & 1860.97273181728 & 145.477127694162 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 270852.793103448 & 1770.31394364456 & 152.997039918153 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 270923.444444444 & 1685.92415359112 & 160.697291077634 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 270995.48 & 1592.54111838073 & 170.16545247858 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 271175.347826087 & 1497.98291336384 & 181.026996641197 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 271418.619047619 & 1371.99408661122 & 197.827834461018 \tabularnewline
Median & 271993 &  &  \tabularnewline
Midrange & 264120 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 270179.133333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 270728.967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 270728.967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 270728.967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 270728.967741935 &  &  \tabularnewline
Midmean - Closest Observation & 270035.59375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 270728.967741935 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 270728.967741935 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102291&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]269495.524590164[/C][C]2634.59278534535[/C][C]102.291149542808[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]268709.481506259[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]267911.004030331[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]270267.094783666[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]269483.262295082[/C][C]2622.00871042449[/C][C]102.777409252563[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]269755.754098361[/C][C]2551.12871833563[/C][C]105.739766151177[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]269745.868852459[/C][C]2514.23178714588[/C][C]107.287589883935[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]269684.68852459[/C][C]2502.57962228365[/C][C]107.762680604942[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]270104.524590164[/C][C]2379.03120724191[/C][C]113.535511332491[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]270215.573770492[/C][C]2341.10581683230[/C][C]115.422195710963[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]269926.049180328[/C][C]2287.56858148275[/C][C]117.996920995203[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]269974.573770492[/C][C]2251.98341012668[/C][C]119.883020699209[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]269944.475409836[/C][C]2236.48319493033[/C][C]120.700426464973[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]270045.950819672[/C][C]2213.83798658213[/C][C]121.980900344287[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]269802.327868852[/C][C]2165.59249577828[/C][C]124.585917431289[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]269783.639344262[/C][C]2108.24014676017[/C][C]127.966275454365[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]269607.393442623[/C][C]2052.75088045322[/C][C]131.339558058354[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]269565.622950820[/C][C]2030.77731640689[/C][C]132.740119151897[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]269845.950819672[/C][C]1906.71907510793[/C][C]141.523706529446[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]270352.442622951[/C][C]1758.60885711079[/C][C]153.730854663789[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]270421.557377049[/C][C]1655.35487544956[/C][C]163.361682372553[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]269774.737704918[/C][C]1512.27357784998[/C][C]178.390168059710[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]269584.114754098[/C][C]1432.39653897323[/C][C]188.204947037460[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]270148.704918033[/C][C]1238.86732627053[/C][C]218.061045916261[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]269677.745762712[/C][C]2556.77355029512[/C][C]105.475803960653[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]269885.877192982[/C][C]2476.25513604532[/C][C]108.989527478175[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]269958.036363636[/C][C]2423.81096899975[/C][C]111.377512444810[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]270039.433962264[/C][C]2375.42423092326[/C][C]113.680508284328[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]270145.509803922[/C][C]2318.37036330882[/C][C]116.523879911217[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]270155.714285714[/C][C]2287.20397828119[/C][C]118.116143925534[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]270142.765957447[/C][C]2256.79925003553[/C][C]119.701726218313[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]270184.733333333[/C][C]2230.17009348134[/C][C]121.149832527603[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]270222[/C][C]2202.16460082464[/C][C]122.707448797792[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]270267.878048780[/C][C]2166.35739912087[/C][C]124.756828286255[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]270302.58974359[/C][C]2121.83209886167[/C][C]127.391130470975[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]270377.567567568[/C][C]2071.68205713538[/C][C]130.511130622733[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]270463.828571429[/C][C]2015.79550470347[/C][C]134.172255042912[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]270585.606060606[/C][C]1950.41997125726[/C][C]138.731970574617[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]270728.967741935[/C][C]1860.97273181728[/C][C]145.477127694162[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]270852.793103448[/C][C]1770.31394364456[/C][C]152.997039918153[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]270923.444444444[/C][C]1685.92415359112[/C][C]160.697291077634[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]270995.48[/C][C]1592.54111838073[/C][C]170.16545247858[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]271175.347826087[/C][C]1497.98291336384[/C][C]181.026996641197[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]271418.619047619[/C][C]1371.99408661122[/C][C]197.827834461018[/C][/ROW]
[ROW][C]Median[/C][C]271993[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]264120[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]270179.133333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]270728.967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]270728.967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]270728.967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]270728.967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]270035.59375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]270728.967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]270728.967741935[/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=102291&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102291&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 Mean269495.5245901642634.59278534535102.291149542808
Geometric Mean268709.481506259
Harmonic Mean267911.004030331
Quadratic Mean270267.094783666
Winsorized Mean ( 1 / 20 )269483.2622950822622.00871042449102.777409252563
Winsorized Mean ( 2 / 20 )269755.7540983612551.12871833563105.739766151177
Winsorized Mean ( 3 / 20 )269745.8688524592514.23178714588107.287589883935
Winsorized Mean ( 4 / 20 )269684.688524592502.57962228365107.762680604942
Winsorized Mean ( 5 / 20 )270104.5245901642379.03120724191113.535511332491
Winsorized Mean ( 6 / 20 )270215.5737704922341.10581683230115.422195710963
Winsorized Mean ( 7 / 20 )269926.0491803282287.56858148275117.996920995203
Winsorized Mean ( 8 / 20 )269974.5737704922251.98341012668119.883020699209
Winsorized Mean ( 9 / 20 )269944.4754098362236.48319493033120.700426464973
Winsorized Mean ( 10 / 20 )270045.9508196722213.83798658213121.980900344287
Winsorized Mean ( 11 / 20 )269802.3278688522165.59249577828124.585917431289
Winsorized Mean ( 12 / 20 )269783.6393442622108.24014676017127.966275454365
Winsorized Mean ( 13 / 20 )269607.3934426232052.75088045322131.339558058354
Winsorized Mean ( 14 / 20 )269565.6229508202030.77731640689132.740119151897
Winsorized Mean ( 15 / 20 )269845.9508196721906.71907510793141.523706529446
Winsorized Mean ( 16 / 20 )270352.4426229511758.60885711079153.730854663789
Winsorized Mean ( 17 / 20 )270421.5573770491655.35487544956163.361682372553
Winsorized Mean ( 18 / 20 )269774.7377049181512.27357784998178.390168059710
Winsorized Mean ( 19 / 20 )269584.1147540981432.39653897323188.204947037460
Winsorized Mean ( 20 / 20 )270148.7049180331238.86732627053218.061045916261
Trimmed Mean ( 1 / 20 )269677.7457627122556.77355029512105.475803960653
Trimmed Mean ( 2 / 20 )269885.8771929822476.25513604532108.989527478175
Trimmed Mean ( 3 / 20 )269958.0363636362423.81096899975111.377512444810
Trimmed Mean ( 4 / 20 )270039.4339622642375.42423092326113.680508284328
Trimmed Mean ( 5 / 20 )270145.5098039222318.37036330882116.523879911217
Trimmed Mean ( 6 / 20 )270155.7142857142287.20397828119118.116143925534
Trimmed Mean ( 7 / 20 )270142.7659574472256.79925003553119.701726218313
Trimmed Mean ( 8 / 20 )270184.7333333332230.17009348134121.149832527603
Trimmed Mean ( 9 / 20 )2702222202.16460082464122.707448797792
Trimmed Mean ( 10 / 20 )270267.8780487802166.35739912087124.756828286255
Trimmed Mean ( 11 / 20 )270302.589743592121.83209886167127.391130470975
Trimmed Mean ( 12 / 20 )270377.5675675682071.68205713538130.511130622733
Trimmed Mean ( 13 / 20 )270463.8285714292015.79550470347134.172255042912
Trimmed Mean ( 14 / 20 )270585.6060606061950.41997125726138.731970574617
Trimmed Mean ( 15 / 20 )270728.9677419351860.97273181728145.477127694162
Trimmed Mean ( 16 / 20 )270852.7931034481770.31394364456152.997039918153
Trimmed Mean ( 17 / 20 )270923.4444444441685.92415359112160.697291077634
Trimmed Mean ( 18 / 20 )270995.481592.54111838073170.16545247858
Trimmed Mean ( 19 / 20 )271175.3478260871497.98291336384181.026996641197
Trimmed Mean ( 20 / 20 )271418.6190476191371.99408661122197.827834461018
Median271993
Midrange264120
Midmean - Weighted Average at Xnp270179.133333333
Midmean - Weighted Average at X(n+1)p270728.967741935
Midmean - Empirical Distribution Function270728.967741935
Midmean - Empirical Distribution Function - Averaging270728.967741935
Midmean - Empirical Distribution Function - Interpolation270728.967741935
Midmean - Closest Observation270035.59375
Midmean - True Basic - Statistics Graphics Toolkit270728.967741935
Midmean - MS Excel (old versions)270728.967741935
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')