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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSun, 21 Dec 2008 04:46:13 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/21/t1229861343uhl06pgb25dwn5j.htm/, Retrieved Sat, 18 May 2024 08:57:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35523, Retrieved Sat, 18 May 2024 08:57:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency V1] [2008-12-21 11:46:13] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
107,1
110,7
117,1
118,7
126,5
127,5
134,6
131,8
135,9
142,7
141,7
153,4
145
137,7
148,3
152,2
169,4
168,6
161,1
174,1
179
190,6
190
181,6
174,8
180,5
196,8
193,8
197
216,3
221,4
217,9
229,7
227,4
204,2
196,6
198,8
207,5
190,7
201,6
210,5
223,5
223,8
231,2
244
234,7
250,2
265,7
287,6
283,3
295,4
312,3
333,8
347,7
383,2
407,1
413,6
362,7
321,9
239,4
191




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35523&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35523&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35523&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean210.8672131147549.489142118718822.2219469870502
Geometric Mean199.426356796692
Harmonic Mean189.227980781031
Quadratic Mean223.310569959726
Winsorized Mean ( 1 / 20 )210.8196721311489.4411145434924722.3299559771214
Winsorized Mean ( 2 / 20 )210.2459016393449.145299361044322.989504590185
Winsorized Mean ( 3 / 20 )209.3163934426238.8267750208981323.7138018072341
Winsorized Mean ( 4 / 20 )208.8442622950828.4644391215584524.6731365535098
Winsorized Mean ( 5 / 20 )207.7868852459028.1483091797365125.500613766919
Winsorized Mean ( 6 / 20 )207.0393442622957.7845743076486526.5961035350219
Winsorized Mean ( 7 / 20 )206.2590163934437.4670629689846927.622509311916
Winsorized Mean ( 8 / 20 )204.2131147540986.9335213596600729.4530158863043
Winsorized Mean ( 9 / 20 )203.3278688524596.6419502744972230.612675562051
Winsorized Mean ( 10 / 20 )203.278688524596.387099838183131.8264460670174
Winsorized Mean ( 11 / 20 )200.2852459016395.7222276968472735.0012716222371
Winsorized Mean ( 12 / 20 )197.6885245901645.091104477398338.8301841904428
Winsorized Mean ( 13 / 20 )197.0704918032794.7476559325515941.5090087830701
Winsorized Mean ( 14 / 20 )196.9098360655744.4240591015467144.5088620079084
Winsorized Mean ( 15 / 20 )196.0491803278694.1928156240949546.7583595141242
Winsorized Mean ( 16 / 20 )197.1508196721313.7172861766155353.0362232836296
Winsorized Mean ( 17 / 20 )198.8229508196723.3252284472592959.7922681022248
Winsorized Mean ( 18 / 20 )198.3803278688523.1853874181444362.2782418047014
Winsorized Mean ( 19 / 20 )198.7229508196722.7978283864480271.027569733096
Winsorized Mean ( 20 / 20 )198.8540983606562.7495698359741472.3218940500939
Trimmed Mean ( 1 / 20 )209.1898305084759.0055855435050223.2288982762865
Trimmed Mean ( 2 / 20 )207.4456140350888.4605094254389524.5192817126759
Trimmed Mean ( 3 / 20 )205.8927272727277.9835583800529425.7895937464620
Trimmed Mean ( 4 / 20 )204.5792452830197.5480311827028727.1036566133741
Trimmed Mean ( 5 / 20 )203.3039215686277.1497730449565228.4350174880081
Trimmed Mean ( 6 / 20 )202.1877551020416.7611583462025229.9043070357318
Trimmed Mean ( 7 / 20 )201.1382978723406.3864294095422831.4946404280003
Trimmed Mean ( 8 / 20 )200.1466666666676.003023312372633.3409777460221
Trimmed Mean ( 9 / 20 )199.4255813953495.6733070594046635.1515578668989
Trimmed Mean ( 10 / 20 )198.7804878048785.326350990321637.320200671356
Trimmed Mean ( 11 / 20 )198.0769230769234.9358768949920540.1300371323872
Trimmed Mean ( 12 / 20 )197.7459459459464.6225595697508142.7784527083132
Trimmed Mean ( 13 / 20 )197.7542857142864.3895106881784345.0515558025331
Trimmed Mean ( 14 / 20 )197.8515151515154.1678766149566347.4705787694183
Trimmed Mean ( 15 / 20 )197.9838709677423.9530989525279150.0832064527846
Trimmed Mean ( 16 / 20 )198.2551724137933.7131061519617753.3933489375324
Trimmed Mean ( 17 / 20 )198.4111111111113.5261834340595956.2679494193773
Trimmed Mean ( 18 / 20 )198.3523.381533774290458.657406147488
Trimmed Mean ( 19 / 20 )198.3478260869573.1992024053263361.9991488368253
Trimmed Mean ( 20 / 20 )198.2904761904763.0640069063230764.716066984468
Median196.8
Midrange260.35
Midmean - Weighted Average at Xnp196.76
Midmean - Weighted Average at X(n+1)p197.983870967742
Midmean - Empirical Distribution Function197.983870967742
Midmean - Empirical Distribution Function - Averaging197.983870967742
Midmean - Empirical Distribution Function - Interpolation197.983870967742
Midmean - Closest Observation196.553125
Midmean - True Basic - Statistics Graphics Toolkit197.983870967742
Midmean - MS Excel (old versions)197.983870967742
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 210.867213114754 & 9.4891421187188 & 22.2219469870502 \tabularnewline
Geometric Mean & 199.426356796692 &  &  \tabularnewline
Harmonic Mean & 189.227980781031 &  &  \tabularnewline
Quadratic Mean & 223.310569959726 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 210.819672131148 & 9.44111454349247 & 22.3299559771214 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 210.245901639344 & 9.1452993610443 & 22.989504590185 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 209.316393442623 & 8.82677502089813 & 23.7138018072341 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 208.844262295082 & 8.46443912155845 & 24.6731365535098 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 207.786885245902 & 8.14830917973651 & 25.500613766919 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 207.039344262295 & 7.78457430764865 & 26.5961035350219 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 206.259016393443 & 7.46706296898469 & 27.622509311916 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 204.213114754098 & 6.93352135966007 & 29.4530158863043 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 203.327868852459 & 6.64195027449722 & 30.612675562051 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 203.27868852459 & 6.3870998381831 & 31.8264460670174 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 200.285245901639 & 5.72222769684727 & 35.0012716222371 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 197.688524590164 & 5.0911044773983 & 38.8301841904428 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 197.070491803279 & 4.74765593255159 & 41.5090087830701 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 196.909836065574 & 4.42405910154671 & 44.5088620079084 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 196.049180327869 & 4.19281562409495 & 46.7583595141242 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 197.150819672131 & 3.71728617661553 & 53.0362232836296 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 198.822950819672 & 3.32522844725929 & 59.7922681022248 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 198.380327868852 & 3.18538741814443 & 62.2782418047014 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 198.722950819672 & 2.79782838644802 & 71.027569733096 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 198.854098360656 & 2.74956983597414 & 72.3218940500939 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 209.189830508475 & 9.00558554350502 & 23.2288982762865 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 207.445614035088 & 8.46050942543895 & 24.5192817126759 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 205.892727272727 & 7.98355838005294 & 25.7895937464620 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 204.579245283019 & 7.54803118270287 & 27.1036566133741 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 203.303921568627 & 7.14977304495652 & 28.4350174880081 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 202.187755102041 & 6.76115834620252 & 29.9043070357318 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 201.138297872340 & 6.38642940954228 & 31.4946404280003 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 200.146666666667 & 6.0030233123726 & 33.3409777460221 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 199.425581395349 & 5.67330705940466 & 35.1515578668989 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 198.780487804878 & 5.3263509903216 & 37.320200671356 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 198.076923076923 & 4.93587689499205 & 40.1300371323872 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 197.745945945946 & 4.62255956975081 & 42.7784527083132 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 197.754285714286 & 4.38951068817843 & 45.0515558025331 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 197.851515151515 & 4.16787661495663 & 47.4705787694183 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 197.983870967742 & 3.95309895252791 & 50.0832064527846 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 198.255172413793 & 3.71310615196177 & 53.3933489375324 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 198.411111111111 & 3.52618343405959 & 56.2679494193773 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 198.352 & 3.3815337742904 & 58.657406147488 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 198.347826086957 & 3.19920240532633 & 61.9991488368253 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 198.290476190476 & 3.06400690632307 & 64.716066984468 \tabularnewline
Median & 196.8 &  &  \tabularnewline
Midrange & 260.35 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 196.76 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 197.983870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 197.983870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 197.983870967742 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 197.983870967742 &  &  \tabularnewline
Midmean - Closest Observation & 196.553125 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 197.983870967742 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 197.983870967742 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35523&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]210.867213114754[/C][C]9.4891421187188[/C][C]22.2219469870502[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]199.426356796692[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]189.227980781031[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]223.310569959726[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]210.819672131148[/C][C]9.44111454349247[/C][C]22.3299559771214[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]210.245901639344[/C][C]9.1452993610443[/C][C]22.989504590185[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]209.316393442623[/C][C]8.82677502089813[/C][C]23.7138018072341[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]208.844262295082[/C][C]8.46443912155845[/C][C]24.6731365535098[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]207.786885245902[/C][C]8.14830917973651[/C][C]25.500613766919[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]207.039344262295[/C][C]7.78457430764865[/C][C]26.5961035350219[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]206.259016393443[/C][C]7.46706296898469[/C][C]27.622509311916[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]204.213114754098[/C][C]6.93352135966007[/C][C]29.4530158863043[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]203.327868852459[/C][C]6.64195027449722[/C][C]30.612675562051[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]203.27868852459[/C][C]6.3870998381831[/C][C]31.8264460670174[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]200.285245901639[/C][C]5.72222769684727[/C][C]35.0012716222371[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]197.688524590164[/C][C]5.0911044773983[/C][C]38.8301841904428[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]197.070491803279[/C][C]4.74765593255159[/C][C]41.5090087830701[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]196.909836065574[/C][C]4.42405910154671[/C][C]44.5088620079084[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]196.049180327869[/C][C]4.19281562409495[/C][C]46.7583595141242[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]197.150819672131[/C][C]3.71728617661553[/C][C]53.0362232836296[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]198.822950819672[/C][C]3.32522844725929[/C][C]59.7922681022248[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]198.380327868852[/C][C]3.18538741814443[/C][C]62.2782418047014[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]198.722950819672[/C][C]2.79782838644802[/C][C]71.027569733096[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]198.854098360656[/C][C]2.74956983597414[/C][C]72.3218940500939[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]209.189830508475[/C][C]9.00558554350502[/C][C]23.2288982762865[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]207.445614035088[/C][C]8.46050942543895[/C][C]24.5192817126759[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]205.892727272727[/C][C]7.98355838005294[/C][C]25.7895937464620[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]204.579245283019[/C][C]7.54803118270287[/C][C]27.1036566133741[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]203.303921568627[/C][C]7.14977304495652[/C][C]28.4350174880081[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]202.187755102041[/C][C]6.76115834620252[/C][C]29.9043070357318[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]201.138297872340[/C][C]6.38642940954228[/C][C]31.4946404280003[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]200.146666666667[/C][C]6.0030233123726[/C][C]33.3409777460221[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]199.425581395349[/C][C]5.67330705940466[/C][C]35.1515578668989[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]198.780487804878[/C][C]5.3263509903216[/C][C]37.320200671356[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]198.076923076923[/C][C]4.93587689499205[/C][C]40.1300371323872[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]197.745945945946[/C][C]4.62255956975081[/C][C]42.7784527083132[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]197.754285714286[/C][C]4.38951068817843[/C][C]45.0515558025331[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]197.851515151515[/C][C]4.16787661495663[/C][C]47.4705787694183[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]197.983870967742[/C][C]3.95309895252791[/C][C]50.0832064527846[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]198.255172413793[/C][C]3.71310615196177[/C][C]53.3933489375324[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]198.411111111111[/C][C]3.52618343405959[/C][C]56.2679494193773[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]198.352[/C][C]3.3815337742904[/C][C]58.657406147488[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]198.347826086957[/C][C]3.19920240532633[/C][C]61.9991488368253[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]198.290476190476[/C][C]3.06400690632307[/C][C]64.716066984468[/C][/ROW]
[ROW][C]Median[/C][C]196.8[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]260.35[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]196.76[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]197.983870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]197.983870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]197.983870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]197.983870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]196.553125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]197.983870967742[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]197.983870967742[/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=35523&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35523&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 Mean210.8672131147549.489142118718822.2219469870502
Geometric Mean199.426356796692
Harmonic Mean189.227980781031
Quadratic Mean223.310569959726
Winsorized Mean ( 1 / 20 )210.8196721311489.4411145434924722.3299559771214
Winsorized Mean ( 2 / 20 )210.2459016393449.145299361044322.989504590185
Winsorized Mean ( 3 / 20 )209.3163934426238.8267750208981323.7138018072341
Winsorized Mean ( 4 / 20 )208.8442622950828.4644391215584524.6731365535098
Winsorized Mean ( 5 / 20 )207.7868852459028.1483091797365125.500613766919
Winsorized Mean ( 6 / 20 )207.0393442622957.7845743076486526.5961035350219
Winsorized Mean ( 7 / 20 )206.2590163934437.4670629689846927.622509311916
Winsorized Mean ( 8 / 20 )204.2131147540986.9335213596600729.4530158863043
Winsorized Mean ( 9 / 20 )203.3278688524596.6419502744972230.612675562051
Winsorized Mean ( 10 / 20 )203.278688524596.387099838183131.8264460670174
Winsorized Mean ( 11 / 20 )200.2852459016395.7222276968472735.0012716222371
Winsorized Mean ( 12 / 20 )197.6885245901645.091104477398338.8301841904428
Winsorized Mean ( 13 / 20 )197.0704918032794.7476559325515941.5090087830701
Winsorized Mean ( 14 / 20 )196.9098360655744.4240591015467144.5088620079084
Winsorized Mean ( 15 / 20 )196.0491803278694.1928156240949546.7583595141242
Winsorized Mean ( 16 / 20 )197.1508196721313.7172861766155353.0362232836296
Winsorized Mean ( 17 / 20 )198.8229508196723.3252284472592959.7922681022248
Winsorized Mean ( 18 / 20 )198.3803278688523.1853874181444362.2782418047014
Winsorized Mean ( 19 / 20 )198.7229508196722.7978283864480271.027569733096
Winsorized Mean ( 20 / 20 )198.8540983606562.7495698359741472.3218940500939
Trimmed Mean ( 1 / 20 )209.1898305084759.0055855435050223.2288982762865
Trimmed Mean ( 2 / 20 )207.4456140350888.4605094254389524.5192817126759
Trimmed Mean ( 3 / 20 )205.8927272727277.9835583800529425.7895937464620
Trimmed Mean ( 4 / 20 )204.5792452830197.5480311827028727.1036566133741
Trimmed Mean ( 5 / 20 )203.3039215686277.1497730449565228.4350174880081
Trimmed Mean ( 6 / 20 )202.1877551020416.7611583462025229.9043070357318
Trimmed Mean ( 7 / 20 )201.1382978723406.3864294095422831.4946404280003
Trimmed Mean ( 8 / 20 )200.1466666666676.003023312372633.3409777460221
Trimmed Mean ( 9 / 20 )199.4255813953495.6733070594046635.1515578668989
Trimmed Mean ( 10 / 20 )198.7804878048785.326350990321637.320200671356
Trimmed Mean ( 11 / 20 )198.0769230769234.9358768949920540.1300371323872
Trimmed Mean ( 12 / 20 )197.7459459459464.6225595697508142.7784527083132
Trimmed Mean ( 13 / 20 )197.7542857142864.3895106881784345.0515558025331
Trimmed Mean ( 14 / 20 )197.8515151515154.1678766149566347.4705787694183
Trimmed Mean ( 15 / 20 )197.9838709677423.9530989525279150.0832064527846
Trimmed Mean ( 16 / 20 )198.2551724137933.7131061519617753.3933489375324
Trimmed Mean ( 17 / 20 )198.4111111111113.5261834340595956.2679494193773
Trimmed Mean ( 18 / 20 )198.3523.381533774290458.657406147488
Trimmed Mean ( 19 / 20 )198.3478260869573.1992024053263361.9991488368253
Trimmed Mean ( 20 / 20 )198.2904761904763.0640069063230764.716066984468
Median196.8
Midrange260.35
Midmean - Weighted Average at Xnp196.76
Midmean - Weighted Average at X(n+1)p197.983870967742
Midmean - Empirical Distribution Function197.983870967742
Midmean - Empirical Distribution Function - Averaging197.983870967742
Midmean - Empirical Distribution Function - Interpolation197.983870967742
Midmean - Closest Observation196.553125
Midmean - True Basic - Statistics Graphics Toolkit197.983870967742
Midmean - MS Excel (old versions)197.983870967742
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')