Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Oct 2008 15:04:55 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Oct/20/t1224536818qnca8z73ju8o91o.htm/, Retrieved Sun, 19 May 2024 15:37:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18154, Retrieved Sun, 19 May 2024 15:37:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Central Tendency] [Central tendency ...] [2008-10-20 21:04:55] [e81ac192d6ae6d77191d83851a692999] [Current]
Feedback Forum
2008-10-23 14:21:30 [Gregory Van Overmeiren] [reply
De mid-range(196450.5) ligt hier veel hoger dan de median (173246.5). Dit komt doordat de mid-range zéér gevoelig is voor outliers en de median er meer robuuster tegen is.
Als je naar de winsorized mean kijkt, kan je afleiden dat we hier wel degelijk met met outliers te maken hebben. (Winsorized Mean ( 13 / 20 )
179993.083333333 <=> Winsorized Mean ( 14 / 20 ) 177918.283333333 )

2008-10-24 12:32:25 [Kim Wester] [reply
Heldere verwoording in het Word-document. Wellicht hadden daar de waarden in kunnen staan om uw tekst te ondersteunen. Goed dat u naar redenen zoekt voor de neerwaartse tendens van de reeks.

Post a new message
Dataseries X:
136088
134858
135998
148719
152125
149825
145065
144940
150683
149678
148957
153314
159109
158653
158054
162421
167026
167581
169255
168718
176984
173170
169821
173700
172552
171853
171087
171508
173323
169977
171670
171645
175267
173860
174767
174839
174577
171196
178204
184869
186326
185203
189578
194721
201484
200504
210832
212925
219381
215688
222266
227621
235098
235932
243127
246454
253324
248665
251207
258043




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18154&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18154&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18154&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean182905.254225.5473719322443.2855755481358
Geometric Mean180220.738011619
Harmonic Mean177729.714050540
Quadratic Mean185762.725708137
Winsorized Mean ( 1 / 20 )182845.64198.8781241907843.546298461625
Winsorized Mean ( 2 / 20 )182778.0333333334178.478414701743.7427252681839
Winsorized Mean ( 3 / 20 )183093.5333333334066.2688769140345.0274044524784
Winsorized Mean ( 4 / 20 )182954.4666666674025.0892296995545.4535182268054
Winsorized Mean ( 5 / 20 )182981.7166666673904.8609208717346.8599830761238
Winsorized Mean ( 6 / 20 )182286.0166666673719.2738726565749.0111841472069
Winsorized Mean ( 7 / 20 )182272.8333333333682.8552686024349.4922607704055
Winsorized Mean ( 8 / 20 )181295.53444.8184318670752.6284631790417
Winsorized Mean ( 9 / 20 )180620.953245.7901179074555.6477601566074
Winsorized Mean ( 10 / 20 )180380.453104.9745472746158.0940188892463
Winsorized Mean ( 11 / 20 )179921.3833333332929.1951111050761.4234888796657
Winsorized Mean ( 12 / 20 )180316.7833333332674.7976480930167.4132428155416
Winsorized Mean ( 13 / 20 )179993.0833333332563.3891169965970.2168399404861
Winsorized Mean ( 14 / 20 )177918.2833333332118.3123411404883.9905805569465
Winsorized Mean ( 15 / 20 )178501.2833333331951.5085687326991.4683574508988
Winsorized Mean ( 16 / 20 )178187.151494.70110267632119.212563422178
Winsorized Mean ( 17 / 20 )176887.2166666671207.38974490302146.503825639892
Winsorized Mean ( 18 / 20 )176252.716666667991.972388640833177.679055067412
Winsorized Mean ( 19 / 20 )176067.15909.328037688885193.623360000518
Winsorized Mean ( 20 / 20 )176144.483333333866.700943637139203.235596576297
Trimmed Mean ( 1 / 20 )182438.1724137934087.6924899508344.6310902452419
Trimmed Mean ( 2 / 20 )182001.6428571433949.7062444960146.0797921644846
Trimmed Mean ( 3 / 20 )181570.3148148153791.4290675733747.8896773693369
Trimmed Mean ( 4 / 20 )180984.4615384623647.3371857220849.6209843847029
Trimmed Mean ( 5 / 20 )180393.463480.898632532651.8238188018566
Trimmed Mean ( 6 / 20 )179746.3958333333310.6680526075754.293089182336
Trimmed Mean ( 7 / 20 )179194.3043478263155.2509522785456.7924095604574
Trimmed Mean ( 8 / 20 )178594.5909090912961.6871245989260.3016400435198
Trimmed Mean ( 9 / 20 )178112.2857142862784.8521462588163.9575375495474
Trimmed Mean ( 10 / 20 )177694.1752612.3342150532468.0212256058433
Trimmed Mean ( 11 / 20 )177270.0263157892421.9659365580673.1926174683175
Trimmed Mean ( 12 / 20 )176868.3055555562216.7902843509579.7857635898745
Trimmed Mean ( 13 / 20 )176361.1764705882009.1220497573187.7802204658954
Trimmed Mean ( 14 / 20 )175837.343751744.35584954951100.803596809338
Trimmed Mean ( 15 / 20 )175540.0666666671545.5518078186113.577601073383
Trimmed Mean ( 16 / 20 )175117.0357142861300.12047516865134.692929662207
Trimmed Mean ( 17 / 20 )174674.2307692311125.23403419732155.233689579816
Trimmed Mean ( 18 / 20 )174348.791666667996.388811141512174.980679948548
Trimmed Mean ( 19 / 20 )174060.318181818896.156220404422194.229883382684
Trimmed Mean ( 20 / 20 )173743.45763.943696172076227.429653350873
Median173246.5
Midrange196450.5
Midmean - Weighted Average at Xnp175010.032258065
Midmean - Weighted Average at X(n+1)p175540.066666667
Midmean - Empirical Distribution Function175010.032258065
Midmean - Empirical Distribution Function - Averaging175540.066666667
Midmean - Empirical Distribution Function - Interpolation175540.066666667
Midmean - Closest Observation175010.032258065
Midmean - True Basic - Statistics Graphics Toolkit175540.066666667
Midmean - MS Excel (old versions)175837.34375
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 182905.25 & 4225.54737193224 & 43.2855755481358 \tabularnewline
Geometric Mean & 180220.738011619 &  &  \tabularnewline
Harmonic Mean & 177729.714050540 &  &  \tabularnewline
Quadratic Mean & 185762.725708137 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 182845.6 & 4198.87812419078 & 43.546298461625 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 182778.033333333 & 4178.4784147017 & 43.7427252681839 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 183093.533333333 & 4066.26887691403 & 45.0274044524784 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 182954.466666667 & 4025.08922969955 & 45.4535182268054 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 182981.716666667 & 3904.86092087173 & 46.8599830761238 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 182286.016666667 & 3719.27387265657 & 49.0111841472069 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 182272.833333333 & 3682.85526860243 & 49.4922607704055 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 181295.5 & 3444.81843186707 & 52.6284631790417 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 180620.95 & 3245.79011790745 & 55.6477601566074 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 180380.45 & 3104.97454727461 & 58.0940188892463 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 179921.383333333 & 2929.19511110507 & 61.4234888796657 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 180316.783333333 & 2674.79764809301 & 67.4132428155416 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 179993.083333333 & 2563.38911699659 & 70.2168399404861 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 177918.283333333 & 2118.31234114048 & 83.9905805569465 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 178501.283333333 & 1951.50856873269 & 91.4683574508988 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 178187.15 & 1494.70110267632 & 119.212563422178 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 176887.216666667 & 1207.38974490302 & 146.503825639892 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 176252.716666667 & 991.972388640833 & 177.679055067412 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 176067.15 & 909.328037688885 & 193.623360000518 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 176144.483333333 & 866.700943637139 & 203.235596576297 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 182438.172413793 & 4087.69248995083 & 44.6310902452419 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 182001.642857143 & 3949.70624449601 & 46.0797921644846 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 181570.314814815 & 3791.42906757337 & 47.8896773693369 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 180984.461538462 & 3647.33718572208 & 49.6209843847029 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 180393.46 & 3480.8986325326 & 51.8238188018566 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 179746.395833333 & 3310.66805260757 & 54.293089182336 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 179194.304347826 & 3155.25095227854 & 56.7924095604574 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 178594.590909091 & 2961.68712459892 & 60.3016400435198 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 178112.285714286 & 2784.85214625881 & 63.9575375495474 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 177694.175 & 2612.33421505324 & 68.0212256058433 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 177270.026315789 & 2421.96593655806 & 73.1926174683175 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 176868.305555556 & 2216.79028435095 & 79.7857635898745 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 176361.176470588 & 2009.12204975731 & 87.7802204658954 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 175837.34375 & 1744.35584954951 & 100.803596809338 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 175540.066666667 & 1545.5518078186 & 113.577601073383 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 175117.035714286 & 1300.12047516865 & 134.692929662207 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 174674.230769231 & 1125.23403419732 & 155.233689579816 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 174348.791666667 & 996.388811141512 & 174.980679948548 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 174060.318181818 & 896.156220404422 & 194.229883382684 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 173743.45 & 763.943696172076 & 227.429653350873 \tabularnewline
Median & 173246.5 &  &  \tabularnewline
Midrange & 196450.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 175010.032258065 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 175540.066666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 175010.032258065 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 175540.066666667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 175540.066666667 &  &  \tabularnewline
Midmean - Closest Observation & 175010.032258065 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 175540.066666667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 175837.34375 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18154&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]182905.25[/C][C]4225.54737193224[/C][C]43.2855755481358[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]180220.738011619[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]177729.714050540[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]185762.725708137[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]182845.6[/C][C]4198.87812419078[/C][C]43.546298461625[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]182778.033333333[/C][C]4178.4784147017[/C][C]43.7427252681839[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]183093.533333333[/C][C]4066.26887691403[/C][C]45.0274044524784[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]182954.466666667[/C][C]4025.08922969955[/C][C]45.4535182268054[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]182981.716666667[/C][C]3904.86092087173[/C][C]46.8599830761238[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]182286.016666667[/C][C]3719.27387265657[/C][C]49.0111841472069[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]182272.833333333[/C][C]3682.85526860243[/C][C]49.4922607704055[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]181295.5[/C][C]3444.81843186707[/C][C]52.6284631790417[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]180620.95[/C][C]3245.79011790745[/C][C]55.6477601566074[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]180380.45[/C][C]3104.97454727461[/C][C]58.0940188892463[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]179921.383333333[/C][C]2929.19511110507[/C][C]61.4234888796657[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]180316.783333333[/C][C]2674.79764809301[/C][C]67.4132428155416[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]179993.083333333[/C][C]2563.38911699659[/C][C]70.2168399404861[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]177918.283333333[/C][C]2118.31234114048[/C][C]83.9905805569465[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]178501.283333333[/C][C]1951.50856873269[/C][C]91.4683574508988[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]178187.15[/C][C]1494.70110267632[/C][C]119.212563422178[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]176887.216666667[/C][C]1207.38974490302[/C][C]146.503825639892[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]176252.716666667[/C][C]991.972388640833[/C][C]177.679055067412[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]176067.15[/C][C]909.328037688885[/C][C]193.623360000518[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]176144.483333333[/C][C]866.700943637139[/C][C]203.235596576297[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]182438.172413793[/C][C]4087.69248995083[/C][C]44.6310902452419[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]182001.642857143[/C][C]3949.70624449601[/C][C]46.0797921644846[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]181570.314814815[/C][C]3791.42906757337[/C][C]47.8896773693369[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]180984.461538462[/C][C]3647.33718572208[/C][C]49.6209843847029[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]180393.46[/C][C]3480.8986325326[/C][C]51.8238188018566[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]179746.395833333[/C][C]3310.66805260757[/C][C]54.293089182336[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]179194.304347826[/C][C]3155.25095227854[/C][C]56.7924095604574[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]178594.590909091[/C][C]2961.68712459892[/C][C]60.3016400435198[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]178112.285714286[/C][C]2784.85214625881[/C][C]63.9575375495474[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]177694.175[/C][C]2612.33421505324[/C][C]68.0212256058433[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]177270.026315789[/C][C]2421.96593655806[/C][C]73.1926174683175[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]176868.305555556[/C][C]2216.79028435095[/C][C]79.7857635898745[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]176361.176470588[/C][C]2009.12204975731[/C][C]87.7802204658954[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]175837.34375[/C][C]1744.35584954951[/C][C]100.803596809338[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]175540.066666667[/C][C]1545.5518078186[/C][C]113.577601073383[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]175117.035714286[/C][C]1300.12047516865[/C][C]134.692929662207[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]174674.230769231[/C][C]1125.23403419732[/C][C]155.233689579816[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]174348.791666667[/C][C]996.388811141512[/C][C]174.980679948548[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]174060.318181818[/C][C]896.156220404422[/C][C]194.229883382684[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]173743.45[/C][C]763.943696172076[/C][C]227.429653350873[/C][/ROW]
[ROW][C]Median[/C][C]173246.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]196450.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]175010.032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]175540.066666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]175010.032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]175540.066666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]175540.066666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]175010.032258065[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]175540.066666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]175837.34375[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=18154&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18154&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 Mean182905.254225.5473719322443.2855755481358
Geometric Mean180220.738011619
Harmonic Mean177729.714050540
Quadratic Mean185762.725708137
Winsorized Mean ( 1 / 20 )182845.64198.8781241907843.546298461625
Winsorized Mean ( 2 / 20 )182778.0333333334178.478414701743.7427252681839
Winsorized Mean ( 3 / 20 )183093.5333333334066.2688769140345.0274044524784
Winsorized Mean ( 4 / 20 )182954.4666666674025.0892296995545.4535182268054
Winsorized Mean ( 5 / 20 )182981.7166666673904.8609208717346.8599830761238
Winsorized Mean ( 6 / 20 )182286.0166666673719.2738726565749.0111841472069
Winsorized Mean ( 7 / 20 )182272.8333333333682.8552686024349.4922607704055
Winsorized Mean ( 8 / 20 )181295.53444.8184318670752.6284631790417
Winsorized Mean ( 9 / 20 )180620.953245.7901179074555.6477601566074
Winsorized Mean ( 10 / 20 )180380.453104.9745472746158.0940188892463
Winsorized Mean ( 11 / 20 )179921.3833333332929.1951111050761.4234888796657
Winsorized Mean ( 12 / 20 )180316.7833333332674.7976480930167.4132428155416
Winsorized Mean ( 13 / 20 )179993.0833333332563.3891169965970.2168399404861
Winsorized Mean ( 14 / 20 )177918.2833333332118.3123411404883.9905805569465
Winsorized Mean ( 15 / 20 )178501.2833333331951.5085687326991.4683574508988
Winsorized Mean ( 16 / 20 )178187.151494.70110267632119.212563422178
Winsorized Mean ( 17 / 20 )176887.2166666671207.38974490302146.503825639892
Winsorized Mean ( 18 / 20 )176252.716666667991.972388640833177.679055067412
Winsorized Mean ( 19 / 20 )176067.15909.328037688885193.623360000518
Winsorized Mean ( 20 / 20 )176144.483333333866.700943637139203.235596576297
Trimmed Mean ( 1 / 20 )182438.1724137934087.6924899508344.6310902452419
Trimmed Mean ( 2 / 20 )182001.6428571433949.7062444960146.0797921644846
Trimmed Mean ( 3 / 20 )181570.3148148153791.4290675733747.8896773693369
Trimmed Mean ( 4 / 20 )180984.4615384623647.3371857220849.6209843847029
Trimmed Mean ( 5 / 20 )180393.463480.898632532651.8238188018566
Trimmed Mean ( 6 / 20 )179746.3958333333310.6680526075754.293089182336
Trimmed Mean ( 7 / 20 )179194.3043478263155.2509522785456.7924095604574
Trimmed Mean ( 8 / 20 )178594.5909090912961.6871245989260.3016400435198
Trimmed Mean ( 9 / 20 )178112.2857142862784.8521462588163.9575375495474
Trimmed Mean ( 10 / 20 )177694.1752612.3342150532468.0212256058433
Trimmed Mean ( 11 / 20 )177270.0263157892421.9659365580673.1926174683175
Trimmed Mean ( 12 / 20 )176868.3055555562216.7902843509579.7857635898745
Trimmed Mean ( 13 / 20 )176361.1764705882009.1220497573187.7802204658954
Trimmed Mean ( 14 / 20 )175837.343751744.35584954951100.803596809338
Trimmed Mean ( 15 / 20 )175540.0666666671545.5518078186113.577601073383
Trimmed Mean ( 16 / 20 )175117.0357142861300.12047516865134.692929662207
Trimmed Mean ( 17 / 20 )174674.2307692311125.23403419732155.233689579816
Trimmed Mean ( 18 / 20 )174348.791666667996.388811141512174.980679948548
Trimmed Mean ( 19 / 20 )174060.318181818896.156220404422194.229883382684
Trimmed Mean ( 20 / 20 )173743.45763.943696172076227.429653350873
Median173246.5
Midrange196450.5
Midmean - Weighted Average at Xnp175010.032258065
Midmean - Weighted Average at X(n+1)p175540.066666667
Midmean - Empirical Distribution Function175010.032258065
Midmean - Empirical Distribution Function - Averaging175540.066666667
Midmean - Empirical Distribution Function - Interpolation175540.066666667
Midmean - Closest Observation175010.032258065
Midmean - True Basic - Statistics Graphics Toolkit175540.066666667
Midmean - MS Excel (old versions)175837.34375
Number of observations60



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')