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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, 18 Dec 2010 14:24:52 +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/Dec/18/t1292682244h6pd2lxw22gxsm6.htm/, Retrieved Tue, 30 Apr 2024 05:59:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111998, Retrieved Tue, 30 Apr 2024 05:59:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact148
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [paper] [2007-12-11 21:01:08] [b3bb3ec527e23fa7d74d4348b38c8499]
- RMPD  [Univariate Explorative Data Analysis] [PAPER] [2009-12-30 15:50:30] [23722951c28e05bb35cc9a97084fe0d9]
- RMPD    [(Partial) Autocorrelation Function] [Central tendency ...] [2010-12-17 14:53:08] [b659239b537e56f17142ee5c56ad6265]
- RM          [Central Tendency] [Central tendency ...] [2010-12-18 14:24:52] [efffa7146cfe4c2b113f6c7f36d84ca0] [Current]
-    D          [Central Tendency] [Central tendency ...] [2010-12-24 12:40:39] [b659239b537e56f17142ee5c56ad6265]
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Post a new message
Dataseries X:
14544
15116
17413
16181
15607
17160
14915
13768
17487
16198
17535
16571
16198
16554
19554
15903
18003
18329
16260
14851
18174
18406
18466
16016
17428
17167
19630
17183
18344
19301
18147
16192
18374
20515
18957
16471
18746
19009
19211
20547
19325
20605
20056
16141
20359
19711
15638
14384
13855
14308
15290
14423
13779
15686
14733
12522
16189
16059
16007
15806
15160




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111998&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111998&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111998&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean16958.4754098361254.83867778964166.5459244920216
Geometric Mean16842.9545296113
Harmonic Mean16726.9857227833
Quadratic Mean17072.9743550404
Winsorized Mean ( 1 / 20 )16977.9508196721249.44995273889568.0615515587744
Winsorized Mean ( 2 / 20 )16977.2622950820249.12343913087268.1479926349416
Winsorized Mean ( 3 / 20 )16973.3278688525246.54351938661168.8451593093232
Winsorized Mean ( 4 / 20 )16983.1639344262236.17098578171.910458764713
Winsorized Mean ( 5 / 20 )16961.1147540984229.10063422041774.0334692298589
Winsorized Mean ( 6 / 20 )16956.9836065574226.80439863773074.7647916372309
Winsorized Mean ( 7 / 20 )16962.1475409836222.55096774391276.2169120760771
Winsorized Mean ( 8 / 20 )16956.9016393443212.43480993620879.8216716198077
Winsorized Mean ( 9 / 20 )16970.7704918033208.78432199562081.2837397444013
Winsorized Mean ( 10 / 20 )16966.5081967213204.29527091310683.0489522390254
Winsorized Mean ( 11 / 20 )16966.3278688525191.77255101583588.4710965097999
Winsorized Mean ( 12 / 20 )16964.7540983607188.57757119638289.9616746081313
Winsorized Mean ( 13 / 20 )16947.4918032787176.41377191037396.0667164459746
Winsorized Mean ( 14 / 20 )16955.9836065574154.701990075195109.604172501696
Winsorized Mean ( 15 / 20 )16948.8524590164151.212252366036112.086502210077
Winsorized Mean ( 16 / 20 )16953.0491803279148.059411399447114.501665379383
Winsorized Mean ( 17 / 20 )16978.131147541142.034217141581119.535499890263
Winsorized Mean ( 18 / 20 )17002.3278688525137.446320811224123.701585960998
Winsorized Mean ( 19 / 20 )16986.4426229508125.48354675112135.367887366470
Winsorized Mean ( 20 / 20 )16980.5409836066123.706106801499137.265179728385
Trimmed Mean ( 1 / 20 )16971.8644067797244.57912352987869.39212211506
Trimmed Mean ( 2 / 20 )16965.3508771930238.55485896089471.1171885204571
Trimmed Mean ( 3 / 20 )16958.7454545455231.30171707535673.3187183777821
Trimmed Mean ( 4 / 20 )16953.1509433962223.52549653783775.8443721453786
Trimmed Mean ( 5 / 20 )16944.1764705882217.89654804900577.7624823444999
Trimmed Mean ( 6 / 20 )16939.9591836735213.15228212115379.4735060544416
Trimmed Mean ( 7 / 20 )16936.2765957447207.72375607132981.5326899342657
Trimmed Mean ( 8 / 20 )16931.2666666667201.89992620607983.859697152068
Trimmed Mean ( 9 / 20 )16926.7209302326197.08375631967685.8859260972115
Trimmed Mean ( 10 / 20 )16919.4390243902191.59260656078788.3094568632122
Trimmed Mean ( 11 / 20 )16912.0769230769185.37908559853491.2296922194476
Trimmed Mean ( 12 / 20 )16903.9459459459180.30693278109993.7509483701777
Trimmed Mean ( 13 / 20 )16895.1142857143174.03997788313197.0760539688157
Trimmed Mean ( 14 / 20 )16887.6666666667168.665094614784100.125439144576
Trimmed Mean ( 15 / 20 )16878.0645161290166.903796483515101.124509278590
Trimmed Mean ( 16 / 20 )16868.1379310345164.719837713313102.405017909213
Trimmed Mean ( 17 / 20 )16856.1481481481161.733572407216104.221701760890
Trimmed Mean ( 18 / 20 )16838.64158.316990875901106.360283295172
Trimmed Mean ( 19 / 20 )16814.5217391304153.539193919428109.512895762330
Trimmed Mean ( 20 / 20 )16788.2380952381149.712484843161112.136526975859
Median16554
Midrange16563.5
Midmean - Weighted Average at Xnp16827.1333333333
Midmean - Weighted Average at X(n+1)p16878.0645161290
Midmean - Empirical Distribution Function16878.0645161290
Midmean - Empirical Distribution Function - Averaging16878.0645161290
Midmean - Empirical Distribution Function - Interpolation16878.0645161290
Midmean - Closest Observation16838.34375
Midmean - True Basic - Statistics Graphics Toolkit16878.0645161290
Midmean - MS Excel (old versions)16878.0645161290
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 16958.4754098361 & 254.838677789641 & 66.5459244920216 \tabularnewline
Geometric Mean & 16842.9545296113 &  &  \tabularnewline
Harmonic Mean & 16726.9857227833 &  &  \tabularnewline
Quadratic Mean & 17072.9743550404 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 16977.9508196721 & 249.449952738895 & 68.0615515587744 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 16977.2622950820 & 249.123439130872 & 68.1479926349416 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 16973.3278688525 & 246.543519386611 & 68.8451593093232 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 16983.1639344262 & 236.170985781 & 71.910458764713 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 16961.1147540984 & 229.100634220417 & 74.0334692298589 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 16956.9836065574 & 226.804398637730 & 74.7647916372309 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 16962.1475409836 & 222.550967743912 & 76.2169120760771 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 16956.9016393443 & 212.434809936208 & 79.8216716198077 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 16970.7704918033 & 208.784321995620 & 81.2837397444013 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 16966.5081967213 & 204.295270913106 & 83.0489522390254 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 16966.3278688525 & 191.772551015835 & 88.4710965097999 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 16964.7540983607 & 188.577571196382 & 89.9616746081313 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 16947.4918032787 & 176.413771910373 & 96.0667164459746 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 16955.9836065574 & 154.701990075195 & 109.604172501696 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 16948.8524590164 & 151.212252366036 & 112.086502210077 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 16953.0491803279 & 148.059411399447 & 114.501665379383 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 16978.131147541 & 142.034217141581 & 119.535499890263 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 17002.3278688525 & 137.446320811224 & 123.701585960998 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 16986.4426229508 & 125.48354675112 & 135.367887366470 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 16980.5409836066 & 123.706106801499 & 137.265179728385 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 16971.8644067797 & 244.579123529878 & 69.39212211506 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 16965.3508771930 & 238.554858960894 & 71.1171885204571 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 16958.7454545455 & 231.301717075356 & 73.3187183777821 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 16953.1509433962 & 223.525496537837 & 75.8443721453786 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 16944.1764705882 & 217.896548049005 & 77.7624823444999 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 16939.9591836735 & 213.152282121153 & 79.4735060544416 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 16936.2765957447 & 207.723756071329 & 81.5326899342657 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 16931.2666666667 & 201.899926206079 & 83.859697152068 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 16926.7209302326 & 197.083756319676 & 85.8859260972115 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 16919.4390243902 & 191.592606560787 & 88.3094568632122 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 16912.0769230769 & 185.379085598534 & 91.2296922194476 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 16903.9459459459 & 180.306932781099 & 93.7509483701777 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 16895.1142857143 & 174.039977883131 & 97.0760539688157 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 16887.6666666667 & 168.665094614784 & 100.125439144576 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 16878.0645161290 & 166.903796483515 & 101.124509278590 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 16868.1379310345 & 164.719837713313 & 102.405017909213 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 16856.1481481481 & 161.733572407216 & 104.221701760890 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 16838.64 & 158.316990875901 & 106.360283295172 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 16814.5217391304 & 153.539193919428 & 109.512895762330 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 16788.2380952381 & 149.712484843161 & 112.136526975859 \tabularnewline
Median & 16554 &  &  \tabularnewline
Midrange & 16563.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 16827.1333333333 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 16878.0645161290 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 16878.0645161290 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 16878.0645161290 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 16878.0645161290 &  &  \tabularnewline
Midmean - Closest Observation & 16838.34375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 16878.0645161290 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 16878.0645161290 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111998&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]16958.4754098361[/C][C]254.838677789641[/C][C]66.5459244920216[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]16842.9545296113[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]16726.9857227833[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17072.9743550404[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]16977.9508196721[/C][C]249.449952738895[/C][C]68.0615515587744[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]16977.2622950820[/C][C]249.123439130872[/C][C]68.1479926349416[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]16973.3278688525[/C][C]246.543519386611[/C][C]68.8451593093232[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]16983.1639344262[/C][C]236.170985781[/C][C]71.910458764713[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]16961.1147540984[/C][C]229.100634220417[/C][C]74.0334692298589[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]16956.9836065574[/C][C]226.804398637730[/C][C]74.7647916372309[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]16962.1475409836[/C][C]222.550967743912[/C][C]76.2169120760771[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]16956.9016393443[/C][C]212.434809936208[/C][C]79.8216716198077[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]16970.7704918033[/C][C]208.784321995620[/C][C]81.2837397444013[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]16966.5081967213[/C][C]204.295270913106[/C][C]83.0489522390254[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]16966.3278688525[/C][C]191.772551015835[/C][C]88.4710965097999[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]16964.7540983607[/C][C]188.577571196382[/C][C]89.9616746081313[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]16947.4918032787[/C][C]176.413771910373[/C][C]96.0667164459746[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]16955.9836065574[/C][C]154.701990075195[/C][C]109.604172501696[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]16948.8524590164[/C][C]151.212252366036[/C][C]112.086502210077[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]16953.0491803279[/C][C]148.059411399447[/C][C]114.501665379383[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]16978.131147541[/C][C]142.034217141581[/C][C]119.535499890263[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]17002.3278688525[/C][C]137.446320811224[/C][C]123.701585960998[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]16986.4426229508[/C][C]125.48354675112[/C][C]135.367887366470[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]16980.5409836066[/C][C]123.706106801499[/C][C]137.265179728385[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]16971.8644067797[/C][C]244.579123529878[/C][C]69.39212211506[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]16965.3508771930[/C][C]238.554858960894[/C][C]71.1171885204571[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]16958.7454545455[/C][C]231.301717075356[/C][C]73.3187183777821[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]16953.1509433962[/C][C]223.525496537837[/C][C]75.8443721453786[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]16944.1764705882[/C][C]217.896548049005[/C][C]77.7624823444999[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]16939.9591836735[/C][C]213.152282121153[/C][C]79.4735060544416[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]16936.2765957447[/C][C]207.723756071329[/C][C]81.5326899342657[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]16931.2666666667[/C][C]201.899926206079[/C][C]83.859697152068[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]16926.7209302326[/C][C]197.083756319676[/C][C]85.8859260972115[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]16919.4390243902[/C][C]191.592606560787[/C][C]88.3094568632122[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]16912.0769230769[/C][C]185.379085598534[/C][C]91.2296922194476[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]16903.9459459459[/C][C]180.306932781099[/C][C]93.7509483701777[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]16895.1142857143[/C][C]174.039977883131[/C][C]97.0760539688157[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]16887.6666666667[/C][C]168.665094614784[/C][C]100.125439144576[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]16878.0645161290[/C][C]166.903796483515[/C][C]101.124509278590[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]16868.1379310345[/C][C]164.719837713313[/C][C]102.405017909213[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]16856.1481481481[/C][C]161.733572407216[/C][C]104.221701760890[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]16838.64[/C][C]158.316990875901[/C][C]106.360283295172[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]16814.5217391304[/C][C]153.539193919428[/C][C]109.512895762330[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]16788.2380952381[/C][C]149.712484843161[/C][C]112.136526975859[/C][/ROW]
[ROW][C]Median[/C][C]16554[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]16563.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]16827.1333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]16878.0645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]16878.0645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]16878.0645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]16878.0645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]16838.34375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]16878.0645161290[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]16878.0645161290[/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=111998&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111998&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 Mean16958.4754098361254.83867778964166.5459244920216
Geometric Mean16842.9545296113
Harmonic Mean16726.9857227833
Quadratic Mean17072.9743550404
Winsorized Mean ( 1 / 20 )16977.9508196721249.44995273889568.0615515587744
Winsorized Mean ( 2 / 20 )16977.2622950820249.12343913087268.1479926349416
Winsorized Mean ( 3 / 20 )16973.3278688525246.54351938661168.8451593093232
Winsorized Mean ( 4 / 20 )16983.1639344262236.17098578171.910458764713
Winsorized Mean ( 5 / 20 )16961.1147540984229.10063422041774.0334692298589
Winsorized Mean ( 6 / 20 )16956.9836065574226.80439863773074.7647916372309
Winsorized Mean ( 7 / 20 )16962.1475409836222.55096774391276.2169120760771
Winsorized Mean ( 8 / 20 )16956.9016393443212.43480993620879.8216716198077
Winsorized Mean ( 9 / 20 )16970.7704918033208.78432199562081.2837397444013
Winsorized Mean ( 10 / 20 )16966.5081967213204.29527091310683.0489522390254
Winsorized Mean ( 11 / 20 )16966.3278688525191.77255101583588.4710965097999
Winsorized Mean ( 12 / 20 )16964.7540983607188.57757119638289.9616746081313
Winsorized Mean ( 13 / 20 )16947.4918032787176.41377191037396.0667164459746
Winsorized Mean ( 14 / 20 )16955.9836065574154.701990075195109.604172501696
Winsorized Mean ( 15 / 20 )16948.8524590164151.212252366036112.086502210077
Winsorized Mean ( 16 / 20 )16953.0491803279148.059411399447114.501665379383
Winsorized Mean ( 17 / 20 )16978.131147541142.034217141581119.535499890263
Winsorized Mean ( 18 / 20 )17002.3278688525137.446320811224123.701585960998
Winsorized Mean ( 19 / 20 )16986.4426229508125.48354675112135.367887366470
Winsorized Mean ( 20 / 20 )16980.5409836066123.706106801499137.265179728385
Trimmed Mean ( 1 / 20 )16971.8644067797244.57912352987869.39212211506
Trimmed Mean ( 2 / 20 )16965.3508771930238.55485896089471.1171885204571
Trimmed Mean ( 3 / 20 )16958.7454545455231.30171707535673.3187183777821
Trimmed Mean ( 4 / 20 )16953.1509433962223.52549653783775.8443721453786
Trimmed Mean ( 5 / 20 )16944.1764705882217.89654804900577.7624823444999
Trimmed Mean ( 6 / 20 )16939.9591836735213.15228212115379.4735060544416
Trimmed Mean ( 7 / 20 )16936.2765957447207.72375607132981.5326899342657
Trimmed Mean ( 8 / 20 )16931.2666666667201.89992620607983.859697152068
Trimmed Mean ( 9 / 20 )16926.7209302326197.08375631967685.8859260972115
Trimmed Mean ( 10 / 20 )16919.4390243902191.59260656078788.3094568632122
Trimmed Mean ( 11 / 20 )16912.0769230769185.37908559853491.2296922194476
Trimmed Mean ( 12 / 20 )16903.9459459459180.30693278109993.7509483701777
Trimmed Mean ( 13 / 20 )16895.1142857143174.03997788313197.0760539688157
Trimmed Mean ( 14 / 20 )16887.6666666667168.665094614784100.125439144576
Trimmed Mean ( 15 / 20 )16878.0645161290166.903796483515101.124509278590
Trimmed Mean ( 16 / 20 )16868.1379310345164.719837713313102.405017909213
Trimmed Mean ( 17 / 20 )16856.1481481481161.733572407216104.221701760890
Trimmed Mean ( 18 / 20 )16838.64158.316990875901106.360283295172
Trimmed Mean ( 19 / 20 )16814.5217391304153.539193919428109.512895762330
Trimmed Mean ( 20 / 20 )16788.2380952381149.712484843161112.136526975859
Median16554
Midrange16563.5
Midmean - Weighted Average at Xnp16827.1333333333
Midmean - Weighted Average at X(n+1)p16878.0645161290
Midmean - Empirical Distribution Function16878.0645161290
Midmean - Empirical Distribution Function - Averaging16878.0645161290
Midmean - Empirical Distribution Function - Interpolation16878.0645161290
Midmean - Closest Observation16838.34375
Midmean - True Basic - Statistics Graphics Toolkit16878.0645161290
Midmean - MS Excel (old versions)16878.0645161290
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')