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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 computationThu, 17 Nov 2011 18:05:32 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/17/t13215711573yrw1vz6cy27s05.htm/, Retrieved Fri, 19 Apr 2024 11:21:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=145339, Retrieved Fri, 19 Apr 2024 11:21:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central tendency ...] [2011-11-17 23:05:32] [0956ee981dded61b2e7128dae94e5715] [Current]
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Dataseries X:
10407
10463
10556
10646
10702
11353
11346
11451
11964
12574
13031
13812
14544
14931
14886
16005
17064
15168
16050
15839
15137
14954
15648
15305
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745
19394
20148
20108
18584
18441
18391
19178
18079
18483
19644
19195
19650
20830
23595
22937
21814
21928
21777
21383
21467
22052
22680
24320
24977
25204




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.wessa.net

\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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145339&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=145339&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145339&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'AstonUniversity' @ aston.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean17114.0819672131501.98505480065334.0928117352207
Geometric Mean16658.4137753341
Harmonic Mean16190.9092876244
Quadratic Mean17550.2461890163
Winsorized Mean ( 1 / 20 )17111.2786885246500.79442142528134.1682693665501
Winsorized Mean ( 2 / 20 )17092.7868852459494.67805786897834.5533556893141
Winsorized Mean ( 3 / 20 )17061.5573770492485.35908487455735.1524426115539
Winsorized Mean ( 4 / 20 )17022.0819672131475.2284255443935.8187369531058
Winsorized Mean ( 5 / 20 )17053.8032786885459.57387117944337.1078608862639
Winsorized Mean ( 6 / 20 )16992.7213114754447.29983350686837.9895542957194
Winsorized Mean ( 7 / 20 )16989.737704918442.2792579612538.4140503971059
Winsorized Mean ( 8 / 20 )17042.0655737705425.77765168160740.0257399759309
Winsorized Mean ( 9 / 20 )17126.6065573771407.41050931843742.0377142112225
Winsorized Mean ( 10 / 20 )17150.7049180328384.13545136691644.6475451745037
Winsorized Mean ( 11 / 20 )17276.3934426229357.25578786983548.3586103548798
Winsorized Mean ( 12 / 20 )17311.6065573771314.40403618035355.0616549574018
Winsorized Mean ( 13 / 20 )17239.1475409836277.59692427949362.1013636434483
Winsorized Mean ( 14 / 20 )17240.2950819672274.54263043437662.7964227438557
Winsorized Mean ( 15 / 20 )17133.3278688525254.64447274186967.2833291230333
Winsorized Mean ( 16 / 20 )17179.7540983607247.66003895228269.3682928058926
Winsorized Mean ( 17 / 20 )17118.7213114754235.0679301088472.8245716187197
Winsorized Mean ( 18 / 20 )17100.4262295082220.12760762522977.6841506342174
Winsorized Mean ( 19 / 20 )17180.4754098361207.99822746007782.5991433659387
Winsorized Mean ( 20 / 20 )16990.6393442623177.09278700492995.9420179196197
Trimmed Mean ( 1 / 20 )17090.6440677966487.06698298720135.0888987854997
Trimmed Mean ( 2 / 20 )17068.5614035088470.18484008481136.3018114332015
Trimmed Mean ( 3 / 20 )17055.1272727273453.44204508649137.6125845795225
Trimmed Mean ( 4 / 20 )17052.6603773585437.20878920494339.0034711067187
Trimmed Mean ( 5 / 20 )17061.8039215686420.94804301402740.5318523383658
Trimmed Mean ( 6 / 20 )17063.7959183673405.96019959611242.0331745214039
Trimmed Mean ( 7 / 20 )17079.170212766390.75331349409343.7083183250451
Trimmed Mean ( 8 / 20 )17096.4888888889372.61757499367145.8821323421991
Trimmed Mean ( 9 / 20 )17106.1395348837353.99122747136548.3236255798669
Trimmed Mean ( 10 / 20 )17102.756097561334.91151321434451.066491962058
Trimmed Mean ( 11 / 20 )17095.2564102564316.35978535427754.037387814991
Trimmed Mean ( 12 / 20 )17068.1081081081299.06257388508957.0720297306954
Trimmed Mean ( 13 / 20 )17032.7428571429287.79844237482159.1828875674033
Trimmed Mean ( 14 / 20 )17003.3939393939282.41299256596660.2075484732605
Trimmed Mean ( 15 / 20 )16970.0967741935274.85231754893261.7426002644944
Trimmed Mean ( 16 / 20 )16947.2068965517269.54168535884162.8741594235781
Trimmed Mean ( 17 / 20 )16914.3703703704262.61709990557664.406965031797
Trimmed Mean ( 18 / 20 )16885.04255.58910696663166.0632223352322
Trimmed Mean ( 19 / 20 )16853.3043478261248.87044770768567.7191868422296
Trimmed Mean ( 20 / 20 )16803.2857142857240.33344042191569.9165529557056
Median16348
Midrange17805.5
Midmean - Weighted Average at Xnp16880.7666666667
Midmean - Weighted Average at X(n+1)p16970.0967741935
Midmean - Empirical Distribution Function16970.0967741935
Midmean - Empirical Distribution Function - Averaging16970.0967741935
Midmean - Empirical Distribution Function - Interpolation16970.0967741935
Midmean - Closest Observation16906.375
Midmean - True Basic - Statistics Graphics Toolkit16970.0967741935
Midmean - MS Excel (old versions)16970.0967741935
Number of observations61

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 17114.0819672131 & 501.985054800653 & 34.0928117352207 \tabularnewline
Geometric Mean & 16658.4137753341 &  &  \tabularnewline
Harmonic Mean & 16190.9092876244 &  &  \tabularnewline
Quadratic Mean & 17550.2461890163 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 17111.2786885246 & 500.794421425281 & 34.1682693665501 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 17092.7868852459 & 494.678057868978 & 34.5533556893141 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 17061.5573770492 & 485.359084874557 & 35.1524426115539 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 17022.0819672131 & 475.22842554439 & 35.8187369531058 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 17053.8032786885 & 459.573871179443 & 37.1078608862639 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 16992.7213114754 & 447.299833506868 & 37.9895542957194 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 16989.737704918 & 442.27925796125 & 38.4140503971059 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 17042.0655737705 & 425.777651681607 & 40.0257399759309 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 17126.6065573771 & 407.410509318437 & 42.0377142112225 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 17150.7049180328 & 384.135451366916 & 44.6475451745037 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 17276.3934426229 & 357.255787869835 & 48.3586103548798 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 17311.6065573771 & 314.404036180353 & 55.0616549574018 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 17239.1475409836 & 277.596924279493 & 62.1013636434483 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 17240.2950819672 & 274.542630434376 & 62.7964227438557 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 17133.3278688525 & 254.644472741869 & 67.2833291230333 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 17179.7540983607 & 247.660038952282 & 69.3682928058926 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 17118.7213114754 & 235.06793010884 & 72.8245716187197 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 17100.4262295082 & 220.127607625229 & 77.6841506342174 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 17180.4754098361 & 207.998227460077 & 82.5991433659387 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 16990.6393442623 & 177.092787004929 & 95.9420179196197 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 17090.6440677966 & 487.066982987201 & 35.0888987854997 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 17068.5614035088 & 470.184840084811 & 36.3018114332015 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 17055.1272727273 & 453.442045086491 & 37.6125845795225 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 17052.6603773585 & 437.208789204943 & 39.0034711067187 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 17061.8039215686 & 420.948043014027 & 40.5318523383658 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 17063.7959183673 & 405.960199596112 & 42.0331745214039 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 17079.170212766 & 390.753313494093 & 43.7083183250451 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 17096.4888888889 & 372.617574993671 & 45.8821323421991 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 17106.1395348837 & 353.991227471365 & 48.3236255798669 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 17102.756097561 & 334.911513214344 & 51.066491962058 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 17095.2564102564 & 316.359785354277 & 54.037387814991 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 17068.1081081081 & 299.062573885089 & 57.0720297306954 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 17032.7428571429 & 287.798442374821 & 59.1828875674033 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 17003.3939393939 & 282.412992565966 & 60.2075484732605 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 16970.0967741935 & 274.852317548932 & 61.7426002644944 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 16947.2068965517 & 269.541685358841 & 62.8741594235781 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 16914.3703703704 & 262.617099905576 & 64.406965031797 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 16885.04 & 255.589106966631 & 66.0632223352322 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 16853.3043478261 & 248.870447707685 & 67.7191868422296 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 16803.2857142857 & 240.333440421915 & 69.9165529557056 \tabularnewline
Median & 16348 &  &  \tabularnewline
Midrange & 17805.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 16880.7666666667 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 16970.0967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 16970.0967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 16970.0967741935 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 16970.0967741935 &  &  \tabularnewline
Midmean - Closest Observation & 16906.375 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 16970.0967741935 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 16970.0967741935 &  &  \tabularnewline
Number of observations & 61 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=145339&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]17114.0819672131[/C][C]501.985054800653[/C][C]34.0928117352207[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]16658.4137753341[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]16190.9092876244[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]17550.2461890163[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]17111.2786885246[/C][C]500.794421425281[/C][C]34.1682693665501[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]17092.7868852459[/C][C]494.678057868978[/C][C]34.5533556893141[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]17061.5573770492[/C][C]485.359084874557[/C][C]35.1524426115539[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]17022.0819672131[/C][C]475.22842554439[/C][C]35.8187369531058[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]17053.8032786885[/C][C]459.573871179443[/C][C]37.1078608862639[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]16992.7213114754[/C][C]447.299833506868[/C][C]37.9895542957194[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]16989.737704918[/C][C]442.27925796125[/C][C]38.4140503971059[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]17042.0655737705[/C][C]425.777651681607[/C][C]40.0257399759309[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]17126.6065573771[/C][C]407.410509318437[/C][C]42.0377142112225[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]17150.7049180328[/C][C]384.135451366916[/C][C]44.6475451745037[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]17276.3934426229[/C][C]357.255787869835[/C][C]48.3586103548798[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]17311.6065573771[/C][C]314.404036180353[/C][C]55.0616549574018[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]17239.1475409836[/C][C]277.596924279493[/C][C]62.1013636434483[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]17240.2950819672[/C][C]274.542630434376[/C][C]62.7964227438557[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]17133.3278688525[/C][C]254.644472741869[/C][C]67.2833291230333[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]17179.7540983607[/C][C]247.660038952282[/C][C]69.3682928058926[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]17118.7213114754[/C][C]235.06793010884[/C][C]72.8245716187197[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]17100.4262295082[/C][C]220.127607625229[/C][C]77.6841506342174[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]17180.4754098361[/C][C]207.998227460077[/C][C]82.5991433659387[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]16990.6393442623[/C][C]177.092787004929[/C][C]95.9420179196197[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]17090.6440677966[/C][C]487.066982987201[/C][C]35.0888987854997[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]17068.5614035088[/C][C]470.184840084811[/C][C]36.3018114332015[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]17055.1272727273[/C][C]453.442045086491[/C][C]37.6125845795225[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]17052.6603773585[/C][C]437.208789204943[/C][C]39.0034711067187[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]17061.8039215686[/C][C]420.948043014027[/C][C]40.5318523383658[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]17063.7959183673[/C][C]405.960199596112[/C][C]42.0331745214039[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]17079.170212766[/C][C]390.753313494093[/C][C]43.7083183250451[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]17096.4888888889[/C][C]372.617574993671[/C][C]45.8821323421991[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]17106.1395348837[/C][C]353.991227471365[/C][C]48.3236255798669[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]17102.756097561[/C][C]334.911513214344[/C][C]51.066491962058[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]17095.2564102564[/C][C]316.359785354277[/C][C]54.037387814991[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]17068.1081081081[/C][C]299.062573885089[/C][C]57.0720297306954[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]17032.7428571429[/C][C]287.798442374821[/C][C]59.1828875674033[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]17003.3939393939[/C][C]282.412992565966[/C][C]60.2075484732605[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]16970.0967741935[/C][C]274.852317548932[/C][C]61.7426002644944[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]16947.2068965517[/C][C]269.541685358841[/C][C]62.8741594235781[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]16914.3703703704[/C][C]262.617099905576[/C][C]64.406965031797[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]16885.04[/C][C]255.589106966631[/C][C]66.0632223352322[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]16853.3043478261[/C][C]248.870447707685[/C][C]67.7191868422296[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]16803.2857142857[/C][C]240.333440421915[/C][C]69.9165529557056[/C][/ROW]
[ROW][C]Median[/C][C]16348[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]17805.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]16880.7666666667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]16970.0967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]16970.0967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]16970.0967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]16970.0967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]16906.375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]16970.0967741935[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]16970.0967741935[/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=145339&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=145339&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 Mean17114.0819672131501.98505480065334.0928117352207
Geometric Mean16658.4137753341
Harmonic Mean16190.9092876244
Quadratic Mean17550.2461890163
Winsorized Mean ( 1 / 20 )17111.2786885246500.79442142528134.1682693665501
Winsorized Mean ( 2 / 20 )17092.7868852459494.67805786897834.5533556893141
Winsorized Mean ( 3 / 20 )17061.5573770492485.35908487455735.1524426115539
Winsorized Mean ( 4 / 20 )17022.0819672131475.2284255443935.8187369531058
Winsorized Mean ( 5 / 20 )17053.8032786885459.57387117944337.1078608862639
Winsorized Mean ( 6 / 20 )16992.7213114754447.29983350686837.9895542957194
Winsorized Mean ( 7 / 20 )16989.737704918442.2792579612538.4140503971059
Winsorized Mean ( 8 / 20 )17042.0655737705425.77765168160740.0257399759309
Winsorized Mean ( 9 / 20 )17126.6065573771407.41050931843742.0377142112225
Winsorized Mean ( 10 / 20 )17150.7049180328384.13545136691644.6475451745037
Winsorized Mean ( 11 / 20 )17276.3934426229357.25578786983548.3586103548798
Winsorized Mean ( 12 / 20 )17311.6065573771314.40403618035355.0616549574018
Winsorized Mean ( 13 / 20 )17239.1475409836277.59692427949362.1013636434483
Winsorized Mean ( 14 / 20 )17240.2950819672274.54263043437662.7964227438557
Winsorized Mean ( 15 / 20 )17133.3278688525254.64447274186967.2833291230333
Winsorized Mean ( 16 / 20 )17179.7540983607247.66003895228269.3682928058926
Winsorized Mean ( 17 / 20 )17118.7213114754235.0679301088472.8245716187197
Winsorized Mean ( 18 / 20 )17100.4262295082220.12760762522977.6841506342174
Winsorized Mean ( 19 / 20 )17180.4754098361207.99822746007782.5991433659387
Winsorized Mean ( 20 / 20 )16990.6393442623177.09278700492995.9420179196197
Trimmed Mean ( 1 / 20 )17090.6440677966487.06698298720135.0888987854997
Trimmed Mean ( 2 / 20 )17068.5614035088470.18484008481136.3018114332015
Trimmed Mean ( 3 / 20 )17055.1272727273453.44204508649137.6125845795225
Trimmed Mean ( 4 / 20 )17052.6603773585437.20878920494339.0034711067187
Trimmed Mean ( 5 / 20 )17061.8039215686420.94804301402740.5318523383658
Trimmed Mean ( 6 / 20 )17063.7959183673405.96019959611242.0331745214039
Trimmed Mean ( 7 / 20 )17079.170212766390.75331349409343.7083183250451
Trimmed Mean ( 8 / 20 )17096.4888888889372.61757499367145.8821323421991
Trimmed Mean ( 9 / 20 )17106.1395348837353.99122747136548.3236255798669
Trimmed Mean ( 10 / 20 )17102.756097561334.91151321434451.066491962058
Trimmed Mean ( 11 / 20 )17095.2564102564316.35978535427754.037387814991
Trimmed Mean ( 12 / 20 )17068.1081081081299.06257388508957.0720297306954
Trimmed Mean ( 13 / 20 )17032.7428571429287.79844237482159.1828875674033
Trimmed Mean ( 14 / 20 )17003.3939393939282.41299256596660.2075484732605
Trimmed Mean ( 15 / 20 )16970.0967741935274.85231754893261.7426002644944
Trimmed Mean ( 16 / 20 )16947.2068965517269.54168535884162.8741594235781
Trimmed Mean ( 17 / 20 )16914.3703703704262.61709990557664.406965031797
Trimmed Mean ( 18 / 20 )16885.04255.58910696663166.0632223352322
Trimmed Mean ( 19 / 20 )16853.3043478261248.87044770768567.7191868422296
Trimmed Mean ( 20 / 20 )16803.2857142857240.33344042191569.9165529557056
Median16348
Midrange17805.5
Midmean - Weighted Average at Xnp16880.7666666667
Midmean - Weighted Average at X(n+1)p16970.0967741935
Midmean - Empirical Distribution Function16970.0967741935
Midmean - Empirical Distribution Function - Averaging16970.0967741935
Midmean - Empirical Distribution Function - Interpolation16970.0967741935
Midmean - Closest Observation16906.375
Midmean - True Basic - Statistics Graphics Toolkit16970.0967741935
Midmean - MS Excel (old versions)16970.0967741935
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')