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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 computationTue, 16 Nov 2010 10:00:40 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/16/t1289901542as9kw3kf92mp8df.htm/, Retrieved Sun, 05 May 2024 06:40:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=95315, Retrieved Sun, 05 May 2024 06:40:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact139
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [aandelenmarkt BEL 20] [2009-12-24 09:08:37] [74be16979710d4c4e7c6647856088456]
- RMP   [Central Tendency] [aandelenmarkt BEL 20] [2009-12-24 09:18:26] [74be16979710d4c4e7c6647856088456]
- R  D    [Central Tendency] [WS6 TUT 1] [2010-11-16 09:25:25] [814f53995537cd15c528d8efbf1cf544]
-    D        [Central Tendency] [WS6 TUT 4 central...] [2010-11-16 10:00:40] [da925928e5a77063c5ecc7b801d712e1] [Current]
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Dataseries X:
10407,00
10463,00
10556,00
10646,00
10702,00
11353,00
11346,00
11451,00
11964,00
12574,00
13031,00
13812,00
14544,00
14931,00
14886,00
16005,00
17064,00
15168,00
16050,00
15839,00
15137,00
14954,00
15648,00
15305,00
15579,00
16348,00
15928,00
16171,00
15937,00
15713,00
15594,00
15683,00
16438,00
17032,00
17696,00
17745,00
19394,00
20148,00
20108,00
18584,00
18441,00
18391,00
19178,00
18079,00
18483,00
19644,00
19195,00
19650,00
20830,00
23595,00
22937,00
21814,00
21928,00
21777,00
21383,00
21467,00
22052,00
22680,00
24320,00
24977,00
25204,00




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

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=95315&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=95315&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95315&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'RServer@AstonUniversity' @ vre.aston.ac.uk







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=95315&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=95315&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=95315&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')