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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, 20 Oct 2009 14:34:30 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/20/t1256071045ll3gipb6dder47i.htm/, Retrieved Thu, 02 May 2024 14:33:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49141, Retrieved Thu, 02 May 2024 14:33:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [Central Tendency ...] [2009-10-20 20:34:30] [557d56ec4b06cd0135c259898de8ce95] [Current]
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Post a new message
Dataseries X:
9904,642857
13710,15385
13747,69231
14517
15185,81818
11422,28571
13819,66667
12749
16217
13238
12391
14780,09091
10815,42857
14770,84615
11831
11931,3125
10611,94118
15923,18182
11094,875
16209,53846
10100
12149,6875
11644,35294
9249,947368
8980,777778
10244,52632
12457,5625
13307,46667
10839,625
11827,625
10925,94118
10675,3
9297,3
10433,21053
12261,41176
10911,22222
9334,421053
11655,05882
11080
9840,142857
7448,916667
8362,6
8465,64
8220,923077
10432,86364
8537,4
8535,464286
7997,464286
6301,413793
7595,566667
7200,483871
6152,482759
6064,259259
7269,909091
6578,44
7708,26087
6401,153846
7042,043478
8296,409091
9613,333333




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49141&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49141&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49141&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean10605.1846946167349.74452720977230.3226608839995
Geometric Mean10259.5128486757
Harmonic Mean9912.00034256587
Quadratic Mean10940.1506036896
Winsorized Mean ( 1 / 20 )10606.5307272833349.39007452369930.3572754370385
Winsorized Mean ( 2 / 20 )10601.94987375345.7881384672830.6602474010346
Winsorized Mean ( 3 / 20 )10570.0686944335.62492057601131.4936944380033
Winsorized Mean ( 4 / 20 )10554.8392866667327.04624080991932.2732322515861
Winsorized Mean ( 5 / 20 )10592.7025131667319.25028414278633.1799313557668
Winsorized Mean ( 6 / 20 )10583.1619374667310.7550207878334.0562862367794
Winsorized Mean ( 7 / 20 )10509.9059913292.69652876122435.9071767464444
Winsorized Mean ( 8 / 20 )10524.1770867667286.45041529071436.7399610019271
Winsorized Mean ( 9 / 20 )10540.5438177667281.42338564644437.4543991557578
Winsorized Mean ( 10 / 20 )10492.2116549333265.6451680953239.497092042602
Winsorized Mean ( 11 / 20 )10532.4967250333254.15690521665541.4409229450404
Winsorized Mean ( 12 / 20 )10479.3884832333229.60364309490745.6412117071752
Winsorized Mean ( 13 / 20 )10432.5989946216.57175497146548.171558641036
Winsorized Mean ( 14 / 20 )10432.5122900333211.55064565389949.3144904275127
Winsorized Mean ( 15 / 20 )10425.8752300333202.26409292245351.5458531437438
Winsorized Mean ( 16 / 20 )10414.7019036333194.66911210120653.4995089422243
Winsorized Mean ( 17 / 20 )10353.3774392667185.43860129813355.8318352640147
Winsorized Mean ( 18 / 20 )10456.2970226667159.56466833496465.5301523311942
Winsorized Mean ( 19 / 20 )10540.4653095146.3440594373872.0252352573985
Winsorized Mean ( 20 / 20 )10498.7274601667135.5272447578577.465807549803
Trimmed Mean ( 1 / 20 )10586.7210761724339.42628107184731.1900452809413
Trimmed Mean ( 2 / 20 )10565.4964499821327.119040944632.2986287177685
Trimmed Mean ( 3 / 20 )10545.2445478889314.27253927702833.5544574532277
Trimmed Mean ( 4 / 20 )10535.6967992308303.29926479942534.7369678136152
Trimmed Mean ( 5 / 20 )10529.954053292.96670136243835.9424945020392
Trimmed Mean ( 6 / 20 )10514.2669379583282.56028337315837.210703544181
Trimmed Mean ( 7 / 20 )10499.2897641522271.96404910593438.6054325881233
Trimmed Mean ( 8 / 20 )10497.2216679545263.78727312416339.7942688577458
Trimmed Mean ( 9 / 20 )10492.4082003095254.79571271262941.1796889696624
Trimmed Mean ( 10 / 20 )10484.3855974244.22241893682742.929660770054
Trimmed Mean ( 11 / 20 )10483.1499041053234.57968676043844.6890779371322
Trimmed Mean ( 12 / 20 )10475.6731130556224.6673068806346.6274922617980
Trimmed Mean ( 13 / 20 )10475.1267350882218.05140821773048.0397114639524
Trimmed Mean ( 14 / 20 )10481.2605438125212.20095980614849.3930873516664
Trimmed Mean ( 15 / 20 )10488.2245800667204.91582555427551.1830872588642
Trimmed Mean ( 16 / 20 )10497.1316300714196.84841140095453.3259656776713
Trimmed Mean ( 17 / 20 )10509.0205329231186.92538172888556.2204042903349
Trimmed Mean ( 18 / 20 )10531.9092231667174.3982331703260.389999552811
Trimmed Mean ( 19 / 20 )10543.3656171818165.74902438277263.610423388276
Trimmed Mean ( 20 / 20 )10543.8235605157.02956755454667.1454664538735
Median10643.62059
Midrange11140.6296295
Midmean - Weighted Average at Xnp10419.6560452258
Midmean - Weighted Average at X(n+1)p10488.2245800667
Midmean - Empirical Distribution Function10419.6560452258
Midmean - Empirical Distribution Function - Averaging10488.2245800667
Midmean - Empirical Distribution Function - Interpolation10488.2245800667
Midmean - Closest Observation10419.6560452258
Midmean - True Basic - Statistics Graphics Toolkit10488.2245800667
Midmean - MS Excel (old versions)10481.2605438125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 10605.1846946167 & 349.744527209772 & 30.3226608839995 \tabularnewline
Geometric Mean & 10259.5128486757 &  &  \tabularnewline
Harmonic Mean & 9912.00034256587 &  &  \tabularnewline
Quadratic Mean & 10940.1506036896 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 10606.5307272833 & 349.390074523699 & 30.3572754370385 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 10601.94987375 & 345.78813846728 & 30.6602474010346 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 10570.0686944 & 335.624920576011 & 31.4936944380033 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 10554.8392866667 & 327.046240809919 & 32.2732322515861 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 10592.7025131667 & 319.250284142786 & 33.1799313557668 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 10583.1619374667 & 310.75502078783 & 34.0562862367794 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 10509.9059913 & 292.696528761224 & 35.9071767464444 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 10524.1770867667 & 286.450415290714 & 36.7399610019271 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 10540.5438177667 & 281.423385646444 & 37.4543991557578 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 10492.2116549333 & 265.64516809532 & 39.497092042602 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 10532.4967250333 & 254.156905216655 & 41.4409229450404 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 10479.3884832333 & 229.603643094907 & 45.6412117071752 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 10432.5989946 & 216.571754971465 & 48.171558641036 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 10432.5122900333 & 211.550645653899 & 49.3144904275127 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 10425.8752300333 & 202.264092922453 & 51.5458531437438 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 10414.7019036333 & 194.669112101206 & 53.4995089422243 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 10353.3774392667 & 185.438601298133 & 55.8318352640147 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 10456.2970226667 & 159.564668334964 & 65.5301523311942 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 10540.4653095 & 146.34405943738 & 72.0252352573985 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 10498.7274601667 & 135.52724475785 & 77.465807549803 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 10586.7210761724 & 339.426281071847 & 31.1900452809413 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 10565.4964499821 & 327.1190409446 & 32.2986287177685 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 10545.2445478889 & 314.272539277028 & 33.5544574532277 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 10535.6967992308 & 303.299264799425 & 34.7369678136152 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 10529.954053 & 292.966701362438 & 35.9424945020392 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 10514.2669379583 & 282.560283373158 & 37.210703544181 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 10499.2897641522 & 271.964049105934 & 38.6054325881233 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 10497.2216679545 & 263.787273124163 & 39.7942688577458 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 10492.4082003095 & 254.795712712629 & 41.1796889696624 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 10484.3855974 & 244.222418936827 & 42.929660770054 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 10483.1499041053 & 234.579686760438 & 44.6890779371322 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 10475.6731130556 & 224.66730688063 & 46.6274922617980 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 10475.1267350882 & 218.051408217730 & 48.0397114639524 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 10481.2605438125 & 212.200959806148 & 49.3930873516664 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 10488.2245800667 & 204.915825554275 & 51.1830872588642 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 10497.1316300714 & 196.848411400954 & 53.3259656776713 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 10509.0205329231 & 186.925381728885 & 56.2204042903349 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 10531.9092231667 & 174.39823317032 & 60.389999552811 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 10543.3656171818 & 165.749024382772 & 63.610423388276 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 10543.8235605 & 157.029567554546 & 67.1454664538735 \tabularnewline
Median & 10643.62059 &  &  \tabularnewline
Midrange & 11140.6296295 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 10419.6560452258 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 10488.2245800667 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 10419.6560452258 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 10488.2245800667 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 10488.2245800667 &  &  \tabularnewline
Midmean - Closest Observation & 10419.6560452258 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 10488.2245800667 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 10481.2605438125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49141&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]10605.1846946167[/C][C]349.744527209772[/C][C]30.3226608839995[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]10259.5128486757[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]9912.00034256587[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]10940.1506036896[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]10606.5307272833[/C][C]349.390074523699[/C][C]30.3572754370385[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]10601.94987375[/C][C]345.78813846728[/C][C]30.6602474010346[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]10570.0686944[/C][C]335.624920576011[/C][C]31.4936944380033[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]10554.8392866667[/C][C]327.046240809919[/C][C]32.2732322515861[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]10592.7025131667[/C][C]319.250284142786[/C][C]33.1799313557668[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]10583.1619374667[/C][C]310.75502078783[/C][C]34.0562862367794[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]10509.9059913[/C][C]292.696528761224[/C][C]35.9071767464444[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]10524.1770867667[/C][C]286.450415290714[/C][C]36.7399610019271[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]10540.5438177667[/C][C]281.423385646444[/C][C]37.4543991557578[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]10492.2116549333[/C][C]265.64516809532[/C][C]39.497092042602[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]10532.4967250333[/C][C]254.156905216655[/C][C]41.4409229450404[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]10479.3884832333[/C][C]229.603643094907[/C][C]45.6412117071752[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]10432.5989946[/C][C]216.571754971465[/C][C]48.171558641036[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]10432.5122900333[/C][C]211.550645653899[/C][C]49.3144904275127[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]10425.8752300333[/C][C]202.264092922453[/C][C]51.5458531437438[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]10414.7019036333[/C][C]194.669112101206[/C][C]53.4995089422243[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]10353.3774392667[/C][C]185.438601298133[/C][C]55.8318352640147[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]10456.2970226667[/C][C]159.564668334964[/C][C]65.5301523311942[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]10540.4653095[/C][C]146.34405943738[/C][C]72.0252352573985[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]10498.7274601667[/C][C]135.52724475785[/C][C]77.465807549803[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]10586.7210761724[/C][C]339.426281071847[/C][C]31.1900452809413[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]10565.4964499821[/C][C]327.1190409446[/C][C]32.2986287177685[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]10545.2445478889[/C][C]314.272539277028[/C][C]33.5544574532277[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]10535.6967992308[/C][C]303.299264799425[/C][C]34.7369678136152[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]10529.954053[/C][C]292.966701362438[/C][C]35.9424945020392[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]10514.2669379583[/C][C]282.560283373158[/C][C]37.210703544181[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]10499.2897641522[/C][C]271.964049105934[/C][C]38.6054325881233[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]10497.2216679545[/C][C]263.787273124163[/C][C]39.7942688577458[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]10492.4082003095[/C][C]254.795712712629[/C][C]41.1796889696624[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]10484.3855974[/C][C]244.222418936827[/C][C]42.929660770054[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]10483.1499041053[/C][C]234.579686760438[/C][C]44.6890779371322[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]10475.6731130556[/C][C]224.66730688063[/C][C]46.6274922617980[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]10475.1267350882[/C][C]218.051408217730[/C][C]48.0397114639524[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]10481.2605438125[/C][C]212.200959806148[/C][C]49.3930873516664[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]10488.2245800667[/C][C]204.915825554275[/C][C]51.1830872588642[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]10497.1316300714[/C][C]196.848411400954[/C][C]53.3259656776713[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]10509.0205329231[/C][C]186.925381728885[/C][C]56.2204042903349[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]10531.9092231667[/C][C]174.39823317032[/C][C]60.389999552811[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]10543.3656171818[/C][C]165.749024382772[/C][C]63.610423388276[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]10543.8235605[/C][C]157.029567554546[/C][C]67.1454664538735[/C][/ROW]
[ROW][C]Median[/C][C]10643.62059[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]11140.6296295[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]10419.6560452258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]10488.2245800667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]10419.6560452258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]10488.2245800667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]10488.2245800667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]10419.6560452258[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]10488.2245800667[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]10481.2605438125[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49141&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49141&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 Mean10605.1846946167349.74452720977230.3226608839995
Geometric Mean10259.5128486757
Harmonic Mean9912.00034256587
Quadratic Mean10940.1506036896
Winsorized Mean ( 1 / 20 )10606.5307272833349.39007452369930.3572754370385
Winsorized Mean ( 2 / 20 )10601.94987375345.7881384672830.6602474010346
Winsorized Mean ( 3 / 20 )10570.0686944335.62492057601131.4936944380033
Winsorized Mean ( 4 / 20 )10554.8392866667327.04624080991932.2732322515861
Winsorized Mean ( 5 / 20 )10592.7025131667319.25028414278633.1799313557668
Winsorized Mean ( 6 / 20 )10583.1619374667310.7550207878334.0562862367794
Winsorized Mean ( 7 / 20 )10509.9059913292.69652876122435.9071767464444
Winsorized Mean ( 8 / 20 )10524.1770867667286.45041529071436.7399610019271
Winsorized Mean ( 9 / 20 )10540.5438177667281.42338564644437.4543991557578
Winsorized Mean ( 10 / 20 )10492.2116549333265.6451680953239.497092042602
Winsorized Mean ( 11 / 20 )10532.4967250333254.15690521665541.4409229450404
Winsorized Mean ( 12 / 20 )10479.3884832333229.60364309490745.6412117071752
Winsorized Mean ( 13 / 20 )10432.5989946216.57175497146548.171558641036
Winsorized Mean ( 14 / 20 )10432.5122900333211.55064565389949.3144904275127
Winsorized Mean ( 15 / 20 )10425.8752300333202.26409292245351.5458531437438
Winsorized Mean ( 16 / 20 )10414.7019036333194.66911210120653.4995089422243
Winsorized Mean ( 17 / 20 )10353.3774392667185.43860129813355.8318352640147
Winsorized Mean ( 18 / 20 )10456.2970226667159.56466833496465.5301523311942
Winsorized Mean ( 19 / 20 )10540.4653095146.3440594373872.0252352573985
Winsorized Mean ( 20 / 20 )10498.7274601667135.5272447578577.465807549803
Trimmed Mean ( 1 / 20 )10586.7210761724339.42628107184731.1900452809413
Trimmed Mean ( 2 / 20 )10565.4964499821327.119040944632.2986287177685
Trimmed Mean ( 3 / 20 )10545.2445478889314.27253927702833.5544574532277
Trimmed Mean ( 4 / 20 )10535.6967992308303.29926479942534.7369678136152
Trimmed Mean ( 5 / 20 )10529.954053292.96670136243835.9424945020392
Trimmed Mean ( 6 / 20 )10514.2669379583282.56028337315837.210703544181
Trimmed Mean ( 7 / 20 )10499.2897641522271.96404910593438.6054325881233
Trimmed Mean ( 8 / 20 )10497.2216679545263.78727312416339.7942688577458
Trimmed Mean ( 9 / 20 )10492.4082003095254.79571271262941.1796889696624
Trimmed Mean ( 10 / 20 )10484.3855974244.22241893682742.929660770054
Trimmed Mean ( 11 / 20 )10483.1499041053234.57968676043844.6890779371322
Trimmed Mean ( 12 / 20 )10475.6731130556224.6673068806346.6274922617980
Trimmed Mean ( 13 / 20 )10475.1267350882218.05140821773048.0397114639524
Trimmed Mean ( 14 / 20 )10481.2605438125212.20095980614849.3930873516664
Trimmed Mean ( 15 / 20 )10488.2245800667204.91582555427551.1830872588642
Trimmed Mean ( 16 / 20 )10497.1316300714196.84841140095453.3259656776713
Trimmed Mean ( 17 / 20 )10509.0205329231186.92538172888556.2204042903349
Trimmed Mean ( 18 / 20 )10531.9092231667174.3982331703260.389999552811
Trimmed Mean ( 19 / 20 )10543.3656171818165.74902438277263.610423388276
Trimmed Mean ( 20 / 20 )10543.8235605157.02956755454667.1454664538735
Median10643.62059
Midrange11140.6296295
Midmean - Weighted Average at Xnp10419.6560452258
Midmean - Weighted Average at X(n+1)p10488.2245800667
Midmean - Empirical Distribution Function10419.6560452258
Midmean - Empirical Distribution Function - Averaging10488.2245800667
Midmean - Empirical Distribution Function - Interpolation10488.2245800667
Midmean - Closest Observation10419.6560452258
Midmean - True Basic - Statistics Graphics Toolkit10488.2245800667
Midmean - MS Excel (old versions)10481.2605438125
Number of observations60



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')