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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 13:44:01 -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/t1256068023wq5ezqcnqrmt83a.htm/, Retrieved Thu, 02 May 2024 17:51:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49088, Retrieved Thu, 02 May 2024 17:51:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact133
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] [ws 3 part 2.1 con...] [2009-10-20 19:44:01] [51d49d3536f6a59f2486a67bf50b2759] [Current]
- RMPD          [Bivariate Explorative Data Analysis] [WS 4 part 2.1] [2009-10-27 17:07:08] [12f02da0296cb21dc23d82ae014a8b71]
-    D            [Bivariate Explorative Data Analysis] [Ws 4 part 2.1] [2009-10-27 17:16:58] [12f02da0296cb21dc23d82ae014a8b71]
-    D            [Bivariate Explorative Data Analysis] [WS 4 part 2.2] [2009-10-27 17:20:41] [12f02da0296cb21dc23d82ae014a8b71]
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Dataseries X:
1901
1395
1639
1643
1751
1797
1373
1558
1555
2061
2010
2119
1985
1963
2017
1975
1589
1679
1392
1511
1449
1767
1899
2179
2217
2049
2343
2175
1607
1702
1764
1766
1615
1953
2091
2411
2550
2351
2786
2525
2474
2332
1978
1789
1904
1997
2207
2453
1948
1384
1989
2140
2100
2045
2083
2022
1950
1422
1859
2147




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49088&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49088&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49088&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1938.9166666666741.969825666523146.1978727782333
Geometric Mean1911.92689497417
Harmonic Mean1884.75813736794
Quadratic Mean1965.53411316110
Winsorized Mean ( 1 / 20 )1935.1666666666740.749650212818347.4891601905809
Winsorized Mean ( 2 / 20 )1934.640.479221146568147.792421524
Winsorized Mean ( 3 / 20 )1932.239.835763110537648.504154285647
Winsorized Mean ( 4 / 20 )1932.639.111590317642949.4124627585961
Winsorized Mean ( 5 / 20 )1931.3537.848708827211151.0281607971649
Winsorized Mean ( 6 / 20 )1931.5535.301697475231554.7154992010007
Winsorized Mean ( 7 / 20 )1935.7534.108862153421856.7521130225039
Winsorized Mean ( 8 / 20 )1934.6833333333333.738387763069357.3436806441319
Winsorized Mean ( 9 / 20 )1922.0833333333329.663939679782964.7952818837244
Winsorized Mean ( 10 / 20 )1923.4166666666728.819821055783566.7393688164722
Winsorized Mean ( 11 / 20 )1919.7527.711208699200169.27702146949
Winsorized Mean ( 12 / 20 )1923.7526.702616569138372.0435016178672
Winsorized Mean ( 13 / 20 )1918.5525.602231375652274.9368276479427
Winsorized Mean ( 14 / 20 )1925.3166666666723.851772626762980.720066252282
Winsorized Mean ( 15 / 20 )1925.8166666666722.063448461284787.2853883220452
Winsorized Mean ( 16 / 20 )1933.8166666666719.1279440578300101.099034000733
Winsorized Mean ( 17 / 20 )1934.9518.1622073778536106.537160365178
Winsorized Mean ( 18 / 20 )1933.1517.7195959863904109.096731183079
Winsorized Mean ( 19 / 20 )1926.516.6929651274351115.407896996908
Winsorized Mean ( 20 / 20 )1929.8333333333314.970897694453128.905652334287
Trimmed Mean ( 1 / 20 )1934.0689655172439.646104331553948.7833293617687
Trimmed Mean ( 2 / 20 )1932.8928571428638.284611524630150.4874616763278
Trimmed Mean ( 3 / 20 )1931.9444444444436.777927409805452.5299977597261
Trimmed Mean ( 4 / 20 )1931.8461538461535.216700247629154.8559672048267
Trimmed Mean ( 5 / 20 )1931.6233.548659634407257.5766668787848
Trimmed Mean ( 6 / 20 )1931.687531.893400074415760.5669980463941
Trimmed Mean ( 7 / 20 )1931.7173913043530.629288232450863.0676552665612
Trimmed Mean ( 8 / 20 )1930.9318181818229.359627644796465.7682665987098
Trimmed Mean ( 9 / 20 )1930.2619047619027.801019782677169.4313345284066
Trimmed Mean ( 10 / 20 )1931.62526.939811534471171.7015038330306
Trimmed Mean ( 11 / 20 )1932.9210526315826.006055252289474.3258073506328
Trimmed Mean ( 12 / 20 )1934.9166666666725.025808107403377.3168506032886
Trimmed Mean ( 13 / 20 )1936.5588235294123.954583854840780.8429332467021
Trimmed Mean ( 14 / 20 )1939.1562522.743977817561485.2602067041549
Trimmed Mean ( 15 / 20 )1941.1333333333321.576207273441689.9663832819542
Trimmed Mean ( 16 / 20 )1943.3214285714320.446669149020295.0434231809612
Trimmed Mean ( 17 / 20 )1944.6923076923119.786302117356198.284777830541
Trimmed Mean ( 18 / 20 )1946.12519.0522082576470102.146951874667
Trimmed Mean ( 19 / 20 )1948.0909090909117.9648416967721108.439080175192
Trimmed Mean ( 20 / 20 )1951.516.4899490918751118.344816538066
Median1969
Midrange2079.5
Midmean - Weighted Average at Xnp1932.67741935484
Midmean - Weighted Average at X(n+1)p1941.13333333333
Midmean - Empirical Distribution Function1932.67741935484
Midmean - Empirical Distribution Function - Averaging1941.13333333333
Midmean - Empirical Distribution Function - Interpolation1941.13333333333
Midmean - Closest Observation1932.67741935484
Midmean - True Basic - Statistics Graphics Toolkit1941.13333333333
Midmean - MS Excel (old versions)1939.15625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1938.91666666667 & 41.9698256665231 & 46.1978727782333 \tabularnewline
Geometric Mean & 1911.92689497417 &  &  \tabularnewline
Harmonic Mean & 1884.75813736794 &  &  \tabularnewline
Quadratic Mean & 1965.53411316110 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 1935.16666666667 & 40.7496502128183 & 47.4891601905809 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 1934.6 & 40.4792211465681 & 47.792421524 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 1932.2 & 39.8357631105376 & 48.504154285647 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 1932.6 & 39.1115903176429 & 49.4124627585961 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 1931.35 & 37.8487088272111 & 51.0281607971649 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 1931.55 & 35.3016974752315 & 54.7154992010007 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 1935.75 & 34.1088621534218 & 56.7521130225039 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 1934.68333333333 & 33.7383877630693 & 57.3436806441319 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 1922.08333333333 & 29.6639396797829 & 64.7952818837244 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 1923.41666666667 & 28.8198210557835 & 66.7393688164722 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 1919.75 & 27.7112086992001 & 69.27702146949 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 1923.75 & 26.7026165691383 & 72.0435016178672 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 1918.55 & 25.6022313756522 & 74.9368276479427 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 1925.31666666667 & 23.8517726267629 & 80.720066252282 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 1925.81666666667 & 22.0634484612847 & 87.2853883220452 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 1933.81666666667 & 19.1279440578300 & 101.099034000733 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 1934.95 & 18.1622073778536 & 106.537160365178 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 1933.15 & 17.7195959863904 & 109.096731183079 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 1926.5 & 16.6929651274351 & 115.407896996908 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 1929.83333333333 & 14.970897694453 & 128.905652334287 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 1934.06896551724 & 39.6461043315539 & 48.7833293617687 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 1932.89285714286 & 38.2846115246301 & 50.4874616763278 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 1931.94444444444 & 36.7779274098054 & 52.5299977597261 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 1931.84615384615 & 35.2167002476291 & 54.8559672048267 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 1931.62 & 33.5486596344072 & 57.5766668787848 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 1931.6875 & 31.8934000744157 & 60.5669980463941 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 1931.71739130435 & 30.6292882324508 & 63.0676552665612 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 1930.93181818182 & 29.3596276447964 & 65.7682665987098 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 1930.26190476190 & 27.8010197826771 & 69.4313345284066 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 1931.625 & 26.9398115344711 & 71.7015038330306 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 1932.92105263158 & 26.0060552522894 & 74.3258073506328 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 1934.91666666667 & 25.0258081074033 & 77.3168506032886 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 1936.55882352941 & 23.9545838548407 & 80.8429332467021 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 1939.15625 & 22.7439778175614 & 85.2602067041549 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 1941.13333333333 & 21.5762072734416 & 89.9663832819542 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 1943.32142857143 & 20.4466691490202 & 95.0434231809612 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 1944.69230769231 & 19.7863021173561 & 98.284777830541 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 1946.125 & 19.0522082576470 & 102.146951874667 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 1948.09090909091 & 17.9648416967721 & 108.439080175192 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 1951.5 & 16.4899490918751 & 118.344816538066 \tabularnewline
Median & 1969 &  &  \tabularnewline
Midrange & 2079.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1932.67741935484 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1941.13333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1932.67741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1941.13333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1941.13333333333 &  &  \tabularnewline
Midmean - Closest Observation & 1932.67741935484 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1941.13333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1939.15625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49088&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]1938.91666666667[/C][C]41.9698256665231[/C][C]46.1978727782333[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1911.92689497417[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1884.75813736794[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1965.53411316110[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]1935.16666666667[/C][C]40.7496502128183[/C][C]47.4891601905809[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]1934.6[/C][C]40.4792211465681[/C][C]47.792421524[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]1932.2[/C][C]39.8357631105376[/C][C]48.504154285647[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]1932.6[/C][C]39.1115903176429[/C][C]49.4124627585961[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]1931.35[/C][C]37.8487088272111[/C][C]51.0281607971649[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]1931.55[/C][C]35.3016974752315[/C][C]54.7154992010007[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]1935.75[/C][C]34.1088621534218[/C][C]56.7521130225039[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]1934.68333333333[/C][C]33.7383877630693[/C][C]57.3436806441319[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]1922.08333333333[/C][C]29.6639396797829[/C][C]64.7952818837244[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]1923.41666666667[/C][C]28.8198210557835[/C][C]66.7393688164722[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]1919.75[/C][C]27.7112086992001[/C][C]69.27702146949[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]1923.75[/C][C]26.7026165691383[/C][C]72.0435016178672[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]1918.55[/C][C]25.6022313756522[/C][C]74.9368276479427[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]1925.31666666667[/C][C]23.8517726267629[/C][C]80.720066252282[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]1925.81666666667[/C][C]22.0634484612847[/C][C]87.2853883220452[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]1933.81666666667[/C][C]19.1279440578300[/C][C]101.099034000733[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]1934.95[/C][C]18.1622073778536[/C][C]106.537160365178[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]1933.15[/C][C]17.7195959863904[/C][C]109.096731183079[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]1926.5[/C][C]16.6929651274351[/C][C]115.407896996908[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]1929.83333333333[/C][C]14.970897694453[/C][C]128.905652334287[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]1934.06896551724[/C][C]39.6461043315539[/C][C]48.7833293617687[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]1932.89285714286[/C][C]38.2846115246301[/C][C]50.4874616763278[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]1931.94444444444[/C][C]36.7779274098054[/C][C]52.5299977597261[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]1931.84615384615[/C][C]35.2167002476291[/C][C]54.8559672048267[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]1931.62[/C][C]33.5486596344072[/C][C]57.5766668787848[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]1931.6875[/C][C]31.8934000744157[/C][C]60.5669980463941[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]1931.71739130435[/C][C]30.6292882324508[/C][C]63.0676552665612[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]1930.93181818182[/C][C]29.3596276447964[/C][C]65.7682665987098[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]1930.26190476190[/C][C]27.8010197826771[/C][C]69.4313345284066[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]1931.625[/C][C]26.9398115344711[/C][C]71.7015038330306[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]1932.92105263158[/C][C]26.0060552522894[/C][C]74.3258073506328[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]1934.91666666667[/C][C]25.0258081074033[/C][C]77.3168506032886[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]1936.55882352941[/C][C]23.9545838548407[/C][C]80.8429332467021[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]1939.15625[/C][C]22.7439778175614[/C][C]85.2602067041549[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]1941.13333333333[/C][C]21.5762072734416[/C][C]89.9663832819542[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]1943.32142857143[/C][C]20.4466691490202[/C][C]95.0434231809612[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]1944.69230769231[/C][C]19.7863021173561[/C][C]98.284777830541[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]1946.125[/C][C]19.0522082576470[/C][C]102.146951874667[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]1948.09090909091[/C][C]17.9648416967721[/C][C]108.439080175192[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]1951.5[/C][C]16.4899490918751[/C][C]118.344816538066[/C][/ROW]
[ROW][C]Median[/C][C]1969[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]2079.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1932.67741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1941.13333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1932.67741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1941.13333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1941.13333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1932.67741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1941.13333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1939.15625[/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=49088&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49088&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 Mean1938.9166666666741.969825666523146.1978727782333
Geometric Mean1911.92689497417
Harmonic Mean1884.75813736794
Quadratic Mean1965.53411316110
Winsorized Mean ( 1 / 20 )1935.1666666666740.749650212818347.4891601905809
Winsorized Mean ( 2 / 20 )1934.640.479221146568147.792421524
Winsorized Mean ( 3 / 20 )1932.239.835763110537648.504154285647
Winsorized Mean ( 4 / 20 )1932.639.111590317642949.4124627585961
Winsorized Mean ( 5 / 20 )1931.3537.848708827211151.0281607971649
Winsorized Mean ( 6 / 20 )1931.5535.301697475231554.7154992010007
Winsorized Mean ( 7 / 20 )1935.7534.108862153421856.7521130225039
Winsorized Mean ( 8 / 20 )1934.6833333333333.738387763069357.3436806441319
Winsorized Mean ( 9 / 20 )1922.0833333333329.663939679782964.7952818837244
Winsorized Mean ( 10 / 20 )1923.4166666666728.819821055783566.7393688164722
Winsorized Mean ( 11 / 20 )1919.7527.711208699200169.27702146949
Winsorized Mean ( 12 / 20 )1923.7526.702616569138372.0435016178672
Winsorized Mean ( 13 / 20 )1918.5525.602231375652274.9368276479427
Winsorized Mean ( 14 / 20 )1925.3166666666723.851772626762980.720066252282
Winsorized Mean ( 15 / 20 )1925.8166666666722.063448461284787.2853883220452
Winsorized Mean ( 16 / 20 )1933.8166666666719.1279440578300101.099034000733
Winsorized Mean ( 17 / 20 )1934.9518.1622073778536106.537160365178
Winsorized Mean ( 18 / 20 )1933.1517.7195959863904109.096731183079
Winsorized Mean ( 19 / 20 )1926.516.6929651274351115.407896996908
Winsorized Mean ( 20 / 20 )1929.8333333333314.970897694453128.905652334287
Trimmed Mean ( 1 / 20 )1934.0689655172439.646104331553948.7833293617687
Trimmed Mean ( 2 / 20 )1932.8928571428638.284611524630150.4874616763278
Trimmed Mean ( 3 / 20 )1931.9444444444436.777927409805452.5299977597261
Trimmed Mean ( 4 / 20 )1931.8461538461535.216700247629154.8559672048267
Trimmed Mean ( 5 / 20 )1931.6233.548659634407257.5766668787848
Trimmed Mean ( 6 / 20 )1931.687531.893400074415760.5669980463941
Trimmed Mean ( 7 / 20 )1931.7173913043530.629288232450863.0676552665612
Trimmed Mean ( 8 / 20 )1930.9318181818229.359627644796465.7682665987098
Trimmed Mean ( 9 / 20 )1930.2619047619027.801019782677169.4313345284066
Trimmed Mean ( 10 / 20 )1931.62526.939811534471171.7015038330306
Trimmed Mean ( 11 / 20 )1932.9210526315826.006055252289474.3258073506328
Trimmed Mean ( 12 / 20 )1934.9166666666725.025808107403377.3168506032886
Trimmed Mean ( 13 / 20 )1936.5588235294123.954583854840780.8429332467021
Trimmed Mean ( 14 / 20 )1939.1562522.743977817561485.2602067041549
Trimmed Mean ( 15 / 20 )1941.1333333333321.576207273441689.9663832819542
Trimmed Mean ( 16 / 20 )1943.3214285714320.446669149020295.0434231809612
Trimmed Mean ( 17 / 20 )1944.6923076923119.786302117356198.284777830541
Trimmed Mean ( 18 / 20 )1946.12519.0522082576470102.146951874667
Trimmed Mean ( 19 / 20 )1948.0909090909117.9648416967721108.439080175192
Trimmed Mean ( 20 / 20 )1951.516.4899490918751118.344816538066
Median1969
Midrange2079.5
Midmean - Weighted Average at Xnp1932.67741935484
Midmean - Weighted Average at X(n+1)p1941.13333333333
Midmean - Empirical Distribution Function1932.67741935484
Midmean - Empirical Distribution Function - Averaging1941.13333333333
Midmean - Empirical Distribution Function - Interpolation1941.13333333333
Midmean - Closest Observation1932.67741935484
Midmean - True Basic - Statistics Graphics Toolkit1941.13333333333
Midmean - MS Excel (old versions)1939.15625
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')