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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, 21 Oct 2008 01:14:25 -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/2008/Oct/21/t1224573330qgzcul9z8nin1yh.htm/, Retrieved Sun, 19 May 2024 18:20:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=18347, Retrieved Sun, 19 May 2024 18:20:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Q9 Tijdreeks3] [2008-10-21 07:14:25] [d7f41258beeebb8716e3f5d39f3cdc01] [Current]
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Dataseries X:
7,4
12
13,8
14,8
16,6
18
10,9
16,5
16,1
17,8
16,9
17,1
22,9
17,9
19,7
24,9
19,4
14,4
25,7
24,5
20
33,8
25,6
14,3
17,5
19,2
19,5
22,4
18,5
23,2
22
28,2
24,5
21,2
21,6
15,1
16,3
21,1
28,2
29,9
22,1
22,2
24,2
23,7
25
20,8
20,7
25,4
29,7
26,6
33,8
33,1
33,3
42,1
39,1
35,6
49,8
52,8
46,5
46,8




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=18347&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=18347&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18347&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 Mean24.0451.2361467948043619.4515733091437
Geometric Mean22.3982148932677
Harmonic Mean20.8790809378274
Quadratic Mean25.8518374588732
Winsorized Mean ( 1 / 20 )24.05333333333331.2051594982390719.9586306779136
Winsorized Mean ( 2 / 20 )23.991.1638230882702720.6130985385889
Winsorized Mean ( 3 / 20 )24.0651.1441297608245821.0334533931327
Winsorized Mean ( 4 / 20 )23.8051.0465963802014822.7451579714209
Winsorized Mean ( 5 / 20 )23.56333333333330.97435757965544424.1834556689813
Winsorized Mean ( 6 / 20 )23.25333333333330.87864645090467626.4649487964029
Winsorized Mean ( 7 / 20 )23.07833333333330.82472077680793427.9832083564787
Winsorized Mean ( 8 / 20 )23.21166666666670.80378023413332828.8781257375588
Winsorized Mean ( 9 / 20 )23.16666666666670.78269657976119229.598528044846
Winsorized Mean ( 10 / 20 )23.16666666666670.7704744545553830.068052911677
Winsorized Mean ( 11 / 20 )22.59833333333330.64677597509382534.9399702579476
Winsorized Mean ( 12 / 20 )22.61833333333330.62980353705890135.9133158237852
Winsorized Mean ( 13 / 20 )22.33666666666670.56329321556746239.6537115118006
Winsorized Mean ( 14 / 20 )22.430.54883183597600440.868620458418
Winsorized Mean ( 15 / 20 )22.1050.46891764422139947.1404739668169
Winsorized Mean ( 16 / 20 )21.89166666666670.42703346477491151.2645225081031
Winsorized Mean ( 17 / 20 )21.89166666666670.41828471142473852.3367602705356
Winsorized Mean ( 18 / 20 )21.98166666666670.38596486818451956.9525065067784
Winsorized Mean ( 19 / 20 )22.07666666666670.33386426643060666.1246766618413
Winsorized Mean ( 20 / 20 )22.110.31925672860107869.2546092822595
Trimmed Mean ( 1 / 20 )23.83620689655171.1408509212054720.8933581535485
Trimmed Mean ( 2 / 20 )23.60357142857141.0596494283234422.2748871444366
Trimmed Mean ( 3 / 20 )23.38888888888890.98613613515359623.7177079868855
Trimmed Mean ( 4 / 20 )23.12884615384620.90114865755045625.6659608379333
Trimmed Mean ( 5 / 20 )22.9260.83634193768738727.4122329240046
Trimmed Mean ( 6 / 20 )22.76666666666670.78159986255990629.1282889842137
Trimmed Mean ( 7 / 20 )22.66086956521740.74519704141911530.4092317946716
Trimmed Mean ( 8 / 20 )22.57954545454550.71527120143411331.5678100967488
Trimmed Mean ( 9 / 20 )22.46666666666670.68140787053276932.9709526969519
Trimmed Mean ( 10 / 20 )22.350.64232151067586334.7956586048051
Trimmed Mean ( 11 / 20 )22.22105263157890.5922707213107937.5184047295132
Trimmed Mean ( 12 / 20 )22.16388888888890.56521035243916939.2135225288081
Trimmed Mean ( 13 / 20 )22.09705882352940.53226528463584641.5151231188171
Trimmed Mean ( 14 / 20 )22.06250.50761837170291943.4627689419247
Trimmed Mean ( 15 / 20 )22.010.47591050061718746.2481915642883
Trimmed Mean ( 16 / 20 )21.99642857142860.45752040874064948.077480591467
Trimmed Mean ( 17 / 20 )22.01153846153850.44332057937194249.6515151467195
Trimmed Mean ( 18 / 20 )22.02916666666670.42300166026786752.0782037893578
Trimmed Mean ( 19 / 20 )22.03636363636360.40277959848864954.7107244732621
Trimmed Mean ( 20 / 20 )22.030.3910915897573756.3295160953658
Median22.05
Midrange30.1
Midmean - Weighted Average at Xnp21.8645161290323
Midmean - Weighted Average at X(n+1)p22.01
Midmean - Empirical Distribution Function21.8645161290323
Midmean - Empirical Distribution Function - Averaging22.01
Midmean - Empirical Distribution Function - Interpolation22.01
Midmean - Closest Observation21.8645161290323
Midmean - True Basic - Statistics Graphics Toolkit22.01
Midmean - MS Excel (old versions)22.2484848484848
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 24.045 & 1.23614679480436 & 19.4515733091437 \tabularnewline
Geometric Mean & 22.3982148932677 &  &  \tabularnewline
Harmonic Mean & 20.8790809378274 &  &  \tabularnewline
Quadratic Mean & 25.8518374588732 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 24.0533333333333 & 1.20515949823907 & 19.9586306779136 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 23.99 & 1.16382308827027 & 20.6130985385889 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 24.065 & 1.14412976082458 & 21.0334533931327 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 23.805 & 1.04659638020148 & 22.7451579714209 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 23.5633333333333 & 0.974357579655444 & 24.1834556689813 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 23.2533333333333 & 0.878646450904676 & 26.4649487964029 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 23.0783333333333 & 0.824720776807934 & 27.9832083564787 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 23.2116666666667 & 0.803780234133328 & 28.8781257375588 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 23.1666666666667 & 0.782696579761192 & 29.598528044846 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 23.1666666666667 & 0.77047445455538 & 30.068052911677 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 22.5983333333333 & 0.646775975093825 & 34.9399702579476 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 22.6183333333333 & 0.629803537058901 & 35.9133158237852 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 22.3366666666667 & 0.563293215567462 & 39.6537115118006 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 22.43 & 0.548831835976004 & 40.868620458418 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 22.105 & 0.468917644221399 & 47.1404739668169 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 21.8916666666667 & 0.427033464774911 & 51.2645225081031 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 21.8916666666667 & 0.418284711424738 & 52.3367602705356 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 21.9816666666667 & 0.385964868184519 & 56.9525065067784 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 22.0766666666667 & 0.333864266430606 & 66.1246766618413 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 22.11 & 0.319256728601078 & 69.2546092822595 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 23.8362068965517 & 1.14085092120547 & 20.8933581535485 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 23.6035714285714 & 1.05964942832344 & 22.2748871444366 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 23.3888888888889 & 0.986136135153596 & 23.7177079868855 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 23.1288461538462 & 0.901148657550456 & 25.6659608379333 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 22.926 & 0.836341937687387 & 27.4122329240046 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 22.7666666666667 & 0.781599862559906 & 29.1282889842137 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 22.6608695652174 & 0.745197041419115 & 30.4092317946716 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 22.5795454545455 & 0.715271201434113 & 31.5678100967488 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 22.4666666666667 & 0.681407870532769 & 32.9709526969519 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 22.35 & 0.642321510675863 & 34.7956586048051 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 22.2210526315789 & 0.59227072131079 & 37.5184047295132 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 22.1638888888889 & 0.565210352439169 & 39.2135225288081 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 22.0970588235294 & 0.532265284635846 & 41.5151231188171 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 22.0625 & 0.507618371702919 & 43.4627689419247 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 22.01 & 0.475910500617187 & 46.2481915642883 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 21.9964285714286 & 0.457520408740649 & 48.077480591467 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 22.0115384615385 & 0.443320579371942 & 49.6515151467195 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 22.0291666666667 & 0.423001660267867 & 52.0782037893578 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 22.0363636363636 & 0.402779598488649 & 54.7107244732621 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 22.03 & 0.39109158975737 & 56.3295160953658 \tabularnewline
Median & 22.05 &  &  \tabularnewline
Midrange & 30.1 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 21.8645161290323 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 22.01 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 21.8645161290323 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 22.01 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 22.01 &  &  \tabularnewline
Midmean - Closest Observation & 21.8645161290323 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 22.01 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 22.2484848484848 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=18347&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]24.045[/C][C]1.23614679480436[/C][C]19.4515733091437[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]22.3982148932677[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]20.8790809378274[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]25.8518374588732[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]24.0533333333333[/C][C]1.20515949823907[/C][C]19.9586306779136[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]23.99[/C][C]1.16382308827027[/C][C]20.6130985385889[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]24.065[/C][C]1.14412976082458[/C][C]21.0334533931327[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]23.805[/C][C]1.04659638020148[/C][C]22.7451579714209[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]23.5633333333333[/C][C]0.974357579655444[/C][C]24.1834556689813[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]23.2533333333333[/C][C]0.878646450904676[/C][C]26.4649487964029[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]23.0783333333333[/C][C]0.824720776807934[/C][C]27.9832083564787[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]23.2116666666667[/C][C]0.803780234133328[/C][C]28.8781257375588[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]23.1666666666667[/C][C]0.782696579761192[/C][C]29.598528044846[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]23.1666666666667[/C][C]0.77047445455538[/C][C]30.068052911677[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]22.5983333333333[/C][C]0.646775975093825[/C][C]34.9399702579476[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]22.6183333333333[/C][C]0.629803537058901[/C][C]35.9133158237852[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]22.3366666666667[/C][C]0.563293215567462[/C][C]39.6537115118006[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]22.43[/C][C]0.548831835976004[/C][C]40.868620458418[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]22.105[/C][C]0.468917644221399[/C][C]47.1404739668169[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]21.8916666666667[/C][C]0.427033464774911[/C][C]51.2645225081031[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]21.8916666666667[/C][C]0.418284711424738[/C][C]52.3367602705356[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]21.9816666666667[/C][C]0.385964868184519[/C][C]56.9525065067784[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]22.0766666666667[/C][C]0.333864266430606[/C][C]66.1246766618413[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]22.11[/C][C]0.319256728601078[/C][C]69.2546092822595[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]23.8362068965517[/C][C]1.14085092120547[/C][C]20.8933581535485[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]23.6035714285714[/C][C]1.05964942832344[/C][C]22.2748871444366[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]23.3888888888889[/C][C]0.986136135153596[/C][C]23.7177079868855[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]23.1288461538462[/C][C]0.901148657550456[/C][C]25.6659608379333[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]22.926[/C][C]0.836341937687387[/C][C]27.4122329240046[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]22.7666666666667[/C][C]0.781599862559906[/C][C]29.1282889842137[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]22.6608695652174[/C][C]0.745197041419115[/C][C]30.4092317946716[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]22.5795454545455[/C][C]0.715271201434113[/C][C]31.5678100967488[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]22.4666666666667[/C][C]0.681407870532769[/C][C]32.9709526969519[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]22.35[/C][C]0.642321510675863[/C][C]34.7956586048051[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]22.2210526315789[/C][C]0.59227072131079[/C][C]37.5184047295132[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]22.1638888888889[/C][C]0.565210352439169[/C][C]39.2135225288081[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]22.0970588235294[/C][C]0.532265284635846[/C][C]41.5151231188171[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]22.0625[/C][C]0.507618371702919[/C][C]43.4627689419247[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]22.01[/C][C]0.475910500617187[/C][C]46.2481915642883[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]21.9964285714286[/C][C]0.457520408740649[/C][C]48.077480591467[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]22.0115384615385[/C][C]0.443320579371942[/C][C]49.6515151467195[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]22.0291666666667[/C][C]0.423001660267867[/C][C]52.0782037893578[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]22.0363636363636[/C][C]0.402779598488649[/C][C]54.7107244732621[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]22.03[/C][C]0.39109158975737[/C][C]56.3295160953658[/C][/ROW]
[ROW][C]Median[/C][C]22.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]30.1[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]21.8645161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]22.01[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]21.8645161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]22.01[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]22.01[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]21.8645161290323[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]22.01[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]22.2484848484848[/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=18347&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=18347&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 Mean24.0451.2361467948043619.4515733091437
Geometric Mean22.3982148932677
Harmonic Mean20.8790809378274
Quadratic Mean25.8518374588732
Winsorized Mean ( 1 / 20 )24.05333333333331.2051594982390719.9586306779136
Winsorized Mean ( 2 / 20 )23.991.1638230882702720.6130985385889
Winsorized Mean ( 3 / 20 )24.0651.1441297608245821.0334533931327
Winsorized Mean ( 4 / 20 )23.8051.0465963802014822.7451579714209
Winsorized Mean ( 5 / 20 )23.56333333333330.97435757965544424.1834556689813
Winsorized Mean ( 6 / 20 )23.25333333333330.87864645090467626.4649487964029
Winsorized Mean ( 7 / 20 )23.07833333333330.82472077680793427.9832083564787
Winsorized Mean ( 8 / 20 )23.21166666666670.80378023413332828.8781257375588
Winsorized Mean ( 9 / 20 )23.16666666666670.78269657976119229.598528044846
Winsorized Mean ( 10 / 20 )23.16666666666670.7704744545553830.068052911677
Winsorized Mean ( 11 / 20 )22.59833333333330.64677597509382534.9399702579476
Winsorized Mean ( 12 / 20 )22.61833333333330.62980353705890135.9133158237852
Winsorized Mean ( 13 / 20 )22.33666666666670.56329321556746239.6537115118006
Winsorized Mean ( 14 / 20 )22.430.54883183597600440.868620458418
Winsorized Mean ( 15 / 20 )22.1050.46891764422139947.1404739668169
Winsorized Mean ( 16 / 20 )21.89166666666670.42703346477491151.2645225081031
Winsorized Mean ( 17 / 20 )21.89166666666670.41828471142473852.3367602705356
Winsorized Mean ( 18 / 20 )21.98166666666670.38596486818451956.9525065067784
Winsorized Mean ( 19 / 20 )22.07666666666670.33386426643060666.1246766618413
Winsorized Mean ( 20 / 20 )22.110.31925672860107869.2546092822595
Trimmed Mean ( 1 / 20 )23.83620689655171.1408509212054720.8933581535485
Trimmed Mean ( 2 / 20 )23.60357142857141.0596494283234422.2748871444366
Trimmed Mean ( 3 / 20 )23.38888888888890.98613613515359623.7177079868855
Trimmed Mean ( 4 / 20 )23.12884615384620.90114865755045625.6659608379333
Trimmed Mean ( 5 / 20 )22.9260.83634193768738727.4122329240046
Trimmed Mean ( 6 / 20 )22.76666666666670.78159986255990629.1282889842137
Trimmed Mean ( 7 / 20 )22.66086956521740.74519704141911530.4092317946716
Trimmed Mean ( 8 / 20 )22.57954545454550.71527120143411331.5678100967488
Trimmed Mean ( 9 / 20 )22.46666666666670.68140787053276932.9709526969519
Trimmed Mean ( 10 / 20 )22.350.64232151067586334.7956586048051
Trimmed Mean ( 11 / 20 )22.22105263157890.5922707213107937.5184047295132
Trimmed Mean ( 12 / 20 )22.16388888888890.56521035243916939.2135225288081
Trimmed Mean ( 13 / 20 )22.09705882352940.53226528463584641.5151231188171
Trimmed Mean ( 14 / 20 )22.06250.50761837170291943.4627689419247
Trimmed Mean ( 15 / 20 )22.010.47591050061718746.2481915642883
Trimmed Mean ( 16 / 20 )21.99642857142860.45752040874064948.077480591467
Trimmed Mean ( 17 / 20 )22.01153846153850.44332057937194249.6515151467195
Trimmed Mean ( 18 / 20 )22.02916666666670.42300166026786752.0782037893578
Trimmed Mean ( 19 / 20 )22.03636363636360.40277959848864954.7107244732621
Trimmed Mean ( 20 / 20 )22.030.3910915897573756.3295160953658
Median22.05
Midrange30.1
Midmean - Weighted Average at Xnp21.8645161290323
Midmean - Weighted Average at X(n+1)p22.01
Midmean - Empirical Distribution Function21.8645161290323
Midmean - Empirical Distribution Function - Averaging22.01
Midmean - Empirical Distribution Function - Interpolation22.01
Midmean - Closest Observation21.8645161290323
Midmean - True Basic - Statistics Graphics Toolkit22.01
Midmean - MS Excel (old versions)22.2484848484848
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')