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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 05 Mar 2012 06:31:49 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Mar/05/t1330947238gpkeo6psemj7ox4.htm/, Retrieved Thu, 02 May 2024 19:46:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=163478, Retrieved Thu, 02 May 2024 19:46:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact191
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [centrummaten (eig...] [2012-03-05 11:31:49] [e15deab13e19d5d27f52a3832c12141e] [Current]
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Dataseries X:
69116
41519
51321
38529
41547
52073
38401
40898
40439
41888
37898
8771
68184
50530
47221
41756
45633
48138
39486
39341
41117
41629
29722
7054
56676
34870
35117
30169
30936
35699
33228
27733
33666
35429
27438
8170
63410
38040
45389
37353
37024
50957
37994
36454
46080
43373
37395
10963
76058
50179
57452
47568
50050
50856
41992
39284
44521
43832
41153
17100




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163478&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=163478&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163478&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'Gertrude Mary Cox' @ cox.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean40596.98333333331720.8766332071723.5908737151444
Geometric Mean37487.0480202221
Harmonic Mean32307.2578171147
Quadratic Mean42694.7142229964
Winsorized Mean ( 1 / 20 )40499.88333333331677.7941893628424.1387671921272
Winsorized Mean ( 2 / 20 )40488.851662.4064353816424.3555662070719
Winsorized Mean ( 3 / 20 )40359.751563.5738457055925.8125000688963
Winsorized Mean ( 4 / 20 )40371.68333333331345.1277698519730.0132702916216
Winsorized Mean ( 5 / 20 )41168.51666666671110.5657026663537.0698613939055
Winsorized Mean ( 6 / 20 )40737.71666666671005.2708525852340.5241200039795
Winsorized Mean ( 7 / 20 )40882.0333333333939.76053536152343.5026070951215
Winsorized Mean ( 8 / 20 )40893.1918.79135010526144.5074934535628
Winsorized Mean ( 9 / 20 )40993893.60929796031745.8735155213441
Winsorized Mean ( 10 / 20 )41320.6666666667814.53200617115950.7293345793755
Winsorized Mean ( 11 / 20 )41336.6166666667788.87241279411552.3996225451161
Winsorized Mean ( 12 / 20 )41551.6166666667745.76148967804555.7170318416482
Winsorized Mean ( 13 / 20 )41190.8666666667660.40894002145662.3717581190351
Winsorized Mean ( 14 / 20 )41130.6666666667625.65037648593165.7406567829207
Winsorized Mean ( 15 / 20 )41111.4166666667600.22904634346768.4928810378524
Winsorized Mean ( 16 / 20 )41008.4833333333518.26821061192479.1259863014061
Winsorized Mean ( 17 / 20 )41043.3333333333473.7025829566686.6436764544483
Winsorized Mean ( 18 / 20 )41068.8333333333447.66045961175991.7410337489957
Winsorized Mean ( 19 / 20 )40807.2666666667401.702695854626101.585742609591
Winsorized Mean ( 20 / 20 )40745.2666666667342.205773548744119.06656700771
Trimmed Mean ( 1 / 20 )40563.91379310341565.3476008493725.913678068113
Trimmed Mean ( 2 / 20 )40632.51785714291422.8976635841328.5561772269651
Trimmed Mean ( 3 / 20 )40712.33333333331248.5211108990532.6084460870805
Trimmed Mean ( 4 / 20 )40847.94230769231074.1962923599938.0265158223084
Trimmed Mean ( 5 / 20 )40990.82951.78809924761543.0671701320946
Trimmed Mean ( 6 / 20 )40946.3958333333890.66720983195745.9727217768113
Trimmed Mean ( 7 / 20 )40991.7608695652848.74675680285548.2968100213745
Trimmed Mean ( 8 / 20 )41013.1363636364815.23783906284850.3081854134528
Trimmed Mean ( 9 / 20 )41034.5714285714777.49720498943652.7777735601365
Trimmed Mean ( 10 / 20 )41041.5734.89435574275955.8468025768402
Trimmed Mean ( 11 / 20 )40997.4210526316701.22454731938158.4654676014342
Trimmed Mean ( 12 / 20 )40946.0277777778662.61045498642761.795022202927
Trimmed Mean ( 13 / 20 )40856.9705882353621.32069313447365.7582646766806
Trimmed Mean ( 14 / 20 )40808.8125591.52392113012168.9892852042801
Trimmed Mean ( 15 / 20 )40762.8333333333559.56564042004772.8472772251242
Trimmed Mean ( 16 / 20 )40713.0357142857520.72035595528478.1859884075319
Trimmed Mean ( 17 / 20 )40670.4230769231493.02560761416282.4915023658395
Trimmed Mean ( 18 / 20 )40615.5833333333466.25728776472787.1098091100034
Trimmed Mean ( 19 / 20 )40546.9090909091432.62213153901893.7236126747996
Trimmed Mean ( 20 / 20 )40505.8399.694202846969101.341975218761
Median41007.5
Midrange41556
Midmean - Weighted Average at Xnp40590.7741935484
Midmean - Weighted Average at X(n+1)p40762.8333333333
Midmean - Empirical Distribution Function40590.7741935484
Midmean - Empirical Distribution Function - Averaging40762.8333333333
Midmean - Empirical Distribution Function - Interpolation40762.8333333333
Midmean - Closest Observation40590.7741935484
Midmean - True Basic - Statistics Graphics Toolkit40762.8333333333
Midmean - MS Excel (old versions)40808.8125
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 40596.9833333333 & 1720.87663320717 & 23.5908737151444 \tabularnewline
Geometric Mean & 37487.0480202221 &  &  \tabularnewline
Harmonic Mean & 32307.2578171147 &  &  \tabularnewline
Quadratic Mean & 42694.7142229964 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 40499.8833333333 & 1677.79418936284 & 24.1387671921272 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 40488.85 & 1662.40643538164 & 24.3555662070719 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 40359.75 & 1563.57384570559 & 25.8125000688963 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 40371.6833333333 & 1345.12776985197 & 30.0132702916216 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 41168.5166666667 & 1110.56570266635 & 37.0698613939055 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 40737.7166666667 & 1005.27085258523 & 40.5241200039795 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 40882.0333333333 & 939.760535361523 & 43.5026070951215 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 40893.1 & 918.791350105261 & 44.5074934535628 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 40993 & 893.609297960317 & 45.8735155213441 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 41320.6666666667 & 814.532006171159 & 50.7293345793755 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 41336.6166666667 & 788.872412794115 & 52.3996225451161 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 41551.6166666667 & 745.761489678045 & 55.7170318416482 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 41190.8666666667 & 660.408940021456 & 62.3717581190351 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 41130.6666666667 & 625.650376485931 & 65.7406567829207 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 41111.4166666667 & 600.229046343467 & 68.4928810378524 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 41008.4833333333 & 518.268210611924 & 79.1259863014061 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 41043.3333333333 & 473.70258295666 & 86.6436764544483 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 41068.8333333333 & 447.660459611759 & 91.7410337489957 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 40807.2666666667 & 401.702695854626 & 101.585742609591 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 40745.2666666667 & 342.205773548744 & 119.06656700771 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 40563.9137931034 & 1565.34760084937 & 25.913678068113 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 40632.5178571429 & 1422.89766358413 & 28.5561772269651 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 40712.3333333333 & 1248.52111089905 & 32.6084460870805 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 40847.9423076923 & 1074.19629235999 & 38.0265158223084 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 40990.82 & 951.788099247615 & 43.0671701320946 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 40946.3958333333 & 890.667209831957 & 45.9727217768113 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 40991.7608695652 & 848.746756802855 & 48.2968100213745 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 41013.1363636364 & 815.237839062848 & 50.3081854134528 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 41034.5714285714 & 777.497204989436 & 52.7777735601365 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 41041.5 & 734.894355742759 & 55.8468025768402 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 40997.4210526316 & 701.224547319381 & 58.4654676014342 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 40946.0277777778 & 662.610454986427 & 61.795022202927 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 40856.9705882353 & 621.320693134473 & 65.7582646766806 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 40808.8125 & 591.523921130121 & 68.9892852042801 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 40762.8333333333 & 559.565640420047 & 72.8472772251242 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 40713.0357142857 & 520.720355955284 & 78.1859884075319 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 40670.4230769231 & 493.025607614162 & 82.4915023658395 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 40615.5833333333 & 466.257287764727 & 87.1098091100034 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 40546.9090909091 & 432.622131539018 & 93.7236126747996 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 40505.8 & 399.694202846969 & 101.341975218761 \tabularnewline
Median & 41007.5 &  &  \tabularnewline
Midrange & 41556 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 40590.7741935484 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 40762.8333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 40590.7741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 40762.8333333333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 40762.8333333333 &  &  \tabularnewline
Midmean - Closest Observation & 40590.7741935484 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 40762.8333333333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 40808.8125 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=163478&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]40596.9833333333[/C][C]1720.87663320717[/C][C]23.5908737151444[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]37487.0480202221[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]32307.2578171147[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]42694.7142229964[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]40499.8833333333[/C][C]1677.79418936284[/C][C]24.1387671921272[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]40488.85[/C][C]1662.40643538164[/C][C]24.3555662070719[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]40359.75[/C][C]1563.57384570559[/C][C]25.8125000688963[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]40371.6833333333[/C][C]1345.12776985197[/C][C]30.0132702916216[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]41168.5166666667[/C][C]1110.56570266635[/C][C]37.0698613939055[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]40737.7166666667[/C][C]1005.27085258523[/C][C]40.5241200039795[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]40882.0333333333[/C][C]939.760535361523[/C][C]43.5026070951215[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]40893.1[/C][C]918.791350105261[/C][C]44.5074934535628[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]40993[/C][C]893.609297960317[/C][C]45.8735155213441[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]41320.6666666667[/C][C]814.532006171159[/C][C]50.7293345793755[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]41336.6166666667[/C][C]788.872412794115[/C][C]52.3996225451161[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]41551.6166666667[/C][C]745.761489678045[/C][C]55.7170318416482[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]41190.8666666667[/C][C]660.408940021456[/C][C]62.3717581190351[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]41130.6666666667[/C][C]625.650376485931[/C][C]65.7406567829207[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]41111.4166666667[/C][C]600.229046343467[/C][C]68.4928810378524[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]41008.4833333333[/C][C]518.268210611924[/C][C]79.1259863014061[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]41043.3333333333[/C][C]473.70258295666[/C][C]86.6436764544483[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]41068.8333333333[/C][C]447.660459611759[/C][C]91.7410337489957[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]40807.2666666667[/C][C]401.702695854626[/C][C]101.585742609591[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]40745.2666666667[/C][C]342.205773548744[/C][C]119.06656700771[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]40563.9137931034[/C][C]1565.34760084937[/C][C]25.913678068113[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]40632.5178571429[/C][C]1422.89766358413[/C][C]28.5561772269651[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]40712.3333333333[/C][C]1248.52111089905[/C][C]32.6084460870805[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]40847.9423076923[/C][C]1074.19629235999[/C][C]38.0265158223084[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]40990.82[/C][C]951.788099247615[/C][C]43.0671701320946[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]40946.3958333333[/C][C]890.667209831957[/C][C]45.9727217768113[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]40991.7608695652[/C][C]848.746756802855[/C][C]48.2968100213745[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]41013.1363636364[/C][C]815.237839062848[/C][C]50.3081854134528[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]41034.5714285714[/C][C]777.497204989436[/C][C]52.7777735601365[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]41041.5[/C][C]734.894355742759[/C][C]55.8468025768402[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]40997.4210526316[/C][C]701.224547319381[/C][C]58.4654676014342[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]40946.0277777778[/C][C]662.610454986427[/C][C]61.795022202927[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]40856.9705882353[/C][C]621.320693134473[/C][C]65.7582646766806[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]40808.8125[/C][C]591.523921130121[/C][C]68.9892852042801[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]40762.8333333333[/C][C]559.565640420047[/C][C]72.8472772251242[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]40713.0357142857[/C][C]520.720355955284[/C][C]78.1859884075319[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]40670.4230769231[/C][C]493.025607614162[/C][C]82.4915023658395[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]40615.5833333333[/C][C]466.257287764727[/C][C]87.1098091100034[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]40546.9090909091[/C][C]432.622131539018[/C][C]93.7236126747996[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]40505.8[/C][C]399.694202846969[/C][C]101.341975218761[/C][/ROW]
[ROW][C]Median[/C][C]41007.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]41556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]40590.7741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]40762.8333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]40590.7741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]40762.8333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]40762.8333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]40590.7741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]40762.8333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]40808.8125[/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=163478&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=163478&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 Mean40596.98333333331720.8766332071723.5908737151444
Geometric Mean37487.0480202221
Harmonic Mean32307.2578171147
Quadratic Mean42694.7142229964
Winsorized Mean ( 1 / 20 )40499.88333333331677.7941893628424.1387671921272
Winsorized Mean ( 2 / 20 )40488.851662.4064353816424.3555662070719
Winsorized Mean ( 3 / 20 )40359.751563.5738457055925.8125000688963
Winsorized Mean ( 4 / 20 )40371.68333333331345.1277698519730.0132702916216
Winsorized Mean ( 5 / 20 )41168.51666666671110.5657026663537.0698613939055
Winsorized Mean ( 6 / 20 )40737.71666666671005.2708525852340.5241200039795
Winsorized Mean ( 7 / 20 )40882.0333333333939.76053536152343.5026070951215
Winsorized Mean ( 8 / 20 )40893.1918.79135010526144.5074934535628
Winsorized Mean ( 9 / 20 )40993893.60929796031745.8735155213441
Winsorized Mean ( 10 / 20 )41320.6666666667814.53200617115950.7293345793755
Winsorized Mean ( 11 / 20 )41336.6166666667788.87241279411552.3996225451161
Winsorized Mean ( 12 / 20 )41551.6166666667745.76148967804555.7170318416482
Winsorized Mean ( 13 / 20 )41190.8666666667660.40894002145662.3717581190351
Winsorized Mean ( 14 / 20 )41130.6666666667625.65037648593165.7406567829207
Winsorized Mean ( 15 / 20 )41111.4166666667600.22904634346768.4928810378524
Winsorized Mean ( 16 / 20 )41008.4833333333518.26821061192479.1259863014061
Winsorized Mean ( 17 / 20 )41043.3333333333473.7025829566686.6436764544483
Winsorized Mean ( 18 / 20 )41068.8333333333447.66045961175991.7410337489957
Winsorized Mean ( 19 / 20 )40807.2666666667401.702695854626101.585742609591
Winsorized Mean ( 20 / 20 )40745.2666666667342.205773548744119.06656700771
Trimmed Mean ( 1 / 20 )40563.91379310341565.3476008493725.913678068113
Trimmed Mean ( 2 / 20 )40632.51785714291422.8976635841328.5561772269651
Trimmed Mean ( 3 / 20 )40712.33333333331248.5211108990532.6084460870805
Trimmed Mean ( 4 / 20 )40847.94230769231074.1962923599938.0265158223084
Trimmed Mean ( 5 / 20 )40990.82951.78809924761543.0671701320946
Trimmed Mean ( 6 / 20 )40946.3958333333890.66720983195745.9727217768113
Trimmed Mean ( 7 / 20 )40991.7608695652848.74675680285548.2968100213745
Trimmed Mean ( 8 / 20 )41013.1363636364815.23783906284850.3081854134528
Trimmed Mean ( 9 / 20 )41034.5714285714777.49720498943652.7777735601365
Trimmed Mean ( 10 / 20 )41041.5734.89435574275955.8468025768402
Trimmed Mean ( 11 / 20 )40997.4210526316701.22454731938158.4654676014342
Trimmed Mean ( 12 / 20 )40946.0277777778662.61045498642761.795022202927
Trimmed Mean ( 13 / 20 )40856.9705882353621.32069313447365.7582646766806
Trimmed Mean ( 14 / 20 )40808.8125591.52392113012168.9892852042801
Trimmed Mean ( 15 / 20 )40762.8333333333559.56564042004772.8472772251242
Trimmed Mean ( 16 / 20 )40713.0357142857520.72035595528478.1859884075319
Trimmed Mean ( 17 / 20 )40670.4230769231493.02560761416282.4915023658395
Trimmed Mean ( 18 / 20 )40615.5833333333466.25728776472787.1098091100034
Trimmed Mean ( 19 / 20 )40546.9090909091432.62213153901893.7236126747996
Trimmed Mean ( 20 / 20 )40505.8399.694202846969101.341975218761
Median41007.5
Midrange41556
Midmean - Weighted Average at Xnp40590.7741935484
Midmean - Weighted Average at X(n+1)p40762.8333333333
Midmean - Empirical Distribution Function40590.7741935484
Midmean - Empirical Distribution Function - Averaging40762.8333333333
Midmean - Empirical Distribution Function - Interpolation40762.8333333333
Midmean - Closest Observation40590.7741935484
Midmean - True Basic - Statistics Graphics Toolkit40762.8333333333
Midmean - MS Excel (old versions)40808.8125
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')