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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 computationWed, 25 Nov 2015 10:10:21 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/25/t14484464386vdnsp4n9gkc0ap.htm/, Retrieved Wed, 15 May 2024 10:31:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284076, Retrieved Wed, 15 May 2024 10:31:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Time needed to su...] [2010-09-25 09:42:08] [b98453cac15ba1066b407e146608df68]
- RM D    [Central Tendency] [Maatstaven voor c...] [2015-11-25 10:10:21] [ff6d1090be03ecb1ea559b1add2eb09a] [Current]
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Dataseries X:
403
436
420
408
401
401
394
396
346
417
374
394
415
363
376
414
379
412
412
379
472
439
409
419
417
413
388
409
416
440
416
403
395
404
398
402
418
446
449
389
395
377
381
388
222
400
378
393
380
376
427
365




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284076&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284076&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284076&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean399.3076923076924.7730972503860583.6579837704744
Geometric Mean397.532645958995
Harmonic Mean395.276942244999
Quadratic Mean400.759951169698
Winsorized Mean ( 1 / 17 )401.253.29608239053403121.735427837709
Winsorized Mean ( 2 / 17 )401.7884615384623.07416330797319130.698476719301
Winsorized Mean ( 3 / 17 )401.5576923076922.95279777107689135.992276965599
Winsorized Mean ( 4 / 17 )402.1730769230772.7797100928851144.681662290061
Winsorized Mean ( 5 / 17 )402.0769230769232.66871802987144150.662946994176
Winsorized Mean ( 6 / 17 )401.0384615384622.4295443865963165.067353266306
Winsorized Mean ( 7 / 17 )400.2307692307692.22043426931659180.248870575193
Winsorized Mean ( 8 / 17 )400.2307692307692.16262217670982185.06735644396
Winsorized Mean ( 9 / 17 )400.2307692307692.09891435426209190.68465962799
Winsorized Mean ( 10 / 17 )400.0384615384622.06748175281826193.49068546465
Winsorized Mean ( 11 / 17 )400.252.02564162227687197.591713952891
Winsorized Mean ( 12 / 17 )400.251.9435617115741205.936347488466
Winsorized Mean ( 13 / 17 )4021.62373050539423247.578030137702
Winsorized Mean ( 14 / 17 )401.7307692307691.57877976264127254.456497819988
Winsorized Mean ( 15 / 17 )401.7307692307691.4827096451655270.943654100212
Winsorized Mean ( 16 / 17 )402.6538461538461.23360579988942326.403982690369
Winsorized Mean ( 17 / 17 )402.6538461538461.1305722117278356.150489085956
Trimmed Mean ( 1 / 17 )401.43.09561902417871129.667118875035
Trimmed Mean ( 2 / 17 )401.56252.83576860039118141.606229769455
Trimmed Mean ( 3 / 17 )401.4347826086962.66297791499693150.746568474323
Trimmed Mean ( 4 / 17 )401.3863636363642.50416479919628160.287519321887
Trimmed Mean ( 5 / 17 )401.1428571428572.37304144527906169.041656622093
Trimmed Mean ( 6 / 17 )400.92.24288047396931178.743363568773
Trimmed Mean ( 7 / 17 )400.8684210526322.15777763967755185.778373860865
Trimmed Mean ( 8 / 17 )4012.11006657534329190.041397122629
Trimmed Mean ( 9 / 17 )401.1470588235292.05890628812531194.835025341918
Trimmed Mean ( 10 / 17 )401.31252.00324207989079200.331504628676
Trimmed Mean ( 11 / 17 )401.5333333333331.92845202249502208.21536063616
Trimmed Mean ( 12 / 17 )401.751.8298126367785219.557998411961
Trimmed Mean ( 13 / 17 )4021.70790019524651235.376751591727
Trimmed Mean ( 14 / 17 )4021.65064765506132243.540769447291
Trimmed Mean ( 15 / 17 )4021.57011769587695256.031761858128
Trimmed Mean ( 16 / 17 )402.11.47416345590875272.764867687026
Trimmed Mean ( 17 / 17 )4021.42801109459083281.510417897128
Median401.5
Midrange347
Midmean - Weighted Average at Xnp401.75
Midmean - Weighted Average at X(n+1)p402.518518518519
Midmean - Empirical Distribution Function401.75
Midmean - Empirical Distribution Function - Averaging402.518518518519
Midmean - Empirical Distribution Function - Interpolation402.518518518519
Midmean - Closest Observation401.75
Midmean - True Basic - Statistics Graphics Toolkit402.518518518519
Midmean - MS Excel (old versions)401.75
Number of observations52

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 399.307692307692 & 4.77309725038605 & 83.6579837704744 \tabularnewline
Geometric Mean & 397.532645958995 &  &  \tabularnewline
Harmonic Mean & 395.276942244999 &  &  \tabularnewline
Quadratic Mean & 400.759951169698 &  &  \tabularnewline
Winsorized Mean ( 1 / 17 ) & 401.25 & 3.29608239053403 & 121.735427837709 \tabularnewline
Winsorized Mean ( 2 / 17 ) & 401.788461538462 & 3.07416330797319 & 130.698476719301 \tabularnewline
Winsorized Mean ( 3 / 17 ) & 401.557692307692 & 2.95279777107689 & 135.992276965599 \tabularnewline
Winsorized Mean ( 4 / 17 ) & 402.173076923077 & 2.7797100928851 & 144.681662290061 \tabularnewline
Winsorized Mean ( 5 / 17 ) & 402.076923076923 & 2.66871802987144 & 150.662946994176 \tabularnewline
Winsorized Mean ( 6 / 17 ) & 401.038461538462 & 2.4295443865963 & 165.067353266306 \tabularnewline
Winsorized Mean ( 7 / 17 ) & 400.230769230769 & 2.22043426931659 & 180.248870575193 \tabularnewline
Winsorized Mean ( 8 / 17 ) & 400.230769230769 & 2.16262217670982 & 185.06735644396 \tabularnewline
Winsorized Mean ( 9 / 17 ) & 400.230769230769 & 2.09891435426209 & 190.68465962799 \tabularnewline
Winsorized Mean ( 10 / 17 ) & 400.038461538462 & 2.06748175281826 & 193.49068546465 \tabularnewline
Winsorized Mean ( 11 / 17 ) & 400.25 & 2.02564162227687 & 197.591713952891 \tabularnewline
Winsorized Mean ( 12 / 17 ) & 400.25 & 1.9435617115741 & 205.936347488466 \tabularnewline
Winsorized Mean ( 13 / 17 ) & 402 & 1.62373050539423 & 247.578030137702 \tabularnewline
Winsorized Mean ( 14 / 17 ) & 401.730769230769 & 1.57877976264127 & 254.456497819988 \tabularnewline
Winsorized Mean ( 15 / 17 ) & 401.730769230769 & 1.4827096451655 & 270.943654100212 \tabularnewline
Winsorized Mean ( 16 / 17 ) & 402.653846153846 & 1.23360579988942 & 326.403982690369 \tabularnewline
Winsorized Mean ( 17 / 17 ) & 402.653846153846 & 1.1305722117278 & 356.150489085956 \tabularnewline
Trimmed Mean ( 1 / 17 ) & 401.4 & 3.09561902417871 & 129.667118875035 \tabularnewline
Trimmed Mean ( 2 / 17 ) & 401.5625 & 2.83576860039118 & 141.606229769455 \tabularnewline
Trimmed Mean ( 3 / 17 ) & 401.434782608696 & 2.66297791499693 & 150.746568474323 \tabularnewline
Trimmed Mean ( 4 / 17 ) & 401.386363636364 & 2.50416479919628 & 160.287519321887 \tabularnewline
Trimmed Mean ( 5 / 17 ) & 401.142857142857 & 2.37304144527906 & 169.041656622093 \tabularnewline
Trimmed Mean ( 6 / 17 ) & 400.9 & 2.24288047396931 & 178.743363568773 \tabularnewline
Trimmed Mean ( 7 / 17 ) & 400.868421052632 & 2.15777763967755 & 185.778373860865 \tabularnewline
Trimmed Mean ( 8 / 17 ) & 401 & 2.11006657534329 & 190.041397122629 \tabularnewline
Trimmed Mean ( 9 / 17 ) & 401.147058823529 & 2.05890628812531 & 194.835025341918 \tabularnewline
Trimmed Mean ( 10 / 17 ) & 401.3125 & 2.00324207989079 & 200.331504628676 \tabularnewline
Trimmed Mean ( 11 / 17 ) & 401.533333333333 & 1.92845202249502 & 208.21536063616 \tabularnewline
Trimmed Mean ( 12 / 17 ) & 401.75 & 1.8298126367785 & 219.557998411961 \tabularnewline
Trimmed Mean ( 13 / 17 ) & 402 & 1.70790019524651 & 235.376751591727 \tabularnewline
Trimmed Mean ( 14 / 17 ) & 402 & 1.65064765506132 & 243.540769447291 \tabularnewline
Trimmed Mean ( 15 / 17 ) & 402 & 1.57011769587695 & 256.031761858128 \tabularnewline
Trimmed Mean ( 16 / 17 ) & 402.1 & 1.47416345590875 & 272.764867687026 \tabularnewline
Trimmed Mean ( 17 / 17 ) & 402 & 1.42801109459083 & 281.510417897128 \tabularnewline
Median & 401.5 &  &  \tabularnewline
Midrange & 347 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 401.75 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 402.518518518519 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 401.75 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 402.518518518519 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 402.518518518519 &  &  \tabularnewline
Midmean - Closest Observation & 401.75 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 402.518518518519 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 401.75 &  &  \tabularnewline
Number of observations & 52 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284076&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]399.307692307692[/C][C]4.77309725038605[/C][C]83.6579837704744[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]397.532645958995[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]395.276942244999[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]400.759951169698[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 17 )[/C][C]401.25[/C][C]3.29608239053403[/C][C]121.735427837709[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 17 )[/C][C]401.788461538462[/C][C]3.07416330797319[/C][C]130.698476719301[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 17 )[/C][C]401.557692307692[/C][C]2.95279777107689[/C][C]135.992276965599[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 17 )[/C][C]402.173076923077[/C][C]2.7797100928851[/C][C]144.681662290061[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 17 )[/C][C]402.076923076923[/C][C]2.66871802987144[/C][C]150.662946994176[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 17 )[/C][C]401.038461538462[/C][C]2.4295443865963[/C][C]165.067353266306[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 17 )[/C][C]400.230769230769[/C][C]2.22043426931659[/C][C]180.248870575193[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 17 )[/C][C]400.230769230769[/C][C]2.16262217670982[/C][C]185.06735644396[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 17 )[/C][C]400.230769230769[/C][C]2.09891435426209[/C][C]190.68465962799[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 17 )[/C][C]400.038461538462[/C][C]2.06748175281826[/C][C]193.49068546465[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 17 )[/C][C]400.25[/C][C]2.02564162227687[/C][C]197.591713952891[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 17 )[/C][C]400.25[/C][C]1.9435617115741[/C][C]205.936347488466[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 17 )[/C][C]402[/C][C]1.62373050539423[/C][C]247.578030137702[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 17 )[/C][C]401.730769230769[/C][C]1.57877976264127[/C][C]254.456497819988[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 17 )[/C][C]401.730769230769[/C][C]1.4827096451655[/C][C]270.943654100212[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 17 )[/C][C]402.653846153846[/C][C]1.23360579988942[/C][C]326.403982690369[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 17 )[/C][C]402.653846153846[/C][C]1.1305722117278[/C][C]356.150489085956[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 17 )[/C][C]401.4[/C][C]3.09561902417871[/C][C]129.667118875035[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 17 )[/C][C]401.5625[/C][C]2.83576860039118[/C][C]141.606229769455[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 17 )[/C][C]401.434782608696[/C][C]2.66297791499693[/C][C]150.746568474323[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 17 )[/C][C]401.386363636364[/C][C]2.50416479919628[/C][C]160.287519321887[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 17 )[/C][C]401.142857142857[/C][C]2.37304144527906[/C][C]169.041656622093[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 17 )[/C][C]400.9[/C][C]2.24288047396931[/C][C]178.743363568773[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 17 )[/C][C]400.868421052632[/C][C]2.15777763967755[/C][C]185.778373860865[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 17 )[/C][C]401[/C][C]2.11006657534329[/C][C]190.041397122629[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 17 )[/C][C]401.147058823529[/C][C]2.05890628812531[/C][C]194.835025341918[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 17 )[/C][C]401.3125[/C][C]2.00324207989079[/C][C]200.331504628676[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 17 )[/C][C]401.533333333333[/C][C]1.92845202249502[/C][C]208.21536063616[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 17 )[/C][C]401.75[/C][C]1.8298126367785[/C][C]219.557998411961[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 17 )[/C][C]402[/C][C]1.70790019524651[/C][C]235.376751591727[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 17 )[/C][C]402[/C][C]1.65064765506132[/C][C]243.540769447291[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 17 )[/C][C]402[/C][C]1.57011769587695[/C][C]256.031761858128[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 17 )[/C][C]402.1[/C][C]1.47416345590875[/C][C]272.764867687026[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 17 )[/C][C]402[/C][C]1.42801109459083[/C][C]281.510417897128[/C][/ROW]
[ROW][C]Median[/C][C]401.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]347[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]401.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]402.518518518519[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]401.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]402.518518518519[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]402.518518518519[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]401.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]402.518518518519[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]401.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]52[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284076&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284076&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 Mean399.3076923076924.7730972503860583.6579837704744
Geometric Mean397.532645958995
Harmonic Mean395.276942244999
Quadratic Mean400.759951169698
Winsorized Mean ( 1 / 17 )401.253.29608239053403121.735427837709
Winsorized Mean ( 2 / 17 )401.7884615384623.07416330797319130.698476719301
Winsorized Mean ( 3 / 17 )401.5576923076922.95279777107689135.992276965599
Winsorized Mean ( 4 / 17 )402.1730769230772.7797100928851144.681662290061
Winsorized Mean ( 5 / 17 )402.0769230769232.66871802987144150.662946994176
Winsorized Mean ( 6 / 17 )401.0384615384622.4295443865963165.067353266306
Winsorized Mean ( 7 / 17 )400.2307692307692.22043426931659180.248870575193
Winsorized Mean ( 8 / 17 )400.2307692307692.16262217670982185.06735644396
Winsorized Mean ( 9 / 17 )400.2307692307692.09891435426209190.68465962799
Winsorized Mean ( 10 / 17 )400.0384615384622.06748175281826193.49068546465
Winsorized Mean ( 11 / 17 )400.252.02564162227687197.591713952891
Winsorized Mean ( 12 / 17 )400.251.9435617115741205.936347488466
Winsorized Mean ( 13 / 17 )4021.62373050539423247.578030137702
Winsorized Mean ( 14 / 17 )401.7307692307691.57877976264127254.456497819988
Winsorized Mean ( 15 / 17 )401.7307692307691.4827096451655270.943654100212
Winsorized Mean ( 16 / 17 )402.6538461538461.23360579988942326.403982690369
Winsorized Mean ( 17 / 17 )402.6538461538461.1305722117278356.150489085956
Trimmed Mean ( 1 / 17 )401.43.09561902417871129.667118875035
Trimmed Mean ( 2 / 17 )401.56252.83576860039118141.606229769455
Trimmed Mean ( 3 / 17 )401.4347826086962.66297791499693150.746568474323
Trimmed Mean ( 4 / 17 )401.3863636363642.50416479919628160.287519321887
Trimmed Mean ( 5 / 17 )401.1428571428572.37304144527906169.041656622093
Trimmed Mean ( 6 / 17 )400.92.24288047396931178.743363568773
Trimmed Mean ( 7 / 17 )400.8684210526322.15777763967755185.778373860865
Trimmed Mean ( 8 / 17 )4012.11006657534329190.041397122629
Trimmed Mean ( 9 / 17 )401.1470588235292.05890628812531194.835025341918
Trimmed Mean ( 10 / 17 )401.31252.00324207989079200.331504628676
Trimmed Mean ( 11 / 17 )401.5333333333331.92845202249502208.21536063616
Trimmed Mean ( 12 / 17 )401.751.8298126367785219.557998411961
Trimmed Mean ( 13 / 17 )4021.70790019524651235.376751591727
Trimmed Mean ( 14 / 17 )4021.65064765506132243.540769447291
Trimmed Mean ( 15 / 17 )4021.57011769587695256.031761858128
Trimmed Mean ( 16 / 17 )402.11.47416345590875272.764867687026
Trimmed Mean ( 17 / 17 )4021.42801109459083281.510417897128
Median401.5
Midrange347
Midmean - Weighted Average at Xnp401.75
Midmean - Weighted Average at X(n+1)p402.518518518519
Midmean - Empirical Distribution Function401.75
Midmean - Empirical Distribution Function - Averaging402.518518518519
Midmean - Empirical Distribution Function - Interpolation402.518518518519
Midmean - Closest Observation401.75
Midmean - True Basic - Statistics Graphics Toolkit402.518518518519
Midmean - MS Excel (old versions)401.75
Number of observations52



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')