Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 29 May 2009 07:45:51 -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/May/29/t1243604818adphdas9qwapr3z.htm/, Retrieved Sat, 27 Apr 2024 14:22:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=40769, Retrieved Sat, 27 Apr 2024 14:22:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact175
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency ...] [2009-05-29 13:45:51] [46186faee359a0c92d914c5fc942bc84] [Current]
Feedback Forum

Post a new message
Dataseries X:
666,27
664,45
660,76
660,40
660,69
660,69
662,23
661,41
659,02
655,43
652,59
652,59
648,20
645,84
644,67
642,71
640,14
640,14
639,64
630,28
614,57
614,70
615,08
615,08
614,43
604,55
598,98
594,05
593,05
593,05
593,34
584,72
580,70
577,08
569,92
569,92
568,86
559,38
548,22
545,61
545,33
530,30
527,76
521,41
1601,93
1577,49
1551,43
1551,43
1516,88
1485,95
1438,22
1385,06
1329,49
1329,49
1276,16
1242,34
1181,59
1160,21
1135,18
1135,18
1084,96
1077,35
1061,13
1029,98
1013,08
1013,08
996,04
975,02
951,89
944,40
932,47
932,47
920,44
900,18
886,90




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=40769&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=40769&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40769&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 Mean847.27546666666737.039165601333422.875122938411
Geometric Mean795.873757474623
Harmonic Mean753.953088724831
Quadratic Mean905.20511529708
Winsorized Mean ( 1 / 25 )847.03426666666736.940788008283122.9295126697552
Winsorized Mean ( 2 / 25 )846.40706666666736.749961594279523.0315088764179
Winsorized Mean ( 3 / 25 )847.00826666666736.681611043821523.0908142408138
Winsorized Mean ( 4 / 25 )845.18053333333336.209841176815623.3411831111395
Winsorized Mean ( 5 / 25 )843.29253333333335.680947366070623.6342528880057
Winsorized Mean ( 6 / 25 )840.36693333333334.672317225718324.2374032246679
Winsorized Mean ( 7 / 25 )836.29013333333333.447462895470925.0030962272649
Winsorized Mean ( 8 / 25 )830.47573333333332.155833013047625.8265967793886
Winsorized Mean ( 9 / 25 )830.47573333333332.155833013047625.8265967793886
Winsorized Mean ( 10 / 25 )824.31973333333330.595406191110426.9425981202643
Winsorized Mean ( 11 / 25 )819.890429.563231424052327.7334499818226
Winsorized Mean ( 12 / 25 )810.813627.672172791055229.3006843417112
Winsorized Mean ( 13 / 25 )808.551626.850583878792530.1129987954795
Winsorized Mean ( 14 / 25 )803.87933333333326.035220002000230.8766099641783
Winsorized Mean ( 15 / 25 )803.93733333333326.028875756842930.886364084395
Winsorized Mean ( 16 / 25 )793.375224.217583981207732.7602951894641
Winsorized Mean ( 17 / 25 )792.76773333333323.814378262315833.2894575118016
Winsorized Mean ( 18 / 25 )790.21173333333323.044469573486934.290732134815
Winsorized Mean ( 19 / 25 )784.82333333333321.539975202486336.4356655917944
Winsorized Mean ( 20 / 25 )780.35420.849399123711437.4281290012106
Winsorized Mean ( 21 / 25 )780.390420.845488582666837.4368965690208
Winsorized Mean ( 22 / 25 )775.50346666666720.085556476551338.6100065274278
Winsorized Mean ( 23 / 25 )769.05733333333319.138371719769840.1840524676874
Winsorized Mean ( 24 / 25 )766.51973333333317.551627506963143.6722881128397
Winsorized Mean ( 25 / 25 )767.14306666666716.873205892186645.4651636190788
Trimmed Mean ( 1 / 25 )841.40164383561636.32634046223223.1623013254090
Trimmed Mean ( 2 / 25 )835.45169014084535.584011569745923.4782885145856
Trimmed Mean ( 3 / 25 )829.4976811594234.808372566536623.83040688196
Trimmed Mean ( 4 / 25 )822.96388059701533.894428544216524.2802111126739
Trimmed Mean ( 5 / 25 )816.5552307692332.959116621455724.7747911495198
Trimmed Mean ( 6 / 25 )810.18920634920631.986523119191325.3290801044615
Trimmed Mean ( 7 / 25 )804.0052459016431.0856170320425.8642202621537
Trimmed Mean ( 8 / 25 )798.14237288135630.300314061461526.3410594115426
Trimmed Mean ( 9 / 25 )792.82438596491229.647793304192426.7414298875593
Trimmed Mean ( 10 / 25 )787.11963636363628.816469430436227.3149227480406
Trimmed Mean ( 11 / 25 )781.85547169811328.134481837344727.7899367835631
Trimmed Mean ( 12 / 25 )776.77058823529427.494605884394428.2517447786432
Trimmed Mean ( 13 / 25 )772.42836734693927.089507216263228.5139320246922
Trimmed Mean ( 14 / 25 )767.99425531914926.710838079873228.7521586938838
Trimmed Mean ( 15 / 25 )763.72222222222226.364457760763428.9678714105329
Trimmed Mean ( 16 / 25 )759.04604651162825.866129574245629.3451729735165
Trimmed Mean ( 17 / 25 )755.12121951219525.593457994123529.5044624171371
Trimmed Mean ( 18 / 25 )750.86256410256425.256075469876029.7299778422878
Trimmed Mean ( 19 / 25 )746.43135135135124.916114622713929.9577748238040
Trimmed Mean ( 20 / 25 )742.10142857142924.741388890393629.9943318404234
Trimmed Mean ( 21 / 25 )737.75454545454524.582210293136930.0117254167547
Trimmed Mean ( 22 / 25 )732.84258064516124.239631415841730.2332394446483
Trimmed Mean ( 23 / 25 )727.82758620689723.867457494567130.4945588097337
Trimmed Mean ( 24 / 25 )722.84814814814823.511975514684930.743828722375
Trimmed Mean ( 25 / 25 )717.389223.320258931667130.762488619963
Median660.69
Midrange1061.67
Midmean - Weighted Average at Xnp742.697631578948
Midmean - Weighted Average at X(n+1)p750.862564102564
Midmean - Empirical Distribution Function750.862564102564
Midmean - Empirical Distribution Function - Averaging750.862564102564
Midmean - Empirical Distribution Function - Interpolation746.431351351352
Midmean - Closest Observation742.697631578948
Midmean - True Basic - Statistics Graphics Toolkit750.862564102564
Midmean - MS Excel (old versions)750.862564102564
Number of observations75

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 847.275466666667 & 37.0391656013334 & 22.875122938411 \tabularnewline
Geometric Mean & 795.873757474623 &  &  \tabularnewline
Harmonic Mean & 753.953088724831 &  &  \tabularnewline
Quadratic Mean & 905.20511529708 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & 847.034266666667 & 36.9407880082831 & 22.9295126697552 \tabularnewline
Winsorized Mean ( 2 / 25 ) & 846.407066666667 & 36.7499615942795 & 23.0315088764179 \tabularnewline
Winsorized Mean ( 3 / 25 ) & 847.008266666667 & 36.6816110438215 & 23.0908142408138 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 845.180533333333 & 36.2098411768156 & 23.3411831111395 \tabularnewline
Winsorized Mean ( 5 / 25 ) & 843.292533333333 & 35.6809473660706 & 23.6342528880057 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 840.366933333333 & 34.6723172257183 & 24.2374032246679 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 836.290133333333 & 33.4474628954709 & 25.0030962272649 \tabularnewline
Winsorized Mean ( 8 / 25 ) & 830.475733333333 & 32.1558330130476 & 25.8265967793886 \tabularnewline
Winsorized Mean ( 9 / 25 ) & 830.475733333333 & 32.1558330130476 & 25.8265967793886 \tabularnewline
Winsorized Mean ( 10 / 25 ) & 824.319733333333 & 30.5954061911104 & 26.9425981202643 \tabularnewline
Winsorized Mean ( 11 / 25 ) & 819.8904 & 29.5632314240523 & 27.7334499818226 \tabularnewline
Winsorized Mean ( 12 / 25 ) & 810.8136 & 27.6721727910552 & 29.3006843417112 \tabularnewline
Winsorized Mean ( 13 / 25 ) & 808.5516 & 26.8505838787925 & 30.1129987954795 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 803.879333333333 & 26.0352200020002 & 30.8766099641783 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 803.937333333333 & 26.0288757568429 & 30.886364084395 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 793.3752 & 24.2175839812077 & 32.7602951894641 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 792.767733333333 & 23.8143782623158 & 33.2894575118016 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 790.211733333333 & 23.0444695734869 & 34.290732134815 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 784.823333333333 & 21.5399752024863 & 36.4356655917944 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 780.354 & 20.8493991237114 & 37.4281290012106 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 780.3904 & 20.8454885826668 & 37.4368965690208 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 775.503466666667 & 20.0855564765513 & 38.6100065274278 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 769.057333333333 & 19.1383717197698 & 40.1840524676874 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 766.519733333333 & 17.5516275069631 & 43.6722881128397 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 767.143066666667 & 16.8732058921866 & 45.4651636190788 \tabularnewline
Trimmed Mean ( 1 / 25 ) & 841.401643835616 & 36.326340462232 & 23.1623013254090 \tabularnewline
Trimmed Mean ( 2 / 25 ) & 835.451690140845 & 35.5840115697459 & 23.4782885145856 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 829.49768115942 & 34.8083725665366 & 23.83040688196 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 822.963880597015 & 33.8944285442165 & 24.2802111126739 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 816.55523076923 & 32.9591166214557 & 24.7747911495198 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 810.189206349206 & 31.9865231191913 & 25.3290801044615 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 804.00524590164 & 31.08561703204 & 25.8642202621537 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 798.142372881356 & 30.3003140614615 & 26.3410594115426 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 792.824385964912 & 29.6477933041924 & 26.7414298875593 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 787.119636363636 & 28.8164694304362 & 27.3149227480406 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 781.855471698113 & 28.1344818373447 & 27.7899367835631 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 776.770588235294 & 27.4946058843944 & 28.2517447786432 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 772.428367346939 & 27.0895072162632 & 28.5139320246922 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 767.994255319149 & 26.7108380798732 & 28.7521586938838 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 763.722222222222 & 26.3644577607634 & 28.9678714105329 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 759.046046511628 & 25.8661295742456 & 29.3451729735165 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 755.121219512195 & 25.5934579941235 & 29.5044624171371 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 750.862564102564 & 25.2560754698760 & 29.7299778422878 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 746.431351351351 & 24.9161146227139 & 29.9577748238040 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 742.101428571429 & 24.7413888903936 & 29.9943318404234 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 737.754545454545 & 24.5822102931369 & 30.0117254167547 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 732.842580645161 & 24.2396314158417 & 30.2332394446483 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 727.827586206897 & 23.8674574945671 & 30.4945588097337 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 722.848148148148 & 23.5119755146849 & 30.743828722375 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 717.3892 & 23.3202589316671 & 30.762488619963 \tabularnewline
Median & 660.69 &  &  \tabularnewline
Midrange & 1061.67 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 742.697631578948 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 750.862564102564 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 750.862564102564 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 750.862564102564 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 746.431351351352 &  &  \tabularnewline
Midmean - Closest Observation & 742.697631578948 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 750.862564102564 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 750.862564102564 &  &  \tabularnewline
Number of observations & 75 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=40769&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]847.275466666667[/C][C]37.0391656013334[/C][C]22.875122938411[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]795.873757474623[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]753.953088724831[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]905.20511529708[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]847.034266666667[/C][C]36.9407880082831[/C][C]22.9295126697552[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]846.407066666667[/C][C]36.7499615942795[/C][C]23.0315088764179[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]847.008266666667[/C][C]36.6816110438215[/C][C]23.0908142408138[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]845.180533333333[/C][C]36.2098411768156[/C][C]23.3411831111395[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]843.292533333333[/C][C]35.6809473660706[/C][C]23.6342528880057[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]840.366933333333[/C][C]34.6723172257183[/C][C]24.2374032246679[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]836.290133333333[/C][C]33.4474628954709[/C][C]25.0030962272649[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]830.475733333333[/C][C]32.1558330130476[/C][C]25.8265967793886[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]830.475733333333[/C][C]32.1558330130476[/C][C]25.8265967793886[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]824.319733333333[/C][C]30.5954061911104[/C][C]26.9425981202643[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]819.8904[/C][C]29.5632314240523[/C][C]27.7334499818226[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]810.8136[/C][C]27.6721727910552[/C][C]29.3006843417112[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]808.5516[/C][C]26.8505838787925[/C][C]30.1129987954795[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]803.879333333333[/C][C]26.0352200020002[/C][C]30.8766099641783[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]803.937333333333[/C][C]26.0288757568429[/C][C]30.886364084395[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]793.3752[/C][C]24.2175839812077[/C][C]32.7602951894641[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]792.767733333333[/C][C]23.8143782623158[/C][C]33.2894575118016[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]790.211733333333[/C][C]23.0444695734869[/C][C]34.290732134815[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]784.823333333333[/C][C]21.5399752024863[/C][C]36.4356655917944[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]780.354[/C][C]20.8493991237114[/C][C]37.4281290012106[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]780.3904[/C][C]20.8454885826668[/C][C]37.4368965690208[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]775.503466666667[/C][C]20.0855564765513[/C][C]38.6100065274278[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]769.057333333333[/C][C]19.1383717197698[/C][C]40.1840524676874[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]766.519733333333[/C][C]17.5516275069631[/C][C]43.6722881128397[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]767.143066666667[/C][C]16.8732058921866[/C][C]45.4651636190788[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]841.401643835616[/C][C]36.326340462232[/C][C]23.1623013254090[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]835.451690140845[/C][C]35.5840115697459[/C][C]23.4782885145856[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]829.49768115942[/C][C]34.8083725665366[/C][C]23.83040688196[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]822.963880597015[/C][C]33.8944285442165[/C][C]24.2802111126739[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]816.55523076923[/C][C]32.9591166214557[/C][C]24.7747911495198[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]810.189206349206[/C][C]31.9865231191913[/C][C]25.3290801044615[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]804.00524590164[/C][C]31.08561703204[/C][C]25.8642202621537[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]798.142372881356[/C][C]30.3003140614615[/C][C]26.3410594115426[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]792.824385964912[/C][C]29.6477933041924[/C][C]26.7414298875593[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]787.119636363636[/C][C]28.8164694304362[/C][C]27.3149227480406[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]781.855471698113[/C][C]28.1344818373447[/C][C]27.7899367835631[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]776.770588235294[/C][C]27.4946058843944[/C][C]28.2517447786432[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]772.428367346939[/C][C]27.0895072162632[/C][C]28.5139320246922[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]767.994255319149[/C][C]26.7108380798732[/C][C]28.7521586938838[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]763.722222222222[/C][C]26.3644577607634[/C][C]28.9678714105329[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]759.046046511628[/C][C]25.8661295742456[/C][C]29.3451729735165[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]755.121219512195[/C][C]25.5934579941235[/C][C]29.5044624171371[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]750.862564102564[/C][C]25.2560754698760[/C][C]29.7299778422878[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]746.431351351351[/C][C]24.9161146227139[/C][C]29.9577748238040[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]742.101428571429[/C][C]24.7413888903936[/C][C]29.9943318404234[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]737.754545454545[/C][C]24.5822102931369[/C][C]30.0117254167547[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]732.842580645161[/C][C]24.2396314158417[/C][C]30.2332394446483[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]727.827586206897[/C][C]23.8674574945671[/C][C]30.4945588097337[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]722.848148148148[/C][C]23.5119755146849[/C][C]30.743828722375[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]717.3892[/C][C]23.3202589316671[/C][C]30.762488619963[/C][/ROW]
[ROW][C]Median[/C][C]660.69[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1061.67[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]742.697631578948[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]750.862564102564[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]750.862564102564[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]750.862564102564[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]746.431351351352[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]742.697631578948[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]750.862564102564[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]750.862564102564[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]75[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=40769&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=40769&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 Mean847.27546666666737.039165601333422.875122938411
Geometric Mean795.873757474623
Harmonic Mean753.953088724831
Quadratic Mean905.20511529708
Winsorized Mean ( 1 / 25 )847.03426666666736.940788008283122.9295126697552
Winsorized Mean ( 2 / 25 )846.40706666666736.749961594279523.0315088764179
Winsorized Mean ( 3 / 25 )847.00826666666736.681611043821523.0908142408138
Winsorized Mean ( 4 / 25 )845.18053333333336.209841176815623.3411831111395
Winsorized Mean ( 5 / 25 )843.29253333333335.680947366070623.6342528880057
Winsorized Mean ( 6 / 25 )840.36693333333334.672317225718324.2374032246679
Winsorized Mean ( 7 / 25 )836.29013333333333.447462895470925.0030962272649
Winsorized Mean ( 8 / 25 )830.47573333333332.155833013047625.8265967793886
Winsorized Mean ( 9 / 25 )830.47573333333332.155833013047625.8265967793886
Winsorized Mean ( 10 / 25 )824.31973333333330.595406191110426.9425981202643
Winsorized Mean ( 11 / 25 )819.890429.563231424052327.7334499818226
Winsorized Mean ( 12 / 25 )810.813627.672172791055229.3006843417112
Winsorized Mean ( 13 / 25 )808.551626.850583878792530.1129987954795
Winsorized Mean ( 14 / 25 )803.87933333333326.035220002000230.8766099641783
Winsorized Mean ( 15 / 25 )803.93733333333326.028875756842930.886364084395
Winsorized Mean ( 16 / 25 )793.375224.217583981207732.7602951894641
Winsorized Mean ( 17 / 25 )792.76773333333323.814378262315833.2894575118016
Winsorized Mean ( 18 / 25 )790.21173333333323.044469573486934.290732134815
Winsorized Mean ( 19 / 25 )784.82333333333321.539975202486336.4356655917944
Winsorized Mean ( 20 / 25 )780.35420.849399123711437.4281290012106
Winsorized Mean ( 21 / 25 )780.390420.845488582666837.4368965690208
Winsorized Mean ( 22 / 25 )775.50346666666720.085556476551338.6100065274278
Winsorized Mean ( 23 / 25 )769.05733333333319.138371719769840.1840524676874
Winsorized Mean ( 24 / 25 )766.51973333333317.551627506963143.6722881128397
Winsorized Mean ( 25 / 25 )767.14306666666716.873205892186645.4651636190788
Trimmed Mean ( 1 / 25 )841.40164383561636.32634046223223.1623013254090
Trimmed Mean ( 2 / 25 )835.45169014084535.584011569745923.4782885145856
Trimmed Mean ( 3 / 25 )829.4976811594234.808372566536623.83040688196
Trimmed Mean ( 4 / 25 )822.96388059701533.894428544216524.2802111126739
Trimmed Mean ( 5 / 25 )816.5552307692332.959116621455724.7747911495198
Trimmed Mean ( 6 / 25 )810.18920634920631.986523119191325.3290801044615
Trimmed Mean ( 7 / 25 )804.0052459016431.0856170320425.8642202621537
Trimmed Mean ( 8 / 25 )798.14237288135630.300314061461526.3410594115426
Trimmed Mean ( 9 / 25 )792.82438596491229.647793304192426.7414298875593
Trimmed Mean ( 10 / 25 )787.11963636363628.816469430436227.3149227480406
Trimmed Mean ( 11 / 25 )781.85547169811328.134481837344727.7899367835631
Trimmed Mean ( 12 / 25 )776.77058823529427.494605884394428.2517447786432
Trimmed Mean ( 13 / 25 )772.42836734693927.089507216263228.5139320246922
Trimmed Mean ( 14 / 25 )767.99425531914926.710838079873228.7521586938838
Trimmed Mean ( 15 / 25 )763.72222222222226.364457760763428.9678714105329
Trimmed Mean ( 16 / 25 )759.04604651162825.866129574245629.3451729735165
Trimmed Mean ( 17 / 25 )755.12121951219525.593457994123529.5044624171371
Trimmed Mean ( 18 / 25 )750.86256410256425.256075469876029.7299778422878
Trimmed Mean ( 19 / 25 )746.43135135135124.916114622713929.9577748238040
Trimmed Mean ( 20 / 25 )742.10142857142924.741388890393629.9943318404234
Trimmed Mean ( 21 / 25 )737.75454545454524.582210293136930.0117254167547
Trimmed Mean ( 22 / 25 )732.84258064516124.239631415841730.2332394446483
Trimmed Mean ( 23 / 25 )727.82758620689723.867457494567130.4945588097337
Trimmed Mean ( 24 / 25 )722.84814814814823.511975514684930.743828722375
Trimmed Mean ( 25 / 25 )717.389223.320258931667130.762488619963
Median660.69
Midrange1061.67
Midmean - Weighted Average at Xnp742.697631578948
Midmean - Weighted Average at X(n+1)p750.862564102564
Midmean - Empirical Distribution Function750.862564102564
Midmean - Empirical Distribution Function - Averaging750.862564102564
Midmean - Empirical Distribution Function - Interpolation746.431351351352
Midmean - Closest Observation742.697631578948
Midmean - True Basic - Statistics Graphics Toolkit750.862564102564
Midmean - MS Excel (old versions)750.862564102564
Number of observations75



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')