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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 02 Dec 2011 06:39:10 -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/2011/Dec/02/t13228260246etx3253myzl48x.htm/, Retrieved Sun, 28 Apr 2024 20:10:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150127, Retrieved Sun, 28 Apr 2024 20:10:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact44
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]
- R  D    [Central Tendency] [D1 - Central Tend...] [2011-12-02 11:39:10] [13dfa60174f50d862e8699db2153bfc5] [Current]
- RM        [Variability] [D1 Variability] [2011-12-02 14:40:33] [0f81819b439c6e991d1a2004e9982756]
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Dataseries X:
617
614
647
580
614
636
388
356
639
753
611
639
630
586
695
552
619
681
421
307
754
690
644
643
608
651
691
627
634
731
475
337
803
722
590
724
627
696
825
677
656
785
412
352
839
729
696
641
695
638
762
635
721
854
418
367
824
687
601
676
740
691
683
594
729
731
386
331
706
715
657
653
642
643
718
654
632
731
392
344
792
852
649
629
685
617
715
715
629
916
531
357
917
828
708
858
775
785
1006
789
734
906
532
387
991
841
892
782
811
792
978
773
796
946
594
438
1023
868
791
760
779
852
1001
734
996
869
599
426
1138




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150127&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150127&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150127&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean681.20930232558114.40429133349147.292108063777
Geometric Mean659.343593658288
Harmonic Mean634.40142052324
Quadratic Mean700.431306770247
Winsorized Mean ( 1 / 43 )680.50387596899214.172683645963548.0151743288791
Winsorized Mean ( 2 / 43 )680.33333333333314.10622651934248.229293099787
Winsorized Mean ( 3 / 43 )680.3798449612414.054681046767448.4094831250354
Winsorized Mean ( 4 / 43 )680.47286821705413.981239495805548.6704249949514
Winsorized Mean ( 5 / 43 )680.43410852713213.918918571698648.8855585311535
Winsorized Mean ( 6 / 43 )679.87596899224813.80672762399349.242368467585
Winsorized Mean ( 7 / 43 )678.68217054263613.426276340740350.5488009719615
Winsorized Mean ( 8 / 43 )678.06201550387612.945813351266252.3769343111653
Winsorized Mean ( 9 / 43 )678.06201550387612.923479473342952.4674501865002
Winsorized Mean ( 10 / 43 )677.36434108527112.799966397426752.9192280708991
Winsorized Mean ( 11 / 43 )676.51162790697712.57647688612153.7918237382962
Winsorized Mean ( 12 / 43 )676.23255813953511.973629129406656.4768250988119
Winsorized Mean ( 13 / 43 )676.73643410852711.857277265447257.0735101287188
Winsorized Mean ( 14 / 43 )675.97674418604711.667191632964857.9382567331903
Winsorized Mean ( 15 / 43 )676.09302325581411.511792707887858.7304723435961
Winsorized Mean ( 16 / 43 )677.33333333333311.231521933750660.3064604537659
Winsorized Mean ( 17 / 43 )682.20930232558110.446851659484665.3028610496453
Winsorized Mean ( 18 / 43 )688.4883720930239.1108930211219875.5676057766111
Winsorized Mean ( 19 / 43 )688.3410852713189.0525991500569876.0379504119527
Winsorized Mean ( 20 / 43 )689.7364341085278.4247302835901581.8704469924704
Winsorized Mean ( 21 / 43 )693.8062015503887.8096376734782188.8397427074724
Winsorized Mean ( 22 / 43 )694.6589147286827.6723455132011590.5406193625459
Winsorized Mean ( 23 / 43 )693.0542635658917.2943404019091695.0126022888234
Winsorized Mean ( 24 / 43 )692.310077519387.0269570094181498.5220311710297
Winsorized Mean ( 25 / 43 )690.9534883720936.86233735621073100.687776264271
Winsorized Mean ( 26 / 43 )691.155038759696.65627626839453103.835089003359
Winsorized Mean ( 27 / 43 )691.5736434108536.61123492457582104.605818928031
Winsorized Mean ( 28 / 43 )692.8759689922486.42566136681365107.829518152126
Winsorized Mean ( 29 / 43 )693.1007751937986.3030005174842109.963623399867
Winsorized Mean ( 30 / 43 )692.8682170542646.12241263818675113.169147197414
Winsorized Mean ( 31 / 43 )692.8682170542646.12241263818675113.169147197414
Winsorized Mean ( 32 / 43 )692.8682170542645.96074224741649116.238580414137
Winsorized Mean ( 33 / 43 )692.1007751937985.87154406188805117.873725871563
Winsorized Mean ( 34 / 43 )691.5736434108535.69771874817961121.377286941692
Winsorized Mean ( 35 / 43 )693.2015503875975.42390742763431127.804826987975
Winsorized Mean ( 36 / 43 )690.1317829457365.07754046093026135.918519656522
Winsorized Mean ( 37 / 43 )690.1317829457364.9587613795388139.174227215975
Winsorized Mean ( 38 / 43 )688.3643410852714.76636737907478144.421167387834
Winsorized Mean ( 39 / 43 )688.3643410852714.70451933552777146.319802723916
Winsorized Mean ( 40 / 43 )684.9534883720934.22186108321308162.239703029452
Winsorized Mean ( 41 / 43 )683.6821705426363.96795522463947172.300878371115
Winsorized Mean ( 42 / 43 )684.0077519379843.93619619923844173.773795135091
Winsorized Mean ( 43 / 43 )683.3410852713183.80523749316179179.579089741263
Trimmed Mean ( 1 / 43 )680.5590551181113.867319275005149.0764683225236
Trimmed Mean ( 2 / 43 )680.61613.530771544174650.301344441295
Trimmed Mean ( 3 / 43 )680.76422764227613.197911585752951.5812083767221
Trimmed Mean ( 4 / 43 )680.90082644628112.850739894439152.9853403025399
Trimmed Mean ( 5 / 43 )681.01680672268912.489534050079854.5269986848177
Trimmed Mean ( 6 / 43 )681.14529914529912.104827919803856.2705478886593
Trimmed Mean ( 7 / 43 )681.38260869565211.702722421233958.2242818525135
Trimmed Mean ( 8 / 43 )681.82300884955711.336782362629460.1425507732352
Trimmed Mean ( 9 / 43 )682.36936936936911.023502016700161.901323947291
Trimmed Mean ( 10 / 43 )682.93577981651410.67652350409263.9661196413577
Trimmed Mean ( 11 / 43 )683.60747663551410.307712802631866.3199964652659
Trimmed Mean ( 12 / 43 )684.49.9289933238424768.9294450784403
Trimmed Mean ( 13 / 43 )685.2524271844669.5998040628066971.3819180788695
Trimmed Mean ( 14 / 43 )686.0891089108919.2452942165447374.2095484298503
Trimmed Mean ( 15 / 43 )687.0303030303038.8703812826308977.4521727014799
Trimmed Mean ( 16 / 43 )6888.4651219942778781.2746704022771
Trimmed Mean ( 17 / 43 )688.9052631578958.0438895964383385.6433016513464
Trimmed Mean ( 18 / 43 )689.4516129032267.6858691385807989.7037928270705
Trimmed Mean ( 19 / 43 )689.5274725274737.4727889058627292.271771786101
Trimmed Mean ( 20 / 43 )689.617977528097.2369869409970595.2907588683697
Trimmed Mean ( 21 / 43 )689.6091954022997.0521855943957297.7865919964334
Trimmed Mean ( 22 / 43 )689.3058823529416.9184125607815499.6335324465059
Trimmed Mean ( 23 / 43 )688.9277108433736.78070032479394101.60126208856
Trimmed Mean ( 24 / 43 )688.6419753086426.66933531406795103.254963632741
Trimmed Mean ( 25 / 43 )688.3924050632916.57257730164371104.737057241021
Trimmed Mean ( 26 / 43 )688.2207792207796.47962323109076106.213085958229
Trimmed Mean ( 27 / 43 )688.0266666666676.39490149769057107.589877172485
Trimmed Mean ( 28 / 43 )687.7945205479456.29950587876797109.182296799834
Trimmed Mean ( 29 / 43 )687.4647887323946.20818668257328110.735199162445
Trimmed Mean ( 30 / 43 )687.1014492753626.11390686655128112.383368649994
Trimmed Mean ( 31 / 43 )686.7313432835826.02364488025296114.005947716948
Trimmed Mean ( 32 / 43 )686.3384615384625.91389648181579116.055203815088
Trimmed Mean ( 33 / 43 )685.9206349206355.80275291710315118.206073000099
Trimmed Mean ( 34 / 43 )685.5245901639345.68045284875006120.681327425291
Trimmed Mean ( 35 / 43 )685.1355932203395.55665036799757123.300108490943
Trimmed Mean ( 36 / 43 )684.6140350877195.44232429441153125.794421289947
Trimmed Mean ( 37 / 43 )684.2545454545455.35690612388154127.733159706511
Trimmed Mean ( 38 / 43 )683.8679245283025.26614166103467129.861285272364
Trimmed Mean ( 39 / 43 )683.568627450985.18279619449721131.891859490202
Trimmed Mean ( 40 / 43 )683.2448979591845.08436734874094134.381497459734
Trimmed Mean ( 41 / 43 )683.1276595744685.04160461341047135.498063009022
Trimmed Mean ( 42 / 43 )683.0888888888895.02275853040637135.998751433831
Trimmed Mean ( 43 / 43 )683.0232558139534.99429224293643136.760770613689
Median687
Midrange722.5
Midmean - Weighted Average at Xnp684.84375
Midmean - Weighted Average at X(n+1)p686.338461538462
Midmean - Empirical Distribution Function686.338461538462
Midmean - Empirical Distribution Function - Averaging686.338461538462
Midmean - Empirical Distribution Function - Interpolation686.338461538462
Midmean - Closest Observation684.179104477612
Midmean - True Basic - Statistics Graphics Toolkit686.338461538462
Midmean - MS Excel (old versions)686.338461538462
Number of observations129

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 681.209302325581 & 14.404291333491 & 47.292108063777 \tabularnewline
Geometric Mean & 659.343593658288 &  &  \tabularnewline
Harmonic Mean & 634.40142052324 &  &  \tabularnewline
Quadratic Mean & 700.431306770247 &  &  \tabularnewline
Winsorized Mean ( 1 / 43 ) & 680.503875968992 & 14.1726836459635 & 48.0151743288791 \tabularnewline
Winsorized Mean ( 2 / 43 ) & 680.333333333333 & 14.106226519342 & 48.229293099787 \tabularnewline
Winsorized Mean ( 3 / 43 ) & 680.37984496124 & 14.0546810467674 & 48.4094831250354 \tabularnewline
Winsorized Mean ( 4 / 43 ) & 680.472868217054 & 13.9812394958055 & 48.6704249949514 \tabularnewline
Winsorized Mean ( 5 / 43 ) & 680.434108527132 & 13.9189185716986 & 48.8855585311535 \tabularnewline
Winsorized Mean ( 6 / 43 ) & 679.875968992248 & 13.806727623993 & 49.242368467585 \tabularnewline
Winsorized Mean ( 7 / 43 ) & 678.682170542636 & 13.4262763407403 & 50.5488009719615 \tabularnewline
Winsorized Mean ( 8 / 43 ) & 678.062015503876 & 12.9458133512662 & 52.3769343111653 \tabularnewline
Winsorized Mean ( 9 / 43 ) & 678.062015503876 & 12.9234794733429 & 52.4674501865002 \tabularnewline
Winsorized Mean ( 10 / 43 ) & 677.364341085271 & 12.7999663974267 & 52.9192280708991 \tabularnewline
Winsorized Mean ( 11 / 43 ) & 676.511627906977 & 12.576476886121 & 53.7918237382962 \tabularnewline
Winsorized Mean ( 12 / 43 ) & 676.232558139535 & 11.9736291294066 & 56.4768250988119 \tabularnewline
Winsorized Mean ( 13 / 43 ) & 676.736434108527 & 11.8572772654472 & 57.0735101287188 \tabularnewline
Winsorized Mean ( 14 / 43 ) & 675.976744186047 & 11.6671916329648 & 57.9382567331903 \tabularnewline
Winsorized Mean ( 15 / 43 ) & 676.093023255814 & 11.5117927078878 & 58.7304723435961 \tabularnewline
Winsorized Mean ( 16 / 43 ) & 677.333333333333 & 11.2315219337506 & 60.3064604537659 \tabularnewline
Winsorized Mean ( 17 / 43 ) & 682.209302325581 & 10.4468516594846 & 65.3028610496453 \tabularnewline
Winsorized Mean ( 18 / 43 ) & 688.488372093023 & 9.11089302112198 & 75.5676057766111 \tabularnewline
Winsorized Mean ( 19 / 43 ) & 688.341085271318 & 9.05259915005698 & 76.0379504119527 \tabularnewline
Winsorized Mean ( 20 / 43 ) & 689.736434108527 & 8.42473028359015 & 81.8704469924704 \tabularnewline
Winsorized Mean ( 21 / 43 ) & 693.806201550388 & 7.80963767347821 & 88.8397427074724 \tabularnewline
Winsorized Mean ( 22 / 43 ) & 694.658914728682 & 7.67234551320115 & 90.5406193625459 \tabularnewline
Winsorized Mean ( 23 / 43 ) & 693.054263565891 & 7.29434040190916 & 95.0126022888234 \tabularnewline
Winsorized Mean ( 24 / 43 ) & 692.31007751938 & 7.02695700941814 & 98.5220311710297 \tabularnewline
Winsorized Mean ( 25 / 43 ) & 690.953488372093 & 6.86233735621073 & 100.687776264271 \tabularnewline
Winsorized Mean ( 26 / 43 ) & 691.15503875969 & 6.65627626839453 & 103.835089003359 \tabularnewline
Winsorized Mean ( 27 / 43 ) & 691.573643410853 & 6.61123492457582 & 104.605818928031 \tabularnewline
Winsorized Mean ( 28 / 43 ) & 692.875968992248 & 6.42566136681365 & 107.829518152126 \tabularnewline
Winsorized Mean ( 29 / 43 ) & 693.100775193798 & 6.3030005174842 & 109.963623399867 \tabularnewline
Winsorized Mean ( 30 / 43 ) & 692.868217054264 & 6.12241263818675 & 113.169147197414 \tabularnewline
Winsorized Mean ( 31 / 43 ) & 692.868217054264 & 6.12241263818675 & 113.169147197414 \tabularnewline
Winsorized Mean ( 32 / 43 ) & 692.868217054264 & 5.96074224741649 & 116.238580414137 \tabularnewline
Winsorized Mean ( 33 / 43 ) & 692.100775193798 & 5.87154406188805 & 117.873725871563 \tabularnewline
Winsorized Mean ( 34 / 43 ) & 691.573643410853 & 5.69771874817961 & 121.377286941692 \tabularnewline
Winsorized Mean ( 35 / 43 ) & 693.201550387597 & 5.42390742763431 & 127.804826987975 \tabularnewline
Winsorized Mean ( 36 / 43 ) & 690.131782945736 & 5.07754046093026 & 135.918519656522 \tabularnewline
Winsorized Mean ( 37 / 43 ) & 690.131782945736 & 4.9587613795388 & 139.174227215975 \tabularnewline
Winsorized Mean ( 38 / 43 ) & 688.364341085271 & 4.76636737907478 & 144.421167387834 \tabularnewline
Winsorized Mean ( 39 / 43 ) & 688.364341085271 & 4.70451933552777 & 146.319802723916 \tabularnewline
Winsorized Mean ( 40 / 43 ) & 684.953488372093 & 4.22186108321308 & 162.239703029452 \tabularnewline
Winsorized Mean ( 41 / 43 ) & 683.682170542636 & 3.96795522463947 & 172.300878371115 \tabularnewline
Winsorized Mean ( 42 / 43 ) & 684.007751937984 & 3.93619619923844 & 173.773795135091 \tabularnewline
Winsorized Mean ( 43 / 43 ) & 683.341085271318 & 3.80523749316179 & 179.579089741263 \tabularnewline
Trimmed Mean ( 1 / 43 ) & 680.55905511811 & 13.8673192750051 & 49.0764683225236 \tabularnewline
Trimmed Mean ( 2 / 43 ) & 680.616 & 13.5307715441746 & 50.301344441295 \tabularnewline
Trimmed Mean ( 3 / 43 ) & 680.764227642276 & 13.1979115857529 & 51.5812083767221 \tabularnewline
Trimmed Mean ( 4 / 43 ) & 680.900826446281 & 12.8507398944391 & 52.9853403025399 \tabularnewline
Trimmed Mean ( 5 / 43 ) & 681.016806722689 & 12.4895340500798 & 54.5269986848177 \tabularnewline
Trimmed Mean ( 6 / 43 ) & 681.145299145299 & 12.1048279198038 & 56.2705478886593 \tabularnewline
Trimmed Mean ( 7 / 43 ) & 681.382608695652 & 11.7027224212339 & 58.2242818525135 \tabularnewline
Trimmed Mean ( 8 / 43 ) & 681.823008849557 & 11.3367823626294 & 60.1425507732352 \tabularnewline
Trimmed Mean ( 9 / 43 ) & 682.369369369369 & 11.0235020167001 & 61.901323947291 \tabularnewline
Trimmed Mean ( 10 / 43 ) & 682.935779816514 & 10.676523504092 & 63.9661196413577 \tabularnewline
Trimmed Mean ( 11 / 43 ) & 683.607476635514 & 10.3077128026318 & 66.3199964652659 \tabularnewline
Trimmed Mean ( 12 / 43 ) & 684.4 & 9.92899332384247 & 68.9294450784403 \tabularnewline
Trimmed Mean ( 13 / 43 ) & 685.252427184466 & 9.59980406280669 & 71.3819180788695 \tabularnewline
Trimmed Mean ( 14 / 43 ) & 686.089108910891 & 9.24529421654473 & 74.2095484298503 \tabularnewline
Trimmed Mean ( 15 / 43 ) & 687.030303030303 & 8.87038128263089 & 77.4521727014799 \tabularnewline
Trimmed Mean ( 16 / 43 ) & 688 & 8.46512199427787 & 81.2746704022771 \tabularnewline
Trimmed Mean ( 17 / 43 ) & 688.905263157895 & 8.04388959643833 & 85.6433016513464 \tabularnewline
Trimmed Mean ( 18 / 43 ) & 689.451612903226 & 7.68586913858079 & 89.7037928270705 \tabularnewline
Trimmed Mean ( 19 / 43 ) & 689.527472527473 & 7.47278890586272 & 92.271771786101 \tabularnewline
Trimmed Mean ( 20 / 43 ) & 689.61797752809 & 7.23698694099705 & 95.2907588683697 \tabularnewline
Trimmed Mean ( 21 / 43 ) & 689.609195402299 & 7.05218559439572 & 97.7865919964334 \tabularnewline
Trimmed Mean ( 22 / 43 ) & 689.305882352941 & 6.91841256078154 & 99.6335324465059 \tabularnewline
Trimmed Mean ( 23 / 43 ) & 688.927710843373 & 6.78070032479394 & 101.60126208856 \tabularnewline
Trimmed Mean ( 24 / 43 ) & 688.641975308642 & 6.66933531406795 & 103.254963632741 \tabularnewline
Trimmed Mean ( 25 / 43 ) & 688.392405063291 & 6.57257730164371 & 104.737057241021 \tabularnewline
Trimmed Mean ( 26 / 43 ) & 688.220779220779 & 6.47962323109076 & 106.213085958229 \tabularnewline
Trimmed Mean ( 27 / 43 ) & 688.026666666667 & 6.39490149769057 & 107.589877172485 \tabularnewline
Trimmed Mean ( 28 / 43 ) & 687.794520547945 & 6.29950587876797 & 109.182296799834 \tabularnewline
Trimmed Mean ( 29 / 43 ) & 687.464788732394 & 6.20818668257328 & 110.735199162445 \tabularnewline
Trimmed Mean ( 30 / 43 ) & 687.101449275362 & 6.11390686655128 & 112.383368649994 \tabularnewline
Trimmed Mean ( 31 / 43 ) & 686.731343283582 & 6.02364488025296 & 114.005947716948 \tabularnewline
Trimmed Mean ( 32 / 43 ) & 686.338461538462 & 5.91389648181579 & 116.055203815088 \tabularnewline
Trimmed Mean ( 33 / 43 ) & 685.920634920635 & 5.80275291710315 & 118.206073000099 \tabularnewline
Trimmed Mean ( 34 / 43 ) & 685.524590163934 & 5.68045284875006 & 120.681327425291 \tabularnewline
Trimmed Mean ( 35 / 43 ) & 685.135593220339 & 5.55665036799757 & 123.300108490943 \tabularnewline
Trimmed Mean ( 36 / 43 ) & 684.614035087719 & 5.44232429441153 & 125.794421289947 \tabularnewline
Trimmed Mean ( 37 / 43 ) & 684.254545454545 & 5.35690612388154 & 127.733159706511 \tabularnewline
Trimmed Mean ( 38 / 43 ) & 683.867924528302 & 5.26614166103467 & 129.861285272364 \tabularnewline
Trimmed Mean ( 39 / 43 ) & 683.56862745098 & 5.18279619449721 & 131.891859490202 \tabularnewline
Trimmed Mean ( 40 / 43 ) & 683.244897959184 & 5.08436734874094 & 134.381497459734 \tabularnewline
Trimmed Mean ( 41 / 43 ) & 683.127659574468 & 5.04160461341047 & 135.498063009022 \tabularnewline
Trimmed Mean ( 42 / 43 ) & 683.088888888889 & 5.02275853040637 & 135.998751433831 \tabularnewline
Trimmed Mean ( 43 / 43 ) & 683.023255813953 & 4.99429224293643 & 136.760770613689 \tabularnewline
Median & 687 &  &  \tabularnewline
Midrange & 722.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 684.84375 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 686.338461538462 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 686.338461538462 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 686.338461538462 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 686.338461538462 &  &  \tabularnewline
Midmean - Closest Observation & 684.179104477612 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 686.338461538462 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 686.338461538462 &  &  \tabularnewline
Number of observations & 129 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150127&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]681.209302325581[/C][C]14.404291333491[/C][C]47.292108063777[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]659.343593658288[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]634.40142052324[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]700.431306770247[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 43 )[/C][C]680.503875968992[/C][C]14.1726836459635[/C][C]48.0151743288791[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 43 )[/C][C]680.333333333333[/C][C]14.106226519342[/C][C]48.229293099787[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 43 )[/C][C]680.37984496124[/C][C]14.0546810467674[/C][C]48.4094831250354[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 43 )[/C][C]680.472868217054[/C][C]13.9812394958055[/C][C]48.6704249949514[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 43 )[/C][C]680.434108527132[/C][C]13.9189185716986[/C][C]48.8855585311535[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 43 )[/C][C]679.875968992248[/C][C]13.806727623993[/C][C]49.242368467585[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 43 )[/C][C]678.682170542636[/C][C]13.4262763407403[/C][C]50.5488009719615[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 43 )[/C][C]678.062015503876[/C][C]12.9458133512662[/C][C]52.3769343111653[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 43 )[/C][C]678.062015503876[/C][C]12.9234794733429[/C][C]52.4674501865002[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 43 )[/C][C]677.364341085271[/C][C]12.7999663974267[/C][C]52.9192280708991[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 43 )[/C][C]676.511627906977[/C][C]12.576476886121[/C][C]53.7918237382962[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 43 )[/C][C]676.232558139535[/C][C]11.9736291294066[/C][C]56.4768250988119[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 43 )[/C][C]676.736434108527[/C][C]11.8572772654472[/C][C]57.0735101287188[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 43 )[/C][C]675.976744186047[/C][C]11.6671916329648[/C][C]57.9382567331903[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 43 )[/C][C]676.093023255814[/C][C]11.5117927078878[/C][C]58.7304723435961[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 43 )[/C][C]677.333333333333[/C][C]11.2315219337506[/C][C]60.3064604537659[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 43 )[/C][C]682.209302325581[/C][C]10.4468516594846[/C][C]65.3028610496453[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 43 )[/C][C]688.488372093023[/C][C]9.11089302112198[/C][C]75.5676057766111[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 43 )[/C][C]688.341085271318[/C][C]9.05259915005698[/C][C]76.0379504119527[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 43 )[/C][C]689.736434108527[/C][C]8.42473028359015[/C][C]81.8704469924704[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 43 )[/C][C]693.806201550388[/C][C]7.80963767347821[/C][C]88.8397427074724[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 43 )[/C][C]694.658914728682[/C][C]7.67234551320115[/C][C]90.5406193625459[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 43 )[/C][C]693.054263565891[/C][C]7.29434040190916[/C][C]95.0126022888234[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 43 )[/C][C]692.31007751938[/C][C]7.02695700941814[/C][C]98.5220311710297[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 43 )[/C][C]690.953488372093[/C][C]6.86233735621073[/C][C]100.687776264271[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 43 )[/C][C]691.15503875969[/C][C]6.65627626839453[/C][C]103.835089003359[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 43 )[/C][C]691.573643410853[/C][C]6.61123492457582[/C][C]104.605818928031[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 43 )[/C][C]692.875968992248[/C][C]6.42566136681365[/C][C]107.829518152126[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 43 )[/C][C]693.100775193798[/C][C]6.3030005174842[/C][C]109.963623399867[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 43 )[/C][C]692.868217054264[/C][C]6.12241263818675[/C][C]113.169147197414[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 43 )[/C][C]692.868217054264[/C][C]6.12241263818675[/C][C]113.169147197414[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 43 )[/C][C]692.868217054264[/C][C]5.96074224741649[/C][C]116.238580414137[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 43 )[/C][C]692.100775193798[/C][C]5.87154406188805[/C][C]117.873725871563[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 43 )[/C][C]691.573643410853[/C][C]5.69771874817961[/C][C]121.377286941692[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 43 )[/C][C]693.201550387597[/C][C]5.42390742763431[/C][C]127.804826987975[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 43 )[/C][C]690.131782945736[/C][C]5.07754046093026[/C][C]135.918519656522[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 43 )[/C][C]690.131782945736[/C][C]4.9587613795388[/C][C]139.174227215975[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 43 )[/C][C]688.364341085271[/C][C]4.76636737907478[/C][C]144.421167387834[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 43 )[/C][C]688.364341085271[/C][C]4.70451933552777[/C][C]146.319802723916[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 43 )[/C][C]684.953488372093[/C][C]4.22186108321308[/C][C]162.239703029452[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 43 )[/C][C]683.682170542636[/C][C]3.96795522463947[/C][C]172.300878371115[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 43 )[/C][C]684.007751937984[/C][C]3.93619619923844[/C][C]173.773795135091[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 43 )[/C][C]683.341085271318[/C][C]3.80523749316179[/C][C]179.579089741263[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 43 )[/C][C]680.55905511811[/C][C]13.8673192750051[/C][C]49.0764683225236[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 43 )[/C][C]680.616[/C][C]13.5307715441746[/C][C]50.301344441295[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 43 )[/C][C]680.764227642276[/C][C]13.1979115857529[/C][C]51.5812083767221[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 43 )[/C][C]680.900826446281[/C][C]12.8507398944391[/C][C]52.9853403025399[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 43 )[/C][C]681.016806722689[/C][C]12.4895340500798[/C][C]54.5269986848177[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 43 )[/C][C]681.145299145299[/C][C]12.1048279198038[/C][C]56.2705478886593[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 43 )[/C][C]681.382608695652[/C][C]11.7027224212339[/C][C]58.2242818525135[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 43 )[/C][C]681.823008849557[/C][C]11.3367823626294[/C][C]60.1425507732352[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 43 )[/C][C]682.369369369369[/C][C]11.0235020167001[/C][C]61.901323947291[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 43 )[/C][C]682.935779816514[/C][C]10.676523504092[/C][C]63.9661196413577[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 43 )[/C][C]683.607476635514[/C][C]10.3077128026318[/C][C]66.3199964652659[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 43 )[/C][C]684.4[/C][C]9.92899332384247[/C][C]68.9294450784403[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 43 )[/C][C]685.252427184466[/C][C]9.59980406280669[/C][C]71.3819180788695[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 43 )[/C][C]686.089108910891[/C][C]9.24529421654473[/C][C]74.2095484298503[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 43 )[/C][C]687.030303030303[/C][C]8.87038128263089[/C][C]77.4521727014799[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 43 )[/C][C]688[/C][C]8.46512199427787[/C][C]81.2746704022771[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 43 )[/C][C]688.905263157895[/C][C]8.04388959643833[/C][C]85.6433016513464[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 43 )[/C][C]689.451612903226[/C][C]7.68586913858079[/C][C]89.7037928270705[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 43 )[/C][C]689.527472527473[/C][C]7.47278890586272[/C][C]92.271771786101[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 43 )[/C][C]689.61797752809[/C][C]7.23698694099705[/C][C]95.2907588683697[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 43 )[/C][C]689.609195402299[/C][C]7.05218559439572[/C][C]97.7865919964334[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 43 )[/C][C]689.305882352941[/C][C]6.91841256078154[/C][C]99.6335324465059[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 43 )[/C][C]688.927710843373[/C][C]6.78070032479394[/C][C]101.60126208856[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 43 )[/C][C]688.641975308642[/C][C]6.66933531406795[/C][C]103.254963632741[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 43 )[/C][C]688.392405063291[/C][C]6.57257730164371[/C][C]104.737057241021[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 43 )[/C][C]688.220779220779[/C][C]6.47962323109076[/C][C]106.213085958229[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 43 )[/C][C]688.026666666667[/C][C]6.39490149769057[/C][C]107.589877172485[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 43 )[/C][C]687.794520547945[/C][C]6.29950587876797[/C][C]109.182296799834[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 43 )[/C][C]687.464788732394[/C][C]6.20818668257328[/C][C]110.735199162445[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 43 )[/C][C]687.101449275362[/C][C]6.11390686655128[/C][C]112.383368649994[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 43 )[/C][C]686.731343283582[/C][C]6.02364488025296[/C][C]114.005947716948[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 43 )[/C][C]686.338461538462[/C][C]5.91389648181579[/C][C]116.055203815088[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 43 )[/C][C]685.920634920635[/C][C]5.80275291710315[/C][C]118.206073000099[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 43 )[/C][C]685.524590163934[/C][C]5.68045284875006[/C][C]120.681327425291[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 43 )[/C][C]685.135593220339[/C][C]5.55665036799757[/C][C]123.300108490943[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 43 )[/C][C]684.614035087719[/C][C]5.44232429441153[/C][C]125.794421289947[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 43 )[/C][C]684.254545454545[/C][C]5.35690612388154[/C][C]127.733159706511[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 43 )[/C][C]683.867924528302[/C][C]5.26614166103467[/C][C]129.861285272364[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 43 )[/C][C]683.56862745098[/C][C]5.18279619449721[/C][C]131.891859490202[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 43 )[/C][C]683.244897959184[/C][C]5.08436734874094[/C][C]134.381497459734[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 43 )[/C][C]683.127659574468[/C][C]5.04160461341047[/C][C]135.498063009022[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 43 )[/C][C]683.088888888889[/C][C]5.02275853040637[/C][C]135.998751433831[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 43 )[/C][C]683.023255813953[/C][C]4.99429224293643[/C][C]136.760770613689[/C][/ROW]
[ROW][C]Median[/C][C]687[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]722.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]684.84375[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]686.338461538462[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]686.338461538462[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]686.338461538462[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]686.338461538462[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]684.179104477612[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]686.338461538462[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]686.338461538462[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]129[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150127&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150127&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 Mean681.20930232558114.40429133349147.292108063777
Geometric Mean659.343593658288
Harmonic Mean634.40142052324
Quadratic Mean700.431306770247
Winsorized Mean ( 1 / 43 )680.50387596899214.172683645963548.0151743288791
Winsorized Mean ( 2 / 43 )680.33333333333314.10622651934248.229293099787
Winsorized Mean ( 3 / 43 )680.3798449612414.054681046767448.4094831250354
Winsorized Mean ( 4 / 43 )680.47286821705413.981239495805548.6704249949514
Winsorized Mean ( 5 / 43 )680.43410852713213.918918571698648.8855585311535
Winsorized Mean ( 6 / 43 )679.87596899224813.80672762399349.242368467585
Winsorized Mean ( 7 / 43 )678.68217054263613.426276340740350.5488009719615
Winsorized Mean ( 8 / 43 )678.06201550387612.945813351266252.3769343111653
Winsorized Mean ( 9 / 43 )678.06201550387612.923479473342952.4674501865002
Winsorized Mean ( 10 / 43 )677.36434108527112.799966397426752.9192280708991
Winsorized Mean ( 11 / 43 )676.51162790697712.57647688612153.7918237382962
Winsorized Mean ( 12 / 43 )676.23255813953511.973629129406656.4768250988119
Winsorized Mean ( 13 / 43 )676.73643410852711.857277265447257.0735101287188
Winsorized Mean ( 14 / 43 )675.97674418604711.667191632964857.9382567331903
Winsorized Mean ( 15 / 43 )676.09302325581411.511792707887858.7304723435961
Winsorized Mean ( 16 / 43 )677.33333333333311.231521933750660.3064604537659
Winsorized Mean ( 17 / 43 )682.20930232558110.446851659484665.3028610496453
Winsorized Mean ( 18 / 43 )688.4883720930239.1108930211219875.5676057766111
Winsorized Mean ( 19 / 43 )688.3410852713189.0525991500569876.0379504119527
Winsorized Mean ( 20 / 43 )689.7364341085278.4247302835901581.8704469924704
Winsorized Mean ( 21 / 43 )693.8062015503887.8096376734782188.8397427074724
Winsorized Mean ( 22 / 43 )694.6589147286827.6723455132011590.5406193625459
Winsorized Mean ( 23 / 43 )693.0542635658917.2943404019091695.0126022888234
Winsorized Mean ( 24 / 43 )692.310077519387.0269570094181498.5220311710297
Winsorized Mean ( 25 / 43 )690.9534883720936.86233735621073100.687776264271
Winsorized Mean ( 26 / 43 )691.155038759696.65627626839453103.835089003359
Winsorized Mean ( 27 / 43 )691.5736434108536.61123492457582104.605818928031
Winsorized Mean ( 28 / 43 )692.8759689922486.42566136681365107.829518152126
Winsorized Mean ( 29 / 43 )693.1007751937986.3030005174842109.963623399867
Winsorized Mean ( 30 / 43 )692.8682170542646.12241263818675113.169147197414
Winsorized Mean ( 31 / 43 )692.8682170542646.12241263818675113.169147197414
Winsorized Mean ( 32 / 43 )692.8682170542645.96074224741649116.238580414137
Winsorized Mean ( 33 / 43 )692.1007751937985.87154406188805117.873725871563
Winsorized Mean ( 34 / 43 )691.5736434108535.69771874817961121.377286941692
Winsorized Mean ( 35 / 43 )693.2015503875975.42390742763431127.804826987975
Winsorized Mean ( 36 / 43 )690.1317829457365.07754046093026135.918519656522
Winsorized Mean ( 37 / 43 )690.1317829457364.9587613795388139.174227215975
Winsorized Mean ( 38 / 43 )688.3643410852714.76636737907478144.421167387834
Winsorized Mean ( 39 / 43 )688.3643410852714.70451933552777146.319802723916
Winsorized Mean ( 40 / 43 )684.9534883720934.22186108321308162.239703029452
Winsorized Mean ( 41 / 43 )683.6821705426363.96795522463947172.300878371115
Winsorized Mean ( 42 / 43 )684.0077519379843.93619619923844173.773795135091
Winsorized Mean ( 43 / 43 )683.3410852713183.80523749316179179.579089741263
Trimmed Mean ( 1 / 43 )680.5590551181113.867319275005149.0764683225236
Trimmed Mean ( 2 / 43 )680.61613.530771544174650.301344441295
Trimmed Mean ( 3 / 43 )680.76422764227613.197911585752951.5812083767221
Trimmed Mean ( 4 / 43 )680.90082644628112.850739894439152.9853403025399
Trimmed Mean ( 5 / 43 )681.01680672268912.489534050079854.5269986848177
Trimmed Mean ( 6 / 43 )681.14529914529912.104827919803856.2705478886593
Trimmed Mean ( 7 / 43 )681.38260869565211.702722421233958.2242818525135
Trimmed Mean ( 8 / 43 )681.82300884955711.336782362629460.1425507732352
Trimmed Mean ( 9 / 43 )682.36936936936911.023502016700161.901323947291
Trimmed Mean ( 10 / 43 )682.93577981651410.67652350409263.9661196413577
Trimmed Mean ( 11 / 43 )683.60747663551410.307712802631866.3199964652659
Trimmed Mean ( 12 / 43 )684.49.9289933238424768.9294450784403
Trimmed Mean ( 13 / 43 )685.2524271844669.5998040628066971.3819180788695
Trimmed Mean ( 14 / 43 )686.0891089108919.2452942165447374.2095484298503
Trimmed Mean ( 15 / 43 )687.0303030303038.8703812826308977.4521727014799
Trimmed Mean ( 16 / 43 )6888.4651219942778781.2746704022771
Trimmed Mean ( 17 / 43 )688.9052631578958.0438895964383385.6433016513464
Trimmed Mean ( 18 / 43 )689.4516129032267.6858691385807989.7037928270705
Trimmed Mean ( 19 / 43 )689.5274725274737.4727889058627292.271771786101
Trimmed Mean ( 20 / 43 )689.617977528097.2369869409970595.2907588683697
Trimmed Mean ( 21 / 43 )689.6091954022997.0521855943957297.7865919964334
Trimmed Mean ( 22 / 43 )689.3058823529416.9184125607815499.6335324465059
Trimmed Mean ( 23 / 43 )688.9277108433736.78070032479394101.60126208856
Trimmed Mean ( 24 / 43 )688.6419753086426.66933531406795103.254963632741
Trimmed Mean ( 25 / 43 )688.3924050632916.57257730164371104.737057241021
Trimmed Mean ( 26 / 43 )688.2207792207796.47962323109076106.213085958229
Trimmed Mean ( 27 / 43 )688.0266666666676.39490149769057107.589877172485
Trimmed Mean ( 28 / 43 )687.7945205479456.29950587876797109.182296799834
Trimmed Mean ( 29 / 43 )687.4647887323946.20818668257328110.735199162445
Trimmed Mean ( 30 / 43 )687.1014492753626.11390686655128112.383368649994
Trimmed Mean ( 31 / 43 )686.7313432835826.02364488025296114.005947716948
Trimmed Mean ( 32 / 43 )686.3384615384625.91389648181579116.055203815088
Trimmed Mean ( 33 / 43 )685.9206349206355.80275291710315118.206073000099
Trimmed Mean ( 34 / 43 )685.5245901639345.68045284875006120.681327425291
Trimmed Mean ( 35 / 43 )685.1355932203395.55665036799757123.300108490943
Trimmed Mean ( 36 / 43 )684.6140350877195.44232429441153125.794421289947
Trimmed Mean ( 37 / 43 )684.2545454545455.35690612388154127.733159706511
Trimmed Mean ( 38 / 43 )683.8679245283025.26614166103467129.861285272364
Trimmed Mean ( 39 / 43 )683.568627450985.18279619449721131.891859490202
Trimmed Mean ( 40 / 43 )683.2448979591845.08436734874094134.381497459734
Trimmed Mean ( 41 / 43 )683.1276595744685.04160461341047135.498063009022
Trimmed Mean ( 42 / 43 )683.0888888888895.02275853040637135.998751433831
Trimmed Mean ( 43 / 43 )683.0232558139534.99429224293643136.760770613689
Median687
Midrange722.5
Midmean - Weighted Average at Xnp684.84375
Midmean - Weighted Average at X(n+1)p686.338461538462
Midmean - Empirical Distribution Function686.338461538462
Midmean - Empirical Distribution Function - Averaging686.338461538462
Midmean - Empirical Distribution Function - Interpolation686.338461538462
Midmean - Closest Observation684.179104477612
Midmean - True Basic - Statistics Graphics Toolkit686.338461538462
Midmean - MS Excel (old versions)686.338461538462
Number of observations129



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')