*The author of this computation has been verified*

R Software Module: /rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Tue, 09 Nov 2010 15:33:51 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Nov/09/t1289317060t91sy3rwo9cueov.htm/, Retrieved Tue, 09 Nov 2010 16:37:40 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Nov/09/t1289317060t91sy3rwo9cueov.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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684.28 722.57 695.96 688.13 720.76 737.26 736.9 727.38 728.83 715.58 735.93 758.69 758.69 740.99 719.44 721.24 737.38 756.52 745.32 733.76 738.46 736.65 737.5 725.22 722.45 720.44 733.6 662.93 763.87 746.67 712.59 655.02 660.2 633.59 627.08 635.63 668.87 656.7 631.9 610.83 632.98 631.06 644.3 647.55 655.14 674.4 676.21 670.43 683.43 703.42 708.48 714.5 706.19 694.15 658.15 648.4 630.82 634.19 658.15 636.11 640.33 601.8 611.07 634.31 625.76 596.86 604.09 587.11 583.13 579.16 551.47 541.83 569.53 564.71 572.06 578.56 595.78 567.84 534.25 519.08 531.96 551.83 560.62 579.52 593.13 626.72 715.1 832.38 837.2 879.46 881.99 1044.9 924.73 987.95 966.15 1016.72 1107.27 1296.67 1379.75 1543.03 1570.12 1538.81 1484.63 1451.27 1414.91 1456.93 1319.19 1267.89 1349.77 1240.2 1189.51 1117.87 1080.06 1054.77 1019.47 1049.96 1060.79 1070.42 1075.24 1080.06 1074.04 1062 1064.4 1071.63 1057.18 898.24 895. etc...

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 4 seconds R Server 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 750.026097560976 10.4714267718288 71.62596978463 Geometric Mean 727.003651097845 Harmonic Mean 706.842081992554 Quadratic Mean 776.460323236961 Winsorized Mean ( 1 / 123 ) 749.969051490515 10.4546471664596 71.735472230622 Winsorized Mean ( 2 / 123 ) 749.979674796748 10.4471268113014 71.7881278118918 Winsorized Mean ( 3 / 123 ) 749.639105691057 10.3512307973927 72.4202870522293 Winsorized Mean ( 4 / 123 ) 749.43379403794 10.2866180950521 72.8552170512113 Winsorized Mean ( 5 / 123 ) 749.412655826558 10.2679710532830 72.9854663533498 Winsorized Mean ( 6 / 123 ) 748.952330623306 10.1502318101615 73.7867217843754 Winsorized Mean ( 7 / 123 ) 748.32403794038 10.0307448439217 74.6030379183494 Winsorized Mean ( 8 / 123 ) 747.685338753387 9.9206778840356 75.3663557564515 Winsorized Mean ( 9 / 123 ) 746.955094850949 9.79876937100221 76.2294801081281 Winsorized Mean ( 10 / 123 ) 746.400081300813 9.69898445122328 76.9565190102633 Winsorized Mean ( 11 / 123 ) 745.579105691057 9.5662966445143 77.9381126675183 Winsorized Mean ( 12 / 123 ) 744.678617886179 9.43522223251288 78.9253924852016 Winsorized Mean ( 13 / 123 ) 742.917100271003 9.18778134760264 80.859249057429 Winsorized Mean ( 14 / 123 ) 741.781544715447 9.024124691185 82.199833235908 Winsorized Mean ( 15 / 123 ) 741.757967479675 8.9999397270508 82.4181038957626 Winsorized Mean ( 16 / 123 ) 741.584959349593 8.8538677464874 83.7583054754576 Winsorized Mean ( 17 / 123 ) 741.653604336043 8.82506393570735 84.03945962762 Winsorized Mean ( 18 / 123 ) 740.996531165312 8.72703375038154 84.9081775503522 Winsorized Mean ( 19 / 123 ) 740.582032520325 8.65355291901788 85.5812681162151 Winsorized Mean ( 20 / 123 ) 740.466043360434 8.61523246022057 85.9484693859876 Winsorized Mean ( 21 / 123 ) 740.22701897019 8.57457824270007 86.328096615175 Winsorized Mean ( 22 / 123 ) 739.629620596206 8.43450305583152 87.690954132127 Winsorized Mean ( 23 / 123 ) 739.898888888889 8.40793399926904 88.0000828923269 Winsorized Mean ( 24 / 123 ) 740.298238482385 8.37896158225186 88.3520268251938 Winsorized Mean ( 25 / 123 ) 740.317886178862 8.31846419517743 88.9969432828786 Winsorized Mean ( 26 / 123 ) 740.312249322493 8.30365952369533 89.1549379174251 Winsorized Mean ( 27 / 123 ) 740.622493224932 8.250578170586 89.7661324954552 Winsorized Mean ( 28 / 123 ) 740.704444444444 8.22868003000277 90.0149770976324 Winsorized Mean ( 29 / 123 ) 740.310704607046 8.17201657633112 90.5909450491366 Winsorized Mean ( 30 / 123 ) 740.685501355014 8.1188626726323 91.2302044289744 Winsorized Mean ( 31 / 123 ) 740.688861788618 8.11220117593803 91.3055341854205 Winsorized Mean ( 32 / 123 ) 741.378292682927 8.04903447830456 92.1077297756948 Winsorized Mean ( 33 / 123 ) 741.087642276423 8.01225672507491 92.4942457169573 Winsorized Mean ( 34 / 123 ) 741.450677506775 7.95136226369378 93.2482577095332 Winsorized Mean ( 35 / 123 ) 741.225880758808 7.88822663642209 93.9660984556866 Winsorized Mean ( 36 / 123 ) 741.430758807588 7.8429629299661 94.5345229128594 Winsorized Mean ( 37 / 123 ) 741.43677506775 7.79121509904699 95.1631761724102 Winsorized Mean ( 38 / 123 ) 741.158726287263 7.74305673150392 95.7191393512248 Winsorized Mean ( 39 / 123 ) 738.891653116531 7.50539347558987 98.448090099428 Winsorized Mean ( 40 / 123 ) 738.637994579946 7.47244631676298 98.8482169384014 Winsorized Mean ( 41 / 123 ) 737.490216802168 7.31217335512336 100.857868240424 Winsorized Mean ( 42 / 123 ) 737.492493224932 7.30035235085949 101.021492906175 Winsorized Mean ( 43 / 123 ) 736.294552845528 7.16240526257717 102.799901129945 Winsorized Mean ( 44 / 123 ) 736.192005420054 7.11682796311245 103.443838917541 Winsorized Mean ( 45 / 123 ) 736.40054200542 7.08242651385176 103.975740597544 Winsorized Mean ( 46 / 123 ) 736.447913279133 7.0752555381032 104.087818356956 Winsorized Mean ( 47 / 123 ) 734.593387533875 6.89148113605683 106.594413164743 Winsorized Mean ( 48 / 123 ) 734.707859078591 6.82965506847246 107.576129645288 Winsorized Mean ( 49 / 123 ) 734.18731707317 6.78088174573527 108.273133878928 Winsorized Mean ( 50 / 123 ) 733.455609756098 6.7111399690355 109.289273229315 Winsorized Mean ( 51 / 123 ) 732.688536585366 6.61679658442526 110.731609659874 Winsorized Mean ( 52 / 123 ) 732.567344173442 6.56590702814129 111.571385496882 Winsorized Mean ( 53 / 123 ) 731.67108401084 6.4824924172603 112.86879134061 Winsorized Mean ( 54 / 123 ) 731.517425474255 6.45296840170477 113.361383465166 Winsorized Mean ( 55 / 123 ) 731.82298102981 6.40399779168644 114.275957743123 Winsorized Mean ( 56 / 123 ) 732.014200542005 6.36236188485824 115.053845378416 Winsorized Mean ( 57 / 123 ) 731.54460704607 6.30790140661623 115.972739567357 Winsorized Mean ( 58 / 123 ) 731.726937669377 6.28713466814043 116.384804253891 Winsorized Mean ( 59 / 123 ) 731.704552845528 6.28468394358549 116.426626925662 Winsorized Mean ( 60 / 123 ) 729.92081300813 6.11717324081977 119.323220754544 Winsorized Mean ( 61 / 123 ) 729.099214092141 6.04064565260848 120.698888168900 Winsorized Mean ( 62 / 123 ) 729.033685636856 6.03503459554511 120.800249624917 Winsorized Mean ( 63 / 123 ) 728.671734417344 5.9833013139078 121.784228503350 Winsorized Mean ( 64 / 123 ) 728.454932249322 5.94452288189597 122.542203423563 Winsorized Mean ( 65 / 123 ) 728.770243902439 5.92346126376583 123.031148757631 Winsorized Mean ( 66 / 123 ) 727.260650406504 5.76033016452744 126.253292716628 Winsorized Mean ( 67 / 123 ) 726.991924119241 5.71590002914191 127.187655559536 Winsorized Mean ( 68 / 123 ) 726.573604336043 5.64608219325441 128.686331418290 Winsorized Mean ( 69 / 123 ) 726.480108401084 5.613164436836 129.424341042569 Winsorized Mean ( 70 / 123 ) 726.666016260163 5.57643054145626 130.310242521267 Winsorized Mean ( 71 / 123 ) 726.267723577236 5.54095035242673 131.072772247302 Winsorized Mean ( 72 / 123 ) 726.291138211382 5.50330661426918 131.973591354737 Winsorized Mean ( 73 / 123 ) 725.950867208672 5.41970756766672 133.946501383138 Winsorized Mean ( 74 / 123 ) 725.960894308943 5.38549774153664 134.799219895654 Winsorized Mean ( 75 / 123 ) 725.952764227642 5.37802962971576 134.984894879802 Winsorized Mean ( 76 / 123 ) 725.38430894309 5.26373356324836 137.807945677144 Winsorized Mean ( 77 / 123 ) 725.5554200542 5.24548810240051 138.319905772384 Winsorized Mean ( 78 / 123 ) 725.59135501355 5.17805359058773 140.128204994339 Winsorized Mean ( 79 / 123 ) 725.405094850948 5.15771954507631 140.644540384798 Winsorized Mean ( 80 / 123 ) 725.069051490515 5.10801886365938 141.947214926899 Winsorized Mean ( 81 / 123 ) 725.2227100271 5.08482270053875 142.624974898390 Winsorized Mean ( 82 / 123 ) 724.158265582656 4.99110322198074 145.089819499920 Winsorized Mean ( 83 / 123 ) 723.654417344174 4.93689124892294 146.580992137927 Winsorized Mean ( 84 / 123 ) 723.699945799458 4.92590424289394 146.917177053017 Winsorized Mean ( 85 / 123 ) 717.57027100271 4.39877516286122 163.129563215948 Winsorized Mean ( 86 / 123 ) 717.104146341463 4.36131089099433 164.423991837457 Winsorized Mean ( 87 / 123 ) 716.085609756097 4.26973466887224 167.711969311956 Winsorized Mean ( 88 / 123 ) 715.52756097561 4.20662631402355 170.095346617851 Winsorized Mean ( 89 / 123 ) 715.310487804878 4.12056686968689 173.595165526153 Winsorized Mean ( 90 / 123 ) 715.33731707317 4.11251989623514 173.941363232804 Winsorized Mean ( 91 / 123 ) 715.026585365854 4.08460384078133 175.054084370904 Winsorized Mean ( 92 / 123 ) 714.69 4.03640303207879 177.061109686048 Winsorized Mean ( 93 / 123 ) 713.487804878049 3.94694998895157 180.769405965433 Winsorized Mean ( 94 / 123 ) 710.802818428184 3.74499303326851 189.800838643435 Winsorized Mean ( 95 / 123 ) 710.524769647697 3.70084642004184 191.989801522124 Winsorized Mean ( 96 / 123 ) 710.493550135501 3.59849618489344 197.441796136444 Winsorized Mean ( 97 / 123 ) 710.372628726287 3.58913580956158 197.923028388569 Winsorized Mean ( 98 / 123 ) 710.221246612466 3.57116767096280 198.876477401855 Winsorized Mean ( 99 / 123 ) 707.559783197832 3.39018629010920 208.708230949468 Winsorized Mean ( 100 / 123 ) 707.64379403794 3.37291242478785 209.802006372119 Winsorized Mean ( 101 / 123 ) 707.350921409214 3.35273656765576 210.977184498511 Winsorized Mean ( 102 / 123 ) 704.67514905149 3.17258251969861 222.114048941565 Winsorized Mean ( 103 / 123 ) 704.70864498645 3.13809123557040 224.566015480541 Winsorized Mean ( 104 / 123 ) 704.443712737127 3.11977735542446 225.799354403380 Winsorized Mean ( 105 / 123 ) 703.47623306233 3.03688329175232 231.644144828633 Winsorized Mean ( 106 / 123 ) 702.31569105691 2.95407928924737 237.744360353931 Winsorized Mean ( 107 / 123 ) 702.179403794038 2.93489486170725 239.251978991021 Winsorized Mean ( 108 / 123 ) 701.898428184282 2.91335030704336 240.924830250369 Winsorized Mean ( 109 / 123 ) 701.880704607046 2.8639819028546 245.07162699159 Winsorized Mean ( 110 / 123 ) 701.546829268293 2.82609283825872 248.239130636822 Winsorized Mean ( 111 / 123 ) 701.510731707317 2.8239143060028 248.417853975283 Winsorized Mean ( 112 / 123 ) 702.336314363144 2.75955943413048 254.510305404763 Winsorized Mean ( 113 / 123 ) 702.614986449864 2.73286980048795 257.097863324632 Winsorized Mean ( 114 / 123 ) 702.831246612466 2.70209702813122 260.105850861524 Winsorized Mean ( 115 / 123 ) 702.550758807588 2.65010902519814 265.102587149244 Winsorized Mean ( 116 / 123 ) 702.921707317073 2.60012978636025 270.341007977547 Winsorized Mean ( 117 / 123 ) 702.779024390244 2.53423281744660 277.314309700377 Winsorized Mean ( 118 / 123 ) 702.90054200542 2.52681311763009 278.176702939027 Winsorized Mean ( 119 / 123 ) 702.313604336043 2.47812362189977 283.405395166540 Winsorized Mean ( 120 / 123 ) 701.016043360434 2.36744967422595 296.105995828459 Winsorized Mean ( 121 / 123 ) 700.888157181572 2.35414377821324 297.725297693388 Winsorized Mean ( 122 / 123 ) 700.200460704607 2.28105146637542 306.963902843114 Winsorized Mean ( 123 / 123 ) 699.907127371274 2.24969567832353 311.111913542388 Trimmed Mean ( 1 / 123 ) 748.69765667575 10.2477111687952 73.0599881616075 Trimmed Mean ( 2 / 123 ) 747.412328767123 10.0310332154552 74.510004374779 Trimmed Mean ( 3 / 123 ) 746.107438016529 9.8079489670461 76.0717088275427 Trimmed Mean ( 4 / 123 ) 744.904127423823 9.61008121577348 77.512781702737 Trimmed Mean ( 5 / 123 ) 743.740167130919 9.42152894893194 78.940495875166 Trimmed Mean ( 6 / 123 ) 742.567535014006 9.22846257192406 80.4649235153355 Trimmed Mean ( 7 / 123 ) 741.461436619718 9.05015120777782 81.9280716528246 Trimmed Mean ( 8 / 123 ) 740.436628895184 8.88482296093715 83.3372406125113 Trimmed Mean ( 9 / 123 ) 739.484074074074 8.72944072262744 84.7115064493501 Trimmed Mean ( 10 / 123 ) 738.606389684814 8.58461656026456 86.0383669439106 Trimmed Mean ( 11 / 123 ) 737.777608069164 8.44651255977899 87.3470089398019 Trimmed Mean ( 12 / 123 ) 737.019043478261 8.31851999206055 88.5997802712135 Trimmed Mean ( 13 / 123 ) 737.019043478261 8.1998688323019 89.8818089107605 Trimmed Mean ( 14 / 123 ) 735.784252199413 8.10223920142202 90.8124573846544 Trimmed Mean ( 15 / 123 ) 735.31796460177 8.01663763938299 91.7239867484349 Trimmed Mean ( 16 / 123 ) 734.847863501484 7.9298640079418 92.6684067678248 Trimmed Mean ( 17 / 123 ) 734.384059701493 7.85227407983528 93.5250160953243 Trimmed Mean ( 18 / 123 ) 733.91021021021 7.77398458827361 94.4059255426427 Trimmed Mean ( 19 / 123 ) 733.471329305136 7.70043109185537 95.2506840923383 Trimmed Mean ( 20 / 123 ) 733.051580547113 7.62959387469164 96.0800263535311 Trimmed Mean ( 21 / 123 ) 732.633241590214 7.55876911367921 96.9249398376725 Trimmed Mean ( 22 / 123 ) 732.222676923077 7.48803825330214 97.7856485442198 Trimmed Mean ( 23 / 123 ) 731.838049535604 7.42411319188197 98.5758205216813 Trimmed Mean ( 24 / 123 ) 731.435171339564 7.3593504530552 99.388550118022 Trimmed Mean ( 25 / 123 ) 731.435171339564 7.29377395886932 100.282127670015 Trimmed Mean ( 26 / 123 ) 731.007993730408 7.22932143402479 101.117096590825 Trimmed Mean ( 27 / 123 ) 730.135777777778 7.16314455627739 101.929504848248 Trimmed Mean ( 28 / 123 ) 729.677891373802 7.09735936308811 102.809771077495 Trimmed Mean ( 29 / 123 ) 729.210643086817 7.03010602270712 103.726834379379 Trimmed Mean ( 30 / 123 ) 728.75355987055 6.96339246732032 104.654959962495 Trimmed Mean ( 31 / 123 ) 728.275504885994 6.89679309317405 105.596252496945 Trimmed Mean ( 32 / 123 ) 727.791049180328 6.82771732960309 106.593611604984 Trimmed Mean ( 33 / 123 ) 727.27396039604 6.7589752760423 107.601216263346 Trimmed Mean ( 34 / 123 ) 726.760797342193 6.68930742177704 108.645148371597 Trimmed Mean ( 35 / 123 ) 726.227591973244 6.61974812956964 109.706227149228 Trimmed Mean ( 36 / 123 ) 725.695185185185 6.55050989934932 110.78453377458 Trimmed Mean ( 37 / 123 ) 725.148440677966 6.48047947933299 111.897343860211 Trimmed Mean ( 38 / 123 ) 724.594027303754 6.40995970845535 113.041900458118 Trimmed Mean ( 39 / 123 ) 724.041271477663 6.338775178773 114.224160197746 Trimmed Mean ( 40 / 123 ) 723.55508650519 6.2770456018483 115.270006369260 Trimmed Mean ( 41 / 123 ) 723.070278745645 6.21421043573582 116.357546340483 Trimmed Mean ( 42 / 123 ) 722.614912280702 6.15667908756296 117.370891352848 Trimmed Mean ( 43 / 123 ) 722.153038869258 6.09707918151021 118.442457014374 Trimmed Mean ( 44 / 123 ) 721.721174377224 6.04167060273842 119.457220003040 Trimmed Mean ( 45 / 123 ) 721.286200716846 5.9858855018611 120.497827847290 Trimmed Mean ( 46 / 123 ) 720.838772563177 5.9290599769534 121.577244177849 Trimmed Mean ( 47 / 123 ) 720.383454545455 5.86987162054232 122.725589436128 Trimmed Mean ( 48 / 123 ) 719.974798534799 5.81696527670171 123.771548270791 Trimmed Mean ( 49 / 123 ) 719.556863468635 5.76435837909758 124.828613376617 Trimmed Mean ( 50 / 123 ) 719.556863468635 5.7116061343119 125.981527183040 Trimmed Mean ( 51 / 123 ) 718.751797752809 5.65968751956195 126.994961341689 Trimmed Mean ( 52 / 123 ) 718.751797752809 5.60972404327323 128.126052584473 Trimmed Mean ( 53 / 123 ) 717.98825095057 5.55964563958002 129.142808282437 Trimmed Mean ( 54 / 123 ) 717.623256704981 5.51107702633099 130.214702729847 Trimmed Mean ( 55 / 123 ) 717.25667953668 5.46146875745549 131.330363935076 Trimmed Mean ( 56 / 123 ) 716.876420233463 5.41148839000208 132.473058901488 Trimmed Mean ( 57 / 123 ) 716.485254901961 5.36079027268066 133.6529165398 Trimmed Mean ( 58 / 123 ) 716.099920948617 5.31007795789442 134.856762297435 Trimmed Mean ( 59 / 123 ) 715.703824701195 5.25763464718873 136.126580245336 Trimmed Mean ( 60 / 123 ) 715.301927710843 5.20258365170403 137.489750400564 Trimmed Mean ( 61 / 123 ) 714.937935222672 5.15270807131263 138.749939901126 Trimmed Mean ( 62 / 123 ) 714.588285714286 5.1038564527749 140.009479562415 Trimmed Mean ( 63 / 123 ) 714.234485596708 5.05269988606796 141.356997585805 Trimmed Mean ( 64 / 123 ) 713.883609958506 5.00124400734578 142.741207769499 Trimmed Mean ( 65 / 123 ) 713.532092050209 4.94883259733074 144.181901088161 Trimmed Mean ( 66 / 123 ) 713.167088607595 4.89442823995757 145.709989735957 Trimmed Mean ( 67 / 123 ) 712.831787234043 4.84487487027543 147.131103758211 Trimmed Mean ( 68 / 123 ) 712.497081545064 4.79467400599125 148.60177785909 Trimmed Mean ( 69 / 123 ) 712.166406926407 4.74496028308388 150.089013276956 Trimmed Mean ( 70 / 123 ) 711.832139737991 4.69398180617771 151.647826755774 Trimmed Mean ( 71 / 123 ) 711.487665198238 4.64172942781678 153.280727854248 Trimmed Mean ( 72 / 123 ) 711.146266666667 4.58824806076817 154.992985829891 Trimmed Mean ( 73 / 123 ) 710.798206278027 4.53340526525533 156.791234113942 Trimmed Mean ( 74 / 123 ) 710.451628959276 4.47936649173615 158.605380977414 Trimmed Mean ( 75 / 123 ) 710.098493150685 4.42372802331785 160.520377701273 Trimmed Mean ( 76 / 123 ) 709.739032258065 4.36510568611813 162.593779691330 Trimmed Mean ( 77 / 123 ) 709.385720930233 4.30861511902964 164.643557461683 Trimmed Mean ( 78 / 123 ) 709.021924882629 4.24946490279795 166.849695455960 Trimmed Mean ( 79 / 123 ) 708.650426540284 4.18989839594057 169.133081419556 Trimmed Mean ( 80 / 123 ) 708.275980861244 4.12764765249783 171.593130153111 Trimmed Mean ( 81 / 123 ) 707.901787439613 4.06403998202925 174.186718282763 Trimmed Mean ( 82 / 123 ) 707.51687804878 3.99738651769259 176.994862747769 Trimmed Mean ( 83 / 123 ) 707.147980295567 3.93165972209125 179.859914204232 Trimmed Mean ( 84 / 123 ) 706.78288557214 3.86459970614236 182.886440851503 Trimmed Mean ( 85 / 123 ) 706.409447236181 3.79353151927415 186.214202688724 Trimmed Mean ( 86 / 123 ) 706.163502538071 3.74742691267569 188.439566399406 Trimmed Mean ( 87 / 123 ) 705.922769230769 3.70032178018162 190.773346526669 Trimmed Mean ( 88 / 123 ) 705.699430051813 3.65500742409929 193.077427257407 Trimmed Mean ( 89 / 123 ) 705.483664921466 3.61001724116733 195.423904594246 Trimmed Mean ( 90 / 123 ) 705.268095238095 3.56639763318197 197.753634837641 Trimmed Mean ( 91 / 123 ) 705.047326203209 3.52022094910759 200.284964039528 Trimmed Mean ( 92 / 123 ) 704.828594594595 3.47242200713146 202.978956229127 Trimmed Mean ( 93 / 123 ) 704.612459016393 3.42394509649656 205.789648828588 Trimmed Mean ( 94 / 123 ) 704.417900552486 3.3772073871917 208.579995183014 Trimmed Mean ( 95 / 123 ) 704.277877094972 3.33850360408999 210.956152999854 Trimmed Mean ( 96 / 123 ) 704.140790960452 3.29942578139645 213.413132348876 Trimmed Mean ( 97 / 123 ) 704.001257142857 3.26289114509558 215.759958220192 Trimmed Mean ( 98 / 123 ) 703.861156069364 3.22424109856482 218.302891921658 Trimmed Mean ( 99 / 123 ) 703.721111111111 3.1837698893375 221.033911234567 Trimmed Mean ( 100 / 123 ) 703.721111111111 3.15056361087015 223.363562215699 Trimmed Mean ( 101 / 123 ) 703.547904191617 3.1157922636377 225.80064544169 Trimmed Mean ( 102 / 123 ) 703.463696969697 3.07955166612494 228.430555235619 Trimmed Mean ( 103 / 123 ) 703.436809815951 3.05059667847411 230.589908780667 Trimmed Mean ( 104 / 123 ) 703.436809815951 3.02124352792948 232.830224810786 Trimmed Mean ( 105 / 123 ) 703.385408805031 2.99060262990221 235.198552215555 Trimmed Mean ( 106 / 123 ) 703.383375796178 2.96211777277213 237.459625090433 Trimmed Mean ( 107 / 123 ) 703.40735483871 2.93584734908361 239.592618825455 Trimmed Mean ( 108 / 123 ) 703.435032679739 2.90846474833896 241.857850634591 Trimmed Mean ( 109 / 123 ) 703.469801324503 2.87999822245193 244.260498440723 Trimmed Mean ( 110 / 123 ) 703.505906040268 2.85196317327457 246.674260254391 Trimmed Mean ( 111 / 123 ) 703.550612244898 2.82369649199369 249.159431348144 Trimmed Mean ( 112 / 123 ) 703.597379310345 2.79310549474879 251.905050000135 Trimmed Mean ( 113 / 123 ) 703.626433566434 2.76380906605107 254.585760720358 Trimmed Mean ( 114 / 123 ) 703.649858156028 2.73356275012547 257.411269642056 Trimmed Mean ( 115 / 123 ) 703.649858156028 2.70253162492516 260.366928426050 Trimmed Mean ( 116 / 123 ) 703.695109489051 2.67195685322013 263.363200884395 Trimmed Mean ( 117 / 123 ) 703.713333333333 2.64178930142076 266.377539251475 Trimmed Mean ( 118 / 123 ) 703.735488721804 2.61305562076617 269.315158517546 Trimmed Mean ( 119 / 123 ) 703.735488721804 2.58205992603784 272.548085203307 Trimmed Mean ( 120 / 123 ) 703.79007751938 2.55130769378259 275.854644751193 Trimmed Mean ( 121 / 123 ) 703.857244094488 2.52482295509908 278.774890997008 Trimmed Mean ( 122 / 123 ) 703.92968 2.49650672310912 281.965865937398 Trimmed Mean ( 123 / 123 ) 704.021382113821 2.47015761431268 285.010712690783 Median 708.75 Midrange 993.795 Midmean - Weighted Average at Xnp 704.188695652174 Midmean - Weighted Average at X(n+1)p 704.828594594595 Midmean - Empirical Distribution Function 704.828594594595 Midmean - Empirical Distribution Function - Averaging 704.828594594595 Midmean - Empirical Distribution Function - Interpolation 704.828594594595 Midmean - Closest Observation 704.40435483871 Midmean - True Basic - Statistics Graphics Toolkit 704.828594594595 Midmean - MS Excel (old versions) 704.828594594595 Number of observations 369

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Nov/09/t1289317060t91sy3rwo9cueov/1diav1289316825.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/09/t1289317060t91sy3rwo9cueov/1diav1289316825.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/09/t1289317060t91sy3rwo9cueov/269az1289316825.png (open in new window) http://www.freestatistics.org/blog/date/2010/Nov/09/t1289317060t91sy3rwo9cueov/269az1289316825.ps (open in new window)

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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/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')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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