Voorspelling review Part 1 deel2

*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: Wed, 21 Oct 2009 14:04:54 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Oct/21/t12561555414fadw1henoea3if.htm/, Retrieved Wed, 21 Oct 2009 22:05:41 +0200

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/2009/Oct/21/t12561555414fadw1henoea3if.htm/}, year = {2009}, } @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 = {2009}, 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:

» Textbox « » Textfile « » CSV «

45.51 45.51 45.32 45.15 45.82 48.95 48.92 48.53 47.78 47.17 46.64 46.05 45.3 45.05 44.63 44.25 43.89 43.55 43.23 42.9 42.17 41.06 40.18 39.42 38.71 37.09 27.7 27 28.29 32.18 34.03 36.02 39.8 41.3 42.57 43.33 43.48 42.49 41.86 44.67 43.53 42.33 41.59 40.71 39.81 38.7 37.57 40.36 39.92 38.93 38.11 37.39 36.61 35.65 34.7 33.69 32.71 36.5 38.93 38.14 36.98 36.01 39.37 39.31 38.26 37.14 36.24 35.13 34.2 40.16 38.5 36.9 35.65 34.39 32.93 34.62 34.27 32.88 31.52 30.02 32.62 33.14 32.77 31.31 30.98 29.55 28.61 28.58 28.24 27.59 26 27.49 28.03 26.61 25.85 26.62 25.18 23.44 24.87 21.68 18.89 20.57 18.55 16.87 18.69 16.82 20.1 20.08 25.67 35.29 49.97 51.38 52.38 51.34 49.74 48.19 46.39 45.21 46.26 44.47 42.88 41.46 39.93 38.48 37.03 35.74 34.43 33.27 32.23 33.72 35.37 34.38 34.5 36.42 34.72 35.54 34.88 33.22 31.74 30.3 28.82 30.19 34.52 33.09 33.16 30.13 29.24 35.7 34.01 34 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 'RServer@AstonUniversity' @ vre.aston.ac.uk Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 35.7681111111111 0.993565615954021 35.9997473108674 Geometric Mean 30.1940615638120 Harmonic Mean 23.1301466074692 Quadratic Mean 40.4197074182604 Winsorized Mean ( 1 / 120 ) 35.7715 0.993199178615735 36.0164413847546 Winsorized Mean ( 2 / 120 ) 35.6927222222222 0.973047153223965 36.6813901093721 Winsorized Mean ( 3 / 120 ) 35.6103055555556 0.955049652935805 37.2863394548023 Winsorized Mean ( 4 / 120 ) 35.4485277777778 0.92462488951892 38.338279857707 Winsorized Mean ( 5 / 120 ) 35.3574166666667 0.909728276021118 38.8659093035005 Winsorized Mean ( 6 / 120 ) 35.3384166666667 0.905991889881102 39.0052240658626 Winsorized Mean ( 7 / 120 ) 35.2725 0.896285846713469 39.3540745168948 Winsorized Mean ( 8 / 120 ) 35.2073888888889 0.88561911884171 39.7545492637243 Winsorized Mean ( 9 / 120 ) 35.2103888888889 0.884122207549762 39.8252510662188 Winsorized Mean ( 10 / 120 ) 35.1523333333333 0.876303676823416 40.1143282437886 Winsorized Mean ( 11 / 120 ) 35.0930555555556 0.868741424317412 40.3952828462496 Winsorized Mean ( 12 / 120 ) 35.0640555555556 0.863362345399004 40.6133713641989 Winsorized Mean ( 13 / 120 ) 35.0550277777778 0.862183539024814 40.6584285028537 Winsorized Mean ( 14 / 120 ) 35.0359722222222 0.858036174051257 40.8327449142363 Winsorized Mean ( 15 / 120 ) 35.0093055555556 0.85380711447122 41.0037641549022 Winsorized Mean ( 16 / 120 ) 34.9768611111111 0.849556125810783 41.1707479334936 Winsorized Mean ( 17 / 120 ) 34.9877222222222 0.847799900568384 41.2688444511089 Winsorized Mean ( 18 / 120 ) 34.9077222222222 0.838738960240198 41.6192926249966 Winsorized Mean ( 19 / 120 ) 34.9008611111111 0.836274617262214 41.7337324255627 Winsorized Mean ( 20 / 120 ) 34.8714166666667 0.832395957370992 41.8928231905441 Winsorized Mean ( 21 / 120 ) 34.87375 0.831729941405851 41.9291746802500 Winsorized Mean ( 22 / 120 ) 34.8218055555556 0.824516820731613 42.232983827616 Winsorized Mean ( 23 / 120 ) 34.8109444444444 0.816656487529123 42.6261775618393 Winsorized Mean ( 24 / 120 ) 34.7996111111111 0.81555133105194 42.6700439152307 Winsorized Mean ( 25 / 120 ) 34.7794722222222 0.813077536566036 42.7750991241381 Winsorized Mean ( 26 / 120 ) 34.75925 0.811131884598025 42.852772354308 Winsorized Mean ( 27 / 120 ) 34.68275 0.79766859864512 43.4801495996087 Winsorized Mean ( 28 / 120 ) 34.6516388888889 0.793949437803454 43.6446418864611 Winsorized Mean ( 29 / 120 ) 34.6564722222222 0.78882457943024 43.9343209199367 Winsorized Mean ( 30 / 120 ) 34.7223055555556 0.782650864255735 44.364999952533 Winsorized Mean ( 31 / 120 ) 34.7343611111111 0.77650787831817 44.7314986505248 Winsorized Mean ( 32 / 120 ) 34.65525 0.757250506810145 45.7645781525883 Winsorized Mean ( 33 / 120 ) 34.6295833333333 0.754857678510186 45.8756455941198 Winsorized Mean ( 34 / 120 ) 34.6456388888889 0.75167843477487 46.09103745176 Winsorized Mean ( 35 / 120 ) 34.6018888888889 0.746746624268885 46.336853444455 Winsorized Mean ( 36 / 120 ) 34.5968888888889 0.746148739300877 46.3672818388802 Winsorized Mean ( 37 / 120 ) 34.49925 0.737239165366731 46.795194315048 Winsorized Mean ( 38 / 120 ) 34.5003055555556 0.732865862790889 47.0758801947357 Winsorized Mean ( 39 / 120 ) 34.4472222222222 0.725254082107508 47.4967643368823 Winsorized Mean ( 40 / 120 ) 34.3938888888889 0.719305581529136 47.8154066534179 Winsorized Mean ( 41 / 120 ) 34.3893333333333 0.710294828738455 48.4155760987473 Winsorized Mean ( 42 / 120 ) 34.3496666666667 0.69920593507719 49.1266806293264 Winsorized Mean ( 43 / 120 ) 34.3699722222222 0.694585948750852 49.4826771028602 Winsorized Mean ( 44 / 120 ) 34.3198611111111 0.687817299633067 49.8967692865822 Winsorized Mean ( 45 / 120 ) 34.3198611111111 0.681634744260152 50.3493423715688 Winsorized Mean ( 46 / 120 ) 34.32625 0.680489556952096 50.4434633115412 Winsorized Mean ( 47 / 120 ) 34.3393055555556 0.678982503620495 50.5746545344693 Winsorized Mean ( 48 / 120 ) 34.3166388888889 0.675599264192375 50.7943698398068 Winsorized Mean ( 49 / 120 ) 34.25675 0.67052950118423 51.089101880676 Winsorized Mean ( 50 / 120 ) 34.2178611111111 0.66638641192081 51.348377606441 Winsorized Mean ( 51 / 120 ) 34.2376944444444 0.661630003652437 51.7474936980487 Winsorized Mean ( 52 / 120 ) 34.3113611111111 0.654403588220279 52.4314990454507 Winsorized Mean ( 53 / 120 ) 34.3584722222222 0.64963361730725 52.8889997482567 Winsorized Mean ( 54 / 120 ) 34.2519722222222 0.62691939195975 54.6353688552376 Winsorized Mean ( 55 / 120 ) 34.2351666666667 0.625748110543662 54.7107791295167 Winsorized Mean ( 56 / 120 ) 34.2911666666667 0.619123056382654 55.386673639679 Winsorized Mean ( 57 / 120 ) 34.3180833333333 0.616256688088322 55.6879689854415 Winsorized Mean ( 58 / 120 ) 34.3390277777778 0.614586949281793 55.8733435812563 Winsorized Mean ( 59 / 120 ) 34.3373888888889 0.613493788213614 55.9702307481764 Winsorized Mean ( 60 / 120 ) 34.2223888888889 0.604343645807639 56.6273661124615 Winsorized Mean ( 61 / 120 ) 34.2410277777778 0.602104334417477 56.8689275603791 Winsorized Mean ( 62 / 120 ) 34.2306944444444 0.596838805138381 57.3533325074395 Winsorized Mean ( 63 / 120 ) 34.2499444444444 0.595053027755498 57.557802156949 Winsorized Mean ( 64 / 120 ) 34.2410555555556 0.592108264976506 57.8290450934918 Winsorized Mean ( 65 / 120 ) 34.4468888888889 0.575772991889226 59.8272051210005 Winsorized Mean ( 66 / 120 ) 34.4157222222222 0.569949114645801 60.3838506593876 Winsorized Mean ( 67 / 120 ) 34.4492222222222 0.566844583887636 60.7736638955891 Winsorized Mean ( 68 / 120 ) 34.4246666666667 0.55760913523203 61.7361956459734 Winsorized Mean ( 69 / 120 ) 34.5109166666667 0.551076628342768 62.6245333075548 Winsorized Mean ( 70 / 120 ) 34.5750833333333 0.542686868673236 63.7109267409818 Winsorized Mean ( 71 / 120 ) 34.5612777777778 0.541761563091016 63.794259564279 Winsorized Mean ( 72 / 120 ) 34.5492777777778 0.540394145651254 63.9334790278692 Winsorized Mean ( 73 / 120 ) 34.5776666666667 0.528876227256766 65.3795063658239 Winsorized Mean ( 74 / 120 ) 34.4748888888889 0.521265827083413 66.1368674056053 Winsorized Mean ( 75 / 120 ) 34.5103055555556 0.518646047195635 66.5392240857823 Winsorized Mean ( 76 / 120 ) 34.6348611111111 0.507780550872865 68.2083255287632 Winsorized Mean ( 77 / 120 ) 34.6498333333333 0.501102533954626 69.1471924116648 Winsorized Mean ( 78 / 120 ) 34.8925 0.480084930956597 72.6798483978131 Winsorized Mean ( 79 / 120 ) 34.8661666666667 0.478352125567853 72.888077219845 Winsorized Mean ( 80 / 120 ) 34.8728333333333 0.475489264953848 73.3409477429909 Winsorized Mean ( 81 / 120 ) 34.9605833333333 0.46914369613728 74.5199895494349 Winsorized Mean ( 82 / 120 ) 34.9286944444444 0.464305286086242 75.2278629840037 Winsorized Mean ( 83 / 120 ) 35.03475 0.453740460255789 77.2131935958493 Winsorized Mean ( 84 / 120 ) 35.03475 0.45064876011655 77.7429188775291 Winsorized Mean ( 85 / 120 ) 35.0371111111111 0.449553717933252 77.9375405283896 Winsorized Mean ( 86 / 120 ) 35.0848888888889 0.444164428541761 78.9907670095877 Winsorized Mean ( 87 / 120 ) 35.0921388888889 0.443683873439305 79.0926625682045 Winsorized Mean ( 88 / 120 ) 35.1116944444444 0.436294722290048 80.4770093485162 Winsorized Mean ( 89 / 120 ) 35.1215833333333 0.434997783655332 80.7396834029888 Winsorized Mean ( 90 / 120 ) 35.1765833333333 0.428468424855271 82.0984261447394 Winsorized Mean ( 91 / 120 ) 35.2271388888889 0.424866592503677 82.9134121402686 Winsorized Mean ( 92 / 120 ) 35.2373611111111 0.422549979215991 83.3921733388588 Winsorized Mean ( 93 / 120 ) 35.2425277777778 0.418872585956862 84.1366299904078 Winsorized Mean ( 94 / 120 ) 35.2373055555556 0.416170368180146 84.6703856154951 Winsorized Mean ( 95 / 120 ) 35.1713333333333 0.41053730485223 85.6714674102345 Winsorized Mean ( 96 / 120 ) 35.198 0.407458435504251 86.3842712114689 Winsorized Mean ( 97 / 120 ) 35.1548888888889 0.404686420202919 86.8694552964278 Winsorized Mean ( 98 / 120 ) 35.1358333333333 0.398245173381078 88.2266394719419 Winsorized Mean ( 99 / 120 ) 35.0945833333333 0.388280228948572 90.3846776550182 Winsorized Mean ( 100 / 120 ) 35.18625 0.380017586594581 92.5911095728793 Winsorized Mean ( 101 / 120 ) 35.1133055555556 0.375070736817405 93.6178222100268 Winsorized Mean ( 102 / 120 ) 35.1218055555556 0.373822804363409 93.9530845780401 Winsorized Mean ( 103 / 120 ) 35.1132222222222 0.372566849611932 94.2467700999065 Winsorized Mean ( 104 / 120 ) 35.1334444444445 0.370570331020731 94.8091131518 Winsorized Mean ( 105 / 120 ) 35.1334444444445 0.369108178566175 95.1846815774245 Winsorized Mean ( 106 / 120 ) 35.157 0.364318527496121 96.5007194161277 Winsorized Mean ( 107 / 120 ) 35.13025 0.362278640057108 96.9702491829554 Winsorized Mean ( 108 / 120 ) 35.05825 0.354455834187868 98.907244904928 Winsorized Mean ( 109 / 120 ) 35.1733055555556 0.346549433859355 101.495781319990 Winsorized Mean ( 110 / 120 ) 35.1580277777778 0.341830081849195 102.852351635010 Winsorized Mean ( 111 / 120 ) 35.1734444444444 0.338600419308836 103.878915791781 Winsorized Mean ( 112 / 120 ) 35.1827777777778 0.334200698607936 105.274399258668 Winsorized Mean ( 113 / 120 ) 35.20475 0.329775595665591 106.753654493280 Winsorized Mean ( 114 / 120 ) 35.1635833333333 0.326085655181052 107.835419236119 Winsorized Mean ( 115 / 120 ) 35.1476111111111 0.324327754448249 108.370654774534 Winsorized Mean ( 116 / 120 ) 35.1605 0.320000617914716 109.876350330582 Winsorized Mean ( 117 / 120 ) 35.07275 0.313486202775660 111.879724496517 Winsorized Mean ( 118 / 120 ) 35.0858611111111 0.312286658009560 112.351457262824 Winsorized Mean ( 119 / 120 ) 35.0528055555556 0.308287796411395 113.701567053855 Winsorized Mean ( 120 / 120 ) 35.0161388888889 0.305682842846176 114.550553648539 Trimmed Mean ( 1 / 120 ) 35.5964804469274 0.959123984327307 37.1135338377482 Trimmed Mean ( 2 / 120 ) 35.4194943820225 0.922850915149319 38.3805160731639 Trimmed Mean ( 3 / 120 ) 35.2805649717514 0.89565470394011 39.3908107851690 Trimmed Mean ( 4 / 120 ) 35.1681534090909 0.87385592917612 40.244795778004 Trimmed Mean ( 5 / 120 ) 35.0960571428571 0.859810821556102 40.8183477841552 Trimmed Mean ( 6 / 120 ) 35.0419827586207 0.848629016409372 41.2924635866053 Trimmed Mean ( 7 / 120 ) 34.9905780346821 0.837728124068313 41.7684174965442 Trimmed Mean ( 8 / 120 ) 34.9484302325581 0.828051780858263 42.2056096495978 Trimmed Mean ( 9 / 120 ) 34.9143567251462 0.819611597021444 42.5986611854062 Trimmed Mean ( 10 / 120 ) 34.8795294117647 0.81105038719128 43.0053791510473 Trimmed Mean ( 11 / 120 ) 34.8504733727811 0.80313749084125 43.3929106413359 Trimmed Mean ( 12 / 120 ) 34.8268452380952 0.795793516584073 43.7636704902909 Trimmed Mean ( 13 / 120 ) 34.8268452380952 0.788745192528086 44.1547480327179 Trimmed Mean ( 14 / 120 ) 34.7847289156626 0.781547614302033 44.5074980450518 Trimmed Mean ( 15 / 120 ) 34.7651515151515 0.774467402302809 44.889108840192 Trimmed Mean ( 16 / 120 ) 34.7472865853659 0.767495804935711 45.2735850305741 Trimmed Mean ( 17 / 120 ) 34.7314417177914 0.760620285497727 45.661997687932 Trimmed Mean ( 18 / 120 ) 34.7146913580247 0.753621098719961 46.063852799488 Trimmed Mean ( 19 / 120 ) 34.702701863354 0.747063847231362 46.452123191295 Trimmed Mean ( 20 / 120 ) 34.69096875 0.74043705321756 46.8520161156858 Trimmed Mean ( 21 / 120 ) 34.6807547169811 0.733834035941838 47.2596704682281 Trimmed Mean ( 22 / 120 ) 34.6702848101266 0.727017028713808 47.6884081676368 Trimmed Mean ( 23 / 120 ) 34.6623885350318 0.72042553649169 48.1137699585579 Trimmed Mean ( 24 / 120 ) 34.6549358974359 0.714093804227907 48.5299489958543 Trimmed Mean ( 25 / 120 ) 34.647935483871 0.707580161186524 48.9667989359265 Trimmed Mean ( 26 / 120 ) 34.647935483871 0.700960352376692 49.4292371407211 Trimmed Mean ( 27 / 120 ) 34.6364705882353 0.694191700535534 49.8946768760199 Trimmed Mean ( 28 / 120 ) 34.6344407894737 0.687963469128034 50.3434300564992 Trimmed Mean ( 29 / 120 ) 34.6337086092715 0.68169979760143 50.8049272291568 Trimmed Mean ( 30 / 120 ) 34.6327666666667 0.675474890577047 51.271730673927 Trimmed Mean ( 31 / 120 ) 34.6291610738255 0.669342414247238 51.7360925241388 Trimmed Mean ( 32 / 120 ) 34.6250337837838 0.663297254494715 52.2013826367492 Trimmed Mean ( 33 / 120 ) 34.6238775510204 0.658051260744696 52.6157757251884 Trimmed Mean ( 34 / 120 ) 34.6236643835616 0.652712987442241 53.0457721076455 Trimmed Mean ( 35 / 120 ) 34.6228620689655 0.647316643495638 53.4867478178766 Trimmed Mean ( 36 / 120 ) 34.6236111111111 0.641947387615581 53.9352784652889 Trimmed Mean ( 37 / 120 ) 34.6245454545455 0.636378472056591 54.40873155663 Trimmed Mean ( 38 / 120 ) 34.628838028169 0.63102184164364 54.8774000246495 Trimmed Mean ( 39 / 120 ) 34.6331560283688 0.625652380462062 55.3552693314956 Trimmed Mean ( 40 / 120 ) 34.6392857142857 0.620425052681766 55.8315393044794 Trimmed Mean ( 41 / 120 ) 34.6472302158273 0.615257601163317 56.3133720742613 Trimmed Mean ( 42 / 120 ) 34.6554347826087 0.610298424246716 56.7844080957336 Trimmed Mean ( 43 / 120 ) 34.665 0.605646172752605 57.2363890990194 Trimmed Mean ( 44 / 120 ) 34.6740808823529 0.60100416308521 57.6935785342254 Trimmed Mean ( 45 / 120 ) 34.6848148148148 0.596465745591069 58.1505561236275 Trimmed Mean ( 46 / 120 ) 34.6957089552239 0.592006914092867 58.6069319956983 Trimmed Mean ( 47 / 120 ) 34.7065789473684 0.587396063275608 59.0854810191058 Trimmed Mean ( 48 / 120 ) 34.7172348484848 0.582641658817966 59.5859124095545 Trimmed Mean ( 49 / 120 ) 34.7172348484848 0.577819035516275 60.0832314523273 Trimmed Mean ( 50 / 120 ) 34.7420384615385 0.572996658861515 60.6321833194757 Trimmed Mean ( 51 / 120 ) 34.7566666666667 0.568130496392898 61.1772592517728 Trimmed Mean ( 52 / 120 ) 34.7566666666667 0.563249841386019 61.7073705358515 Trimmed Mean ( 53 / 120 ) 34.7835039370079 0.558469004047475 62.2836785657149 Trimmed Mean ( 54 / 120 ) 34.7949603174603 0.553675597237758 62.8435865532985 Trimmed Mean ( 55 / 120 ) 34.80944 0.549651039667196 63.3300721510079 Trimmed Mean ( 56 / 120 ) 34.8245967741936 0.545476102016566 63.8425710043956 Trimmed Mean ( 57 / 120 ) 34.8385365853659 0.541390026073028 64.3501632973683 Trimmed Mean ( 58 / 120 ) 34.8520081967213 0.537226586254322 64.8739453490532 Trimmed Mean ( 59 / 120 ) 34.8651652892562 0.532927234481041 65.4219995403454 Trimmed Mean ( 60 / 120 ) 34.8785833333333 0.528455753336589 66.0009529901326 Trimmed Mean ( 61 / 120 ) 34.8951260504202 0.524144706552887 66.5753667148772 Trimmed Mean ( 62 / 120 ) 34.9114830508475 0.519709813565343 67.174954444954 Trimmed Mean ( 63 / 120 ) 34.9114830508475 0.515273513072799 67.7533041484224 Trimmed Mean ( 64 / 120 ) 34.9450862068966 0.510683321454534 68.4280937692767 Trimmed Mean ( 65 / 120 ) 34.9623043478261 0.505977354181655 69.0985556149495 Trimmed Mean ( 66 / 120 ) 34.9748245614035 0.501774394090386 69.702290458256 Trimmed Mean ( 67 / 120 ) 34.9883185840708 0.497596819829531 70.3145944462773 Trimmed Mean ( 68 / 120 ) 35.00125 0.493331456415312 70.948749658757 Trimmed Mean ( 69 / 120 ) 35.015 0.489237379276313 71.5705738833667 Trimmed Mean ( 70 / 120 ) 35.0269545454545 0.485214443772572 72.1886064914264 Trimmed Mean ( 71 / 120 ) 35.0376146788991 0.481343192278728 72.7913373263418 Trimmed Mean ( 72 / 120 ) 35.0487962962963 0.477290445087174 73.4328471417333 Trimmed Mean ( 73 / 120 ) 35.0604672897196 0.473064351801941 74.113526322944 Trimmed Mean ( 74 / 120 ) 35.0716981132075 0.469115664878895 74.7613024652704 Trimmed Mean ( 75 / 120 ) 35.0855238095238 0.465263001259857 75.4100878739936 Trimmed Mean ( 76 / 120 ) 35.0987980769231 0.461304009171525 76.0860460327636 Trimmed Mean ( 77 / 120 ) 35.1094660194175 0.457614443560102 76.7228100281897 Trimmed Mean ( 78 / 120 ) 35.12 0.454003356396236 77.3562563034197 Trimmed Mean ( 79 / 120 ) 35.125198019802 0.451125953511553 77.8611776741912 Trimmed Mean ( 80 / 120 ) 35.1311 0.448140915730486 78.3929758851298 Trimmed Mean ( 81 / 120 ) 35.1369696969697 0.445093310110218 78.9429292663796 Trimmed Mean ( 82 / 120 ) 35.1409693877551 0.442138324694538 79.4795823502365 Trimmed Mean ( 83 / 120 ) 35.1457731958763 0.43920576294788 80.0212022719907 Trimmed Mean ( 84 / 120 ) 35.14828125 0.436556647278521 80.5125324951828 Trimmed Mean ( 85 / 120 ) 35.1508421052632 0.433866347377724 81.0176735709368 Trimmed Mean ( 86 / 120 ) 35.1534042553191 0.431041902843514 81.5544939445975 Trimmed Mean ( 87 / 120 ) 35.1549462365591 0.428270857099177 82.0857773855439 Trimmed Mean ( 88 / 120 ) 35.1563586956522 0.425329434335582 82.6567734503745 Trimmed Mean ( 89 / 120 ) 35.1573626373626 0.422526498911457 83.2074739168729 Trimmed Mean ( 90 / 120 ) 35.1581666666667 0.419585215914513 83.792672699483 Trimmed Mean ( 91 / 120 ) 35.1577528089888 0.416742555183588 84.3632414585084 Trimmed Mean ( 92 / 120 ) 35.1561931818182 0.413863964939035 84.9462532622208 Trimmed Mean ( 93 / 120 ) 35.1543678160920 0.410885318649921 85.5576147904275 Trimmed Mean ( 94 / 120 ) 35.1523837209302 0.407865535362539 86.1862076423897 Trimmed Mean ( 95 / 120 ) 35.1504705882353 0.404753643702255 86.8441115605934 Trimmed Mean ( 96 / 120 ) 35.15 0.401689607680064 87.5053756132923 Trimmed Mean ( 97 / 120 ) 35.1489156626506 0.398546208277207 88.1928241510278 Trimmed Mean ( 98 / 120 ) 35.1489156626506 0.395302449383711 88.9165137161404 Trimmed Mean ( 99 / 120 ) 35.1490740740741 0.392139503391394 89.6341066638009 Trimmed Mean ( 100 / 120 ) 35.1503125 0.389242455098642 90.3044157685527 Trimmed Mean ( 101 / 120 ) 35.1494936708861 0.386538061466049 90.9341075949214 Trimmed Mean ( 102 / 120 ) 35.1503205128205 0.383865298738306 91.5694141365554 Trimmed Mean ( 103 / 120 ) 35.150974025974 0.381031560695428 92.2521325052951 Trimmed Mean ( 104 / 120 ) 35.150974025974 0.378023957465234 92.9861013615963 Trimmed Mean ( 105 / 120 ) 35.1522666666667 0.374869166100343 93.772093961063 Trimmed Mean ( 106 / 120 ) 35.1527027027027 0.371524707816399 94.6174021892364 Trimmed Mean ( 107 / 120 ) 35.152602739726 0.368164901835762 95.480591888163 Trimmed Mean ( 108 / 120 ) 35.153125 0.364628440016867 96.408072278657 Trimmed Mean ( 109 / 120 ) 35.153125 0.361240021082387 97.3123766704208 Trimmed Mean ( 110 / 120 ) 35.1549285714286 0.358018563546746 98.1930328504834 Trimmed Mean ( 111 / 120 ) 35.1548550724638 0.354783264945283 99.0882562566348 Trimmed Mean ( 112 / 120 ) 35.1544117647059 0.35144178239492 100.029118692559 Trimmed Mean ( 113 / 120 ) 35.1537313432836 0.348057592773596 100.999754273858 Trimmed Mean ( 114 / 120 ) 35.1525 0.344628192356518 102.001231412997 Trimmed Mean ( 115 / 120 ) 35.1525 0.341103356602257 103.055274360696 Trimmed Mean ( 116 / 120 ) 35.15234375 0.337345774115623 104.202709644591 Trimmed Mean ( 117 / 120 ) 35.1521428571429 0.333507356614663 105.401401678098 Trimmed Mean ( 118 / 120 ) 35.1541129032258 0.32973001958112 106.614838854784 Trimmed Mean ( 119 / 120 ) 35.1558196721311 0.32564714347501 107.956788126499 Trimmed Mean ( 120 / 120 ) 35.1584166666667 0.321428272551474 109.381842448338 Median 35.005 Midrange 66.49 Midmean - Weighted Average at Xnp 35.1013259668508 Midmean - Weighted Average at X(n+1)p 35.1581666666667 Midmean - Empirical Distribution Function 35.1013259668508 Midmean - Empirical Distribution Function - Averaging 35.1581666666667 Midmean - Empirical Distribution Function - Interpolation 35.1581666666667 Midmean - Closest Observation 35.1013259668508 Midmean - True Basic - Statistics Graphics Toolkit 35.1581666666667 Midmean - MS Excel (old versions) 35.1573626373626 Number of observations 360

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Oct/21/t12561555414fadw1henoea3if/15bkp1256155487.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t12561555414fadw1henoea3if/15bkp1256155487.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t12561555414fadw1henoea3if/2oghl1256155487.png (open in new window) http://www.freestatistics.org/blog/date/2009/Oct/21/t12561555414fadw1henoea3if/2oghl1256155487.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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