Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 21 Dec 2007 09:04:13 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2007/Dec/21/t1198252054jxbhovk9xvu6xag.htm/, Retrieved Tue, 07 May 2024 13:14:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4809, Retrieved Tue, 07 May 2024 13:14:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact211
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Paper - Centr. Te...] [2007-12-21 16:04:13] [6bdd947de0ee04552c8f0fc807f31807] [Current]
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Dataseries X:
622.755354196211
419.557064448606
337.667064448595
587.237064448597
-78.5029355514001
568.837064448604
111.996766841012
336.956766841012
-410.723233158992
506.376766841009
-207.193233158988
342.366766841013
395.671231421387
256.272941673806
221.182941673811
-171.54705832619
-252.987058326191
-506.447058326191
-1043.78735593379
-941.627355933786
-841.907355933784
-600.707355933784
-876.677355933786
-265.917355933785
-632.912891353406
-85.1111811009849
-339.801181100985
-361.331181100985
-139.271181100985
302.068818899015
-360.67147870858
645.48852129142
410.608521291422
-300.891478708579
1072.53852129142
-225.101478708580
109.802985871800
706.304696124221
382.814696124222
358.684696124221
1231.64469612422
593.68469612422
1026.44439851663
641.904398516626
79.9243985166273
249.724398516626
720.354398516625
-9.28560148337375
-389.081136902994
-315.179426650573
-800.369426650573
-673.499426650573
-920.739426650575
-1487.59942665057
370.863251817773
198.223251817774
-9.05674818222588
870.343251817775
572.773251817774
-117.366748182226
593.537716398154
-31.160573349427
87.7494266505743
798.919426650575
-181.820573349426
199.819426650573
314.47912904298
58.83912904298
-547.640870957020
49.7591290429804
-771.71087095702
-701.150870957021
-141.946406376641
-1102.04469612422
-506.434696124219
209.935303875781
-826.90469612422
-268.264696124222
-677.204993731815
-493.544993731816
-136.324993731815
-191.124993731815
-1176.29499373181
438.965006268185
-431.030529151435
-146.428818899016
86.0811811009855
-81.7488188990137
-65.288818899014
493.651181100984
-478.489116506611
-296.029116506610
53.1908834933911
305.190883493390
-424.979116506609
84.5808834933917
-889.51465192623
-80.7129416738088
432.597058326191
-769.932941673809
828.527058326191
1028.86705832619
638.626760718596
307.086760718597
1529.50676071860
-202.193239281403
800.236760718596
299.296760718597
-377.998774701024
378.502935551396
98.5129355513976
103.282935551397
405.342935551397
-924.617064448604
97.7426379438026
-457.297362056198
-127.577362056198
-686.477362056198
290.952637943803
153.612637943802
1140.71710252418




Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4809&T=0

[TABLE]
[ROW][C]Summary of compuational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4809&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4809&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean6.79676700596141e-1451.40381166163431.32223015886471e-15
Geometric MeanNaN
Harmonic Mean-611.289101333921
Quadratic Mean563.100543776485
Winsorized Mean ( 1 / 40 )0.11109395309411750.28515313154020.00220927940307763
Winsorized Mean ( 2 / 40 )-0.16456383190505549.755227392081-0.00330746819039254
Winsorized Mean ( 3 / 40 )-0.41054501477273849.1790186519547-0.00834797086290416
Winsorized Mean ( 4 / 40 )1.5229603417487248.34667036051390.0315008320199143
Winsorized Mean ( 5 / 40 )2.1257550390884648.21551582245420.0440886092957340
Winsorized Mean ( 6 / 40 )-5.4225181295475346.8958439787222-0.115628969850886
Winsorized Mean ( 7 / 40 )-6.0352448350902946.2348717823591-0.130534477601667
Winsorized Mean ( 8 / 40 )-7.0569308922903645.8221821129901-0.154006871058412
Winsorized Mean ( 9 / 40 )-4.5687160709033445.4045078558647-0.100622521565625
Winsorized Mean ( 10 / 40 )-9.821804362174944.2887281034489-0.221767586985865
Winsorized Mean ( 11 / 40 )-8.6867528093346443.7466491673476-0.198569558461598
Winsorized Mean ( 12 / 40 )-11.875938178516242.5211194835424-0.279295049677908
Winsorized Mean ( 13 / 40 )-12.069992024719442.4431587778793-0.284380153887370
Winsorized Mean ( 14 / 40 )-4.4909667283341741.2414884693981-0.108894389970104
Winsorized Mean ( 15 / 40 )-4.6394664334864940.7324547537251-0.113900978017098
Winsorized Mean ( 16 / 40 )-7.2574221025916740.0745897365988-0.181097851538670
Winsorized Mean ( 17 / 40 )-6.7574552840958739.999585454884-0.168938132914345
Winsorized Mean ( 18 / 40 )-1.6570759431290939.0559994314315-0.0424282048149434
Winsorized Mean ( 19 / 40 )1.1288144121368738.0977812983840.0296294002870123
Winsorized Mean ( 20 / 40 )9.2495247604995236.88646558749090.250756601728636
Winsorized Mean ( 21 / 40 )5.558647202548434.65742258649330.160388360925452
Winsorized Mean ( 22 / 40 )3.2471520138114934.38031210469420.0944480086138638
Winsorized Mean ( 23 / 40 )-4.6976320037844832.8740874791258-0.142897715617729
Winsorized Mean ( 24 / 40 )-2.9744063608335132.364368498813-0.091903735459649
Winsorized Mean ( 25 / 40 )-1.2901583085963131.531501963147-0.0409164875845179
Winsorized Mean ( 26 / 40 )2.4311270917099130.64500231200810.0793319271755214
Winsorized Mean ( 27 / 40 )2.6064768969134430.35600696587020.0858636282381918
Winsorized Mean ( 28 / 40 )3.667278699334929.72403437115720.123377555467149
Winsorized Mean ( 29 / 40 )5.7729090117824728.78874223639470.200526614340392
Winsorized Mean ( 30 / 40 )7.4515705727272628.35948244841120.262754110068209
Winsorized Mean ( 31 / 40 )9.7645061583379727.66580325355270.352944972132124
Winsorized Mean ( 32 / 40 )6.7181978472908227.29806715778500.246105257506295
Winsorized Mean ( 33 / 40 )7.9597528448509226.18793817302550.303947290247147
Winsorized Mean ( 34 / 40 )13.557684828088925.28948934713460.536099588330557
Winsorized Mean ( 35 / 40 )17.485104346307024.82275872352220.704398110663583
Winsorized Mean ( 36 / 40 )12.244195904503123.95761462079260.511077421450651
Winsorized Mean ( 37 / 40 )18.473666368521222.81973934144660.809547650483814
Winsorized Mean ( 38 / 40 )18.615448126196722.67988519962520.82079110905307
Winsorized Mean ( 39 / 40 )21.776779427978022.14044164780520.98357475313221
Winsorized Mean ( 40 / 40 )30.078769985727821.10195778839361.42540186495263
Trimmed Mean ( 1 / 40 )-0.35216247115984649.0724324811779-0.00717638098121426
Trimmed Mean ( 2 / 40 )-0.8312567218840347.7259980443493-0.0174172726804285
Trimmed Mean ( 3 / 40 )-1.1819951553077546.5418036441373-0.0253964191922039
Trimmed Mean ( 4 / 40 )-1.4573505152037345.4627304726741-0.0320559390087599
Trimmed Mean ( 5 / 40 )-2.2695523478416744.5310602695066-0.050965603201588
Trimmed Mean ( 6 / 40 )-3.2453912355821343.527300576408-0.0745599013172239
Trimmed Mean ( 7 / 40 )-2.8350604658472142.719415667803-0.0663646826982223
Trimmed Mean ( 8 / 40 )-2.3082273928153641.9545070095494-0.0550173880553518
Trimmed Mean ( 9 / 40 )-1.6109056410720641.1759871110444-0.0391224535000881
Trimmed Mean ( 10 / 40 )-1.2171817004674640.3763977231560-0.0301458715760917
Trimmed Mean ( 11 / 40 )-0.16550559736988639.6633760804966-0.00417275617269678
Trimmed Mean ( 12 / 40 )0.80082140604879738.94482992073070.0205629709432243
Trimmed Mean ( 13 / 40 )2.1463371163403538.31697204232690.0560153112821492
Trimmed Mean ( 14 / 40 )3.5691459054786737.61433363091470.094887920666106
Trimmed Mean ( 15 / 40 )4.3346668071202336.98888215665520.117188369974580
Trimmed Mean ( 16 / 40 )5.1480526663812236.34482006269620.141644742153094
Trimmed Mean ( 17 / 40 )6.2264021254657835.69594191997320.174428850747930
Trimmed Mean ( 18 / 40 )7.3136317078581434.95996942248740.209200174618968
Trimmed Mean ( 19 / 40 )8.0401749647319434.2422682551320.234802639382014
Trimmed Mean ( 20 / 40 )8.58356328628133.54271791761380.255899456548619
Trimmed Mean ( 21 / 40 )8.5325624392047732.89422334068190.259393947406326
Trimmed Mean ( 22 / 40 )8.7551003140566132.42956442489270.269972800107555
Trimmed Mean ( 23 / 40 )9.1590165227412631.9172770211520.286961087459668
Trimmed Mean ( 24 / 40 )10.157619543414031.5032356524110.322430992660167
Trimmed Mean ( 25 / 40 )11.090116688023231.07414712754960.356892069877308
Trimmed Mean ( 26 / 40 )11.958530180539730.66734626113150.389943429689453
Trimmed Mean ( 27 / 40 )12.620307318167930.29170124943460.416625900745785
Trimmed Mean ( 28 / 40 )13.310719558037929.87077593185490.445610103614449
Trimmed Mean ( 29 / 40 )13.972202746191529.44173874636320.474571249563766
Trimmed Mean ( 30 / 40 )14.533036291620329.04334076850750.500391342974528
Trimmed Mean ( 31 / 40 )14.533036291620328.60837217668670.50799941366337
Trimmed Mean ( 32 / 40 )15.376824249503128.16676432923750.545920861543255
Trimmed Mean ( 33 / 40 )15.972104814655227.66523129536180.577334945951925
Trimmed Mean ( 34 / 40 )16.526418472943627.20674037823440.607438386340647
Trimmed Mean ( 35 / 40 )16.733579240548826.76585075532980.625183910405564
Trimmed Mean ( 36 / 40 )16.680556186439926.2722108002230.634912543648528
Trimmed Mean ( 37 / 40 )16.997813629769925.78053222383320.659327491077008
Trimmed Mean ( 38 / 40 )16.890559466773625.34026894196290.66655012641966
Trimmed Mean ( 39 / 40 )16.762829033609424.77269622919800.676665506189517
Trimmed Mean ( 40 / 40 )16.383411899326424.12047213001430.679232637363664
Median49.7591290429804
Midrange20.953667034015
Midmean - Weighted Average at Xnp8.46687130395737
Midmean - Weighted Average at X(n+1)p14.5330362916203
Midmean - Empirical Distribution Function14.5330362916203
Midmean - Empirical Distribution Function - Averaging14.5330362916203
Midmean - Empirical Distribution Function - Interpolation14.5330362916203
Midmean - Closest Observation8.02313027235234
Midmean - True Basic - Statistics Graphics Toolkit14.5330362916203
Midmean - MS Excel (old versions)14.5330362916203
Number of observations121

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 6.79676700596141e-14 & 51.4038116616343 & 1.32223015886471e-15 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & -611.289101333921 &  &  \tabularnewline
Quadratic Mean & 563.100543776485 &  &  \tabularnewline
Winsorized Mean ( 1 / 40 ) & 0.111093953094117 & 50.2851531315402 & 0.00220927940307763 \tabularnewline
Winsorized Mean ( 2 / 40 ) & -0.164563831905055 & 49.755227392081 & -0.00330746819039254 \tabularnewline
Winsorized Mean ( 3 / 40 ) & -0.410545014772738 & 49.1790186519547 & -0.00834797086290416 \tabularnewline
Winsorized Mean ( 4 / 40 ) & 1.52296034174872 & 48.3466703605139 & 0.0315008320199143 \tabularnewline
Winsorized Mean ( 5 / 40 ) & 2.12575503908846 & 48.2155158224542 & 0.0440886092957340 \tabularnewline
Winsorized Mean ( 6 / 40 ) & -5.42251812954753 & 46.8958439787222 & -0.115628969850886 \tabularnewline
Winsorized Mean ( 7 / 40 ) & -6.03524483509029 & 46.2348717823591 & -0.130534477601667 \tabularnewline
Winsorized Mean ( 8 / 40 ) & -7.05693089229036 & 45.8221821129901 & -0.154006871058412 \tabularnewline
Winsorized Mean ( 9 / 40 ) & -4.56871607090334 & 45.4045078558647 & -0.100622521565625 \tabularnewline
Winsorized Mean ( 10 / 40 ) & -9.8218043621749 & 44.2887281034489 & -0.221767586985865 \tabularnewline
Winsorized Mean ( 11 / 40 ) & -8.68675280933464 & 43.7466491673476 & -0.198569558461598 \tabularnewline
Winsorized Mean ( 12 / 40 ) & -11.8759381785162 & 42.5211194835424 & -0.279295049677908 \tabularnewline
Winsorized Mean ( 13 / 40 ) & -12.0699920247194 & 42.4431587778793 & -0.284380153887370 \tabularnewline
Winsorized Mean ( 14 / 40 ) & -4.49096672833417 & 41.2414884693981 & -0.108894389970104 \tabularnewline
Winsorized Mean ( 15 / 40 ) & -4.63946643348649 & 40.7324547537251 & -0.113900978017098 \tabularnewline
Winsorized Mean ( 16 / 40 ) & -7.25742210259167 & 40.0745897365988 & -0.181097851538670 \tabularnewline
Winsorized Mean ( 17 / 40 ) & -6.75745528409587 & 39.999585454884 & -0.168938132914345 \tabularnewline
Winsorized Mean ( 18 / 40 ) & -1.65707594312909 & 39.0559994314315 & -0.0424282048149434 \tabularnewline
Winsorized Mean ( 19 / 40 ) & 1.12881441213687 & 38.097781298384 & 0.0296294002870123 \tabularnewline
Winsorized Mean ( 20 / 40 ) & 9.24952476049952 & 36.8864655874909 & 0.250756601728636 \tabularnewline
Winsorized Mean ( 21 / 40 ) & 5.5586472025484 & 34.6574225864933 & 0.160388360925452 \tabularnewline
Winsorized Mean ( 22 / 40 ) & 3.24715201381149 & 34.3803121046942 & 0.0944480086138638 \tabularnewline
Winsorized Mean ( 23 / 40 ) & -4.69763200378448 & 32.8740874791258 & -0.142897715617729 \tabularnewline
Winsorized Mean ( 24 / 40 ) & -2.97440636083351 & 32.364368498813 & -0.091903735459649 \tabularnewline
Winsorized Mean ( 25 / 40 ) & -1.29015830859631 & 31.531501963147 & -0.0409164875845179 \tabularnewline
Winsorized Mean ( 26 / 40 ) & 2.43112709170991 & 30.6450023120081 & 0.0793319271755214 \tabularnewline
Winsorized Mean ( 27 / 40 ) & 2.60647689691344 & 30.3560069658702 & 0.0858636282381918 \tabularnewline
Winsorized Mean ( 28 / 40 ) & 3.6672786993349 & 29.7240343711572 & 0.123377555467149 \tabularnewline
Winsorized Mean ( 29 / 40 ) & 5.77290901178247 & 28.7887422363947 & 0.200526614340392 \tabularnewline
Winsorized Mean ( 30 / 40 ) & 7.45157057272726 & 28.3594824484112 & 0.262754110068209 \tabularnewline
Winsorized Mean ( 31 / 40 ) & 9.76450615833797 & 27.6658032535527 & 0.352944972132124 \tabularnewline
Winsorized Mean ( 32 / 40 ) & 6.71819784729082 & 27.2980671577850 & 0.246105257506295 \tabularnewline
Winsorized Mean ( 33 / 40 ) & 7.95975284485092 & 26.1879381730255 & 0.303947290247147 \tabularnewline
Winsorized Mean ( 34 / 40 ) & 13.5576848280889 & 25.2894893471346 & 0.536099588330557 \tabularnewline
Winsorized Mean ( 35 / 40 ) & 17.4851043463070 & 24.8227587235222 & 0.704398110663583 \tabularnewline
Winsorized Mean ( 36 / 40 ) & 12.2441959045031 & 23.9576146207926 & 0.511077421450651 \tabularnewline
Winsorized Mean ( 37 / 40 ) & 18.4736663685212 & 22.8197393414466 & 0.809547650483814 \tabularnewline
Winsorized Mean ( 38 / 40 ) & 18.6154481261967 & 22.6798851996252 & 0.82079110905307 \tabularnewline
Winsorized Mean ( 39 / 40 ) & 21.7767794279780 & 22.1404416478052 & 0.98357475313221 \tabularnewline
Winsorized Mean ( 40 / 40 ) & 30.0787699857278 & 21.1019577883936 & 1.42540186495263 \tabularnewline
Trimmed Mean ( 1 / 40 ) & -0.352162471159846 & 49.0724324811779 & -0.00717638098121426 \tabularnewline
Trimmed Mean ( 2 / 40 ) & -0.83125672188403 & 47.7259980443493 & -0.0174172726804285 \tabularnewline
Trimmed Mean ( 3 / 40 ) & -1.18199515530775 & 46.5418036441373 & -0.0253964191922039 \tabularnewline
Trimmed Mean ( 4 / 40 ) & -1.45735051520373 & 45.4627304726741 & -0.0320559390087599 \tabularnewline
Trimmed Mean ( 5 / 40 ) & -2.26955234784167 & 44.5310602695066 & -0.050965603201588 \tabularnewline
Trimmed Mean ( 6 / 40 ) & -3.24539123558213 & 43.527300576408 & -0.0745599013172239 \tabularnewline
Trimmed Mean ( 7 / 40 ) & -2.83506046584721 & 42.719415667803 & -0.0663646826982223 \tabularnewline
Trimmed Mean ( 8 / 40 ) & -2.30822739281536 & 41.9545070095494 & -0.0550173880553518 \tabularnewline
Trimmed Mean ( 9 / 40 ) & -1.61090564107206 & 41.1759871110444 & -0.0391224535000881 \tabularnewline
Trimmed Mean ( 10 / 40 ) & -1.21718170046746 & 40.3763977231560 & -0.0301458715760917 \tabularnewline
Trimmed Mean ( 11 / 40 ) & -0.165505597369886 & 39.6633760804966 & -0.00417275617269678 \tabularnewline
Trimmed Mean ( 12 / 40 ) & 0.800821406048797 & 38.9448299207307 & 0.0205629709432243 \tabularnewline
Trimmed Mean ( 13 / 40 ) & 2.14633711634035 & 38.3169720423269 & 0.0560153112821492 \tabularnewline
Trimmed Mean ( 14 / 40 ) & 3.56914590547867 & 37.6143336309147 & 0.094887920666106 \tabularnewline
Trimmed Mean ( 15 / 40 ) & 4.33466680712023 & 36.9888821566552 & 0.117188369974580 \tabularnewline
Trimmed Mean ( 16 / 40 ) & 5.14805266638122 & 36.3448200626962 & 0.141644742153094 \tabularnewline
Trimmed Mean ( 17 / 40 ) & 6.22640212546578 & 35.6959419199732 & 0.174428850747930 \tabularnewline
Trimmed Mean ( 18 / 40 ) & 7.31363170785814 & 34.9599694224874 & 0.209200174618968 \tabularnewline
Trimmed Mean ( 19 / 40 ) & 8.04017496473194 & 34.242268255132 & 0.234802639382014 \tabularnewline
Trimmed Mean ( 20 / 40 ) & 8.583563286281 & 33.5427179176138 & 0.255899456548619 \tabularnewline
Trimmed Mean ( 21 / 40 ) & 8.53256243920477 & 32.8942233406819 & 0.259393947406326 \tabularnewline
Trimmed Mean ( 22 / 40 ) & 8.75510031405661 & 32.4295644248927 & 0.269972800107555 \tabularnewline
Trimmed Mean ( 23 / 40 ) & 9.15901652274126 & 31.917277021152 & 0.286961087459668 \tabularnewline
Trimmed Mean ( 24 / 40 ) & 10.1576195434140 & 31.503235652411 & 0.322430992660167 \tabularnewline
Trimmed Mean ( 25 / 40 ) & 11.0901166880232 & 31.0741471275496 & 0.356892069877308 \tabularnewline
Trimmed Mean ( 26 / 40 ) & 11.9585301805397 & 30.6673462611315 & 0.389943429689453 \tabularnewline
Trimmed Mean ( 27 / 40 ) & 12.6203073181679 & 30.2917012494346 & 0.416625900745785 \tabularnewline
Trimmed Mean ( 28 / 40 ) & 13.3107195580379 & 29.8707759318549 & 0.445610103614449 \tabularnewline
Trimmed Mean ( 29 / 40 ) & 13.9722027461915 & 29.4417387463632 & 0.474571249563766 \tabularnewline
Trimmed Mean ( 30 / 40 ) & 14.5330362916203 & 29.0433407685075 & 0.500391342974528 \tabularnewline
Trimmed Mean ( 31 / 40 ) & 14.5330362916203 & 28.6083721766867 & 0.50799941366337 \tabularnewline
Trimmed Mean ( 32 / 40 ) & 15.3768242495031 & 28.1667643292375 & 0.545920861543255 \tabularnewline
Trimmed Mean ( 33 / 40 ) & 15.9721048146552 & 27.6652312953618 & 0.577334945951925 \tabularnewline
Trimmed Mean ( 34 / 40 ) & 16.5264184729436 & 27.2067403782344 & 0.607438386340647 \tabularnewline
Trimmed Mean ( 35 / 40 ) & 16.7335792405488 & 26.7658507553298 & 0.625183910405564 \tabularnewline
Trimmed Mean ( 36 / 40 ) & 16.6805561864399 & 26.272210800223 & 0.634912543648528 \tabularnewline
Trimmed Mean ( 37 / 40 ) & 16.9978136297699 & 25.7805322238332 & 0.659327491077008 \tabularnewline
Trimmed Mean ( 38 / 40 ) & 16.8905594667736 & 25.3402689419629 & 0.66655012641966 \tabularnewline
Trimmed Mean ( 39 / 40 ) & 16.7628290336094 & 24.7726962291980 & 0.676665506189517 \tabularnewline
Trimmed Mean ( 40 / 40 ) & 16.3834118993264 & 24.1204721300143 & 0.679232637363664 \tabularnewline
Median & 49.7591290429804 &  &  \tabularnewline
Midrange & 20.953667034015 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 8.46687130395737 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 14.5330362916203 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 14.5330362916203 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 14.5330362916203 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 14.5330362916203 &  &  \tabularnewline
Midmean - Closest Observation & 8.02313027235234 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 14.5330362916203 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 14.5330362916203 &  &  \tabularnewline
Number of observations & 121 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4809&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]6.79676700596141e-14[/C][C]51.4038116616343[/C][C]1.32223015886471e-15[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]-611.289101333921[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]563.100543776485[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 40 )[/C][C]0.111093953094117[/C][C]50.2851531315402[/C][C]0.00220927940307763[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 40 )[/C][C]-0.164563831905055[/C][C]49.755227392081[/C][C]-0.00330746819039254[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 40 )[/C][C]-0.410545014772738[/C][C]49.1790186519547[/C][C]-0.00834797086290416[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 40 )[/C][C]1.52296034174872[/C][C]48.3466703605139[/C][C]0.0315008320199143[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 40 )[/C][C]2.12575503908846[/C][C]48.2155158224542[/C][C]0.0440886092957340[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 40 )[/C][C]-5.42251812954753[/C][C]46.8958439787222[/C][C]-0.115628969850886[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 40 )[/C][C]-6.03524483509029[/C][C]46.2348717823591[/C][C]-0.130534477601667[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 40 )[/C][C]-7.05693089229036[/C][C]45.8221821129901[/C][C]-0.154006871058412[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 40 )[/C][C]-4.56871607090334[/C][C]45.4045078558647[/C][C]-0.100622521565625[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 40 )[/C][C]-9.8218043621749[/C][C]44.2887281034489[/C][C]-0.221767586985865[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 40 )[/C][C]-8.68675280933464[/C][C]43.7466491673476[/C][C]-0.198569558461598[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 40 )[/C][C]-11.8759381785162[/C][C]42.5211194835424[/C][C]-0.279295049677908[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 40 )[/C][C]-12.0699920247194[/C][C]42.4431587778793[/C][C]-0.284380153887370[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 40 )[/C][C]-4.49096672833417[/C][C]41.2414884693981[/C][C]-0.108894389970104[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 40 )[/C][C]-4.63946643348649[/C][C]40.7324547537251[/C][C]-0.113900978017098[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 40 )[/C][C]-7.25742210259167[/C][C]40.0745897365988[/C][C]-0.181097851538670[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 40 )[/C][C]-6.75745528409587[/C][C]39.999585454884[/C][C]-0.168938132914345[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 40 )[/C][C]-1.65707594312909[/C][C]39.0559994314315[/C][C]-0.0424282048149434[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 40 )[/C][C]1.12881441213687[/C][C]38.097781298384[/C][C]0.0296294002870123[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 40 )[/C][C]9.24952476049952[/C][C]36.8864655874909[/C][C]0.250756601728636[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 40 )[/C][C]5.5586472025484[/C][C]34.6574225864933[/C][C]0.160388360925452[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 40 )[/C][C]3.24715201381149[/C][C]34.3803121046942[/C][C]0.0944480086138638[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 40 )[/C][C]-4.69763200378448[/C][C]32.8740874791258[/C][C]-0.142897715617729[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 40 )[/C][C]-2.97440636083351[/C][C]32.364368498813[/C][C]-0.091903735459649[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 40 )[/C][C]-1.29015830859631[/C][C]31.531501963147[/C][C]-0.0409164875845179[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 40 )[/C][C]2.43112709170991[/C][C]30.6450023120081[/C][C]0.0793319271755214[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 40 )[/C][C]2.60647689691344[/C][C]30.3560069658702[/C][C]0.0858636282381918[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 40 )[/C][C]3.6672786993349[/C][C]29.7240343711572[/C][C]0.123377555467149[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 40 )[/C][C]5.77290901178247[/C][C]28.7887422363947[/C][C]0.200526614340392[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 40 )[/C][C]7.45157057272726[/C][C]28.3594824484112[/C][C]0.262754110068209[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 40 )[/C][C]9.76450615833797[/C][C]27.6658032535527[/C][C]0.352944972132124[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 40 )[/C][C]6.71819784729082[/C][C]27.2980671577850[/C][C]0.246105257506295[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 40 )[/C][C]7.95975284485092[/C][C]26.1879381730255[/C][C]0.303947290247147[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 40 )[/C][C]13.5576848280889[/C][C]25.2894893471346[/C][C]0.536099588330557[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 40 )[/C][C]17.4851043463070[/C][C]24.8227587235222[/C][C]0.704398110663583[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 40 )[/C][C]12.2441959045031[/C][C]23.9576146207926[/C][C]0.511077421450651[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 40 )[/C][C]18.4736663685212[/C][C]22.8197393414466[/C][C]0.809547650483814[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 40 )[/C][C]18.6154481261967[/C][C]22.6798851996252[/C][C]0.82079110905307[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 40 )[/C][C]21.7767794279780[/C][C]22.1404416478052[/C][C]0.98357475313221[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 40 )[/C][C]30.0787699857278[/C][C]21.1019577883936[/C][C]1.42540186495263[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 40 )[/C][C]-0.352162471159846[/C][C]49.0724324811779[/C][C]-0.00717638098121426[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 40 )[/C][C]-0.83125672188403[/C][C]47.7259980443493[/C][C]-0.0174172726804285[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 40 )[/C][C]-1.18199515530775[/C][C]46.5418036441373[/C][C]-0.0253964191922039[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 40 )[/C][C]-1.45735051520373[/C][C]45.4627304726741[/C][C]-0.0320559390087599[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 40 )[/C][C]-2.26955234784167[/C][C]44.5310602695066[/C][C]-0.050965603201588[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 40 )[/C][C]-3.24539123558213[/C][C]43.527300576408[/C][C]-0.0745599013172239[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 40 )[/C][C]-2.83506046584721[/C][C]42.719415667803[/C][C]-0.0663646826982223[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 40 )[/C][C]-2.30822739281536[/C][C]41.9545070095494[/C][C]-0.0550173880553518[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 40 )[/C][C]-1.61090564107206[/C][C]41.1759871110444[/C][C]-0.0391224535000881[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 40 )[/C][C]-1.21718170046746[/C][C]40.3763977231560[/C][C]-0.0301458715760917[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 40 )[/C][C]-0.165505597369886[/C][C]39.6633760804966[/C][C]-0.00417275617269678[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 40 )[/C][C]0.800821406048797[/C][C]38.9448299207307[/C][C]0.0205629709432243[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 40 )[/C][C]2.14633711634035[/C][C]38.3169720423269[/C][C]0.0560153112821492[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 40 )[/C][C]3.56914590547867[/C][C]37.6143336309147[/C][C]0.094887920666106[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 40 )[/C][C]4.33466680712023[/C][C]36.9888821566552[/C][C]0.117188369974580[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 40 )[/C][C]5.14805266638122[/C][C]36.3448200626962[/C][C]0.141644742153094[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 40 )[/C][C]6.22640212546578[/C][C]35.6959419199732[/C][C]0.174428850747930[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 40 )[/C][C]7.31363170785814[/C][C]34.9599694224874[/C][C]0.209200174618968[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 40 )[/C][C]8.04017496473194[/C][C]34.242268255132[/C][C]0.234802639382014[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 40 )[/C][C]8.583563286281[/C][C]33.5427179176138[/C][C]0.255899456548619[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 40 )[/C][C]8.53256243920477[/C][C]32.8942233406819[/C][C]0.259393947406326[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 40 )[/C][C]8.75510031405661[/C][C]32.4295644248927[/C][C]0.269972800107555[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 40 )[/C][C]9.15901652274126[/C][C]31.917277021152[/C][C]0.286961087459668[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 40 )[/C][C]10.1576195434140[/C][C]31.503235652411[/C][C]0.322430992660167[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 40 )[/C][C]11.0901166880232[/C][C]31.0741471275496[/C][C]0.356892069877308[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 40 )[/C][C]11.9585301805397[/C][C]30.6673462611315[/C][C]0.389943429689453[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 40 )[/C][C]12.6203073181679[/C][C]30.2917012494346[/C][C]0.416625900745785[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 40 )[/C][C]13.3107195580379[/C][C]29.8707759318549[/C][C]0.445610103614449[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 40 )[/C][C]13.9722027461915[/C][C]29.4417387463632[/C][C]0.474571249563766[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 40 )[/C][C]14.5330362916203[/C][C]29.0433407685075[/C][C]0.500391342974528[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 40 )[/C][C]14.5330362916203[/C][C]28.6083721766867[/C][C]0.50799941366337[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 40 )[/C][C]15.3768242495031[/C][C]28.1667643292375[/C][C]0.545920861543255[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 40 )[/C][C]15.9721048146552[/C][C]27.6652312953618[/C][C]0.577334945951925[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 40 )[/C][C]16.5264184729436[/C][C]27.2067403782344[/C][C]0.607438386340647[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 40 )[/C][C]16.7335792405488[/C][C]26.7658507553298[/C][C]0.625183910405564[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 40 )[/C][C]16.6805561864399[/C][C]26.272210800223[/C][C]0.634912543648528[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 40 )[/C][C]16.9978136297699[/C][C]25.7805322238332[/C][C]0.659327491077008[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 40 )[/C][C]16.8905594667736[/C][C]25.3402689419629[/C][C]0.66655012641966[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 40 )[/C][C]16.7628290336094[/C][C]24.7726962291980[/C][C]0.676665506189517[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 40 )[/C][C]16.3834118993264[/C][C]24.1204721300143[/C][C]0.679232637363664[/C][/ROW]
[ROW][C]Median[/C][C]49.7591290429804[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]20.953667034015[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]8.46687130395737[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]14.5330362916203[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]14.5330362916203[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]14.5330362916203[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]14.5330362916203[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]8.02313027235234[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]14.5330362916203[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]14.5330362916203[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]121[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4809&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4809&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 Mean6.79676700596141e-1451.40381166163431.32223015886471e-15
Geometric MeanNaN
Harmonic Mean-611.289101333921
Quadratic Mean563.100543776485
Winsorized Mean ( 1 / 40 )0.11109395309411750.28515313154020.00220927940307763
Winsorized Mean ( 2 / 40 )-0.16456383190505549.755227392081-0.00330746819039254
Winsorized Mean ( 3 / 40 )-0.41054501477273849.1790186519547-0.00834797086290416
Winsorized Mean ( 4 / 40 )1.5229603417487248.34667036051390.0315008320199143
Winsorized Mean ( 5 / 40 )2.1257550390884648.21551582245420.0440886092957340
Winsorized Mean ( 6 / 40 )-5.4225181295475346.8958439787222-0.115628969850886
Winsorized Mean ( 7 / 40 )-6.0352448350902946.2348717823591-0.130534477601667
Winsorized Mean ( 8 / 40 )-7.0569308922903645.8221821129901-0.154006871058412
Winsorized Mean ( 9 / 40 )-4.5687160709033445.4045078558647-0.100622521565625
Winsorized Mean ( 10 / 40 )-9.821804362174944.2887281034489-0.221767586985865
Winsorized Mean ( 11 / 40 )-8.6867528093346443.7466491673476-0.198569558461598
Winsorized Mean ( 12 / 40 )-11.875938178516242.5211194835424-0.279295049677908
Winsorized Mean ( 13 / 40 )-12.069992024719442.4431587778793-0.284380153887370
Winsorized Mean ( 14 / 40 )-4.4909667283341741.2414884693981-0.108894389970104
Winsorized Mean ( 15 / 40 )-4.6394664334864940.7324547537251-0.113900978017098
Winsorized Mean ( 16 / 40 )-7.2574221025916740.0745897365988-0.181097851538670
Winsorized Mean ( 17 / 40 )-6.7574552840958739.999585454884-0.168938132914345
Winsorized Mean ( 18 / 40 )-1.6570759431290939.0559994314315-0.0424282048149434
Winsorized Mean ( 19 / 40 )1.1288144121368738.0977812983840.0296294002870123
Winsorized Mean ( 20 / 40 )9.2495247604995236.88646558749090.250756601728636
Winsorized Mean ( 21 / 40 )5.558647202548434.65742258649330.160388360925452
Winsorized Mean ( 22 / 40 )3.2471520138114934.38031210469420.0944480086138638
Winsorized Mean ( 23 / 40 )-4.6976320037844832.8740874791258-0.142897715617729
Winsorized Mean ( 24 / 40 )-2.9744063608335132.364368498813-0.091903735459649
Winsorized Mean ( 25 / 40 )-1.2901583085963131.531501963147-0.0409164875845179
Winsorized Mean ( 26 / 40 )2.4311270917099130.64500231200810.0793319271755214
Winsorized Mean ( 27 / 40 )2.6064768969134430.35600696587020.0858636282381918
Winsorized Mean ( 28 / 40 )3.667278699334929.72403437115720.123377555467149
Winsorized Mean ( 29 / 40 )5.7729090117824728.78874223639470.200526614340392
Winsorized Mean ( 30 / 40 )7.4515705727272628.35948244841120.262754110068209
Winsorized Mean ( 31 / 40 )9.7645061583379727.66580325355270.352944972132124
Winsorized Mean ( 32 / 40 )6.7181978472908227.29806715778500.246105257506295
Winsorized Mean ( 33 / 40 )7.9597528448509226.18793817302550.303947290247147
Winsorized Mean ( 34 / 40 )13.557684828088925.28948934713460.536099588330557
Winsorized Mean ( 35 / 40 )17.485104346307024.82275872352220.704398110663583
Winsorized Mean ( 36 / 40 )12.244195904503123.95761462079260.511077421450651
Winsorized Mean ( 37 / 40 )18.473666368521222.81973934144660.809547650483814
Winsorized Mean ( 38 / 40 )18.615448126196722.67988519962520.82079110905307
Winsorized Mean ( 39 / 40 )21.776779427978022.14044164780520.98357475313221
Winsorized Mean ( 40 / 40 )30.078769985727821.10195778839361.42540186495263
Trimmed Mean ( 1 / 40 )-0.35216247115984649.0724324811779-0.00717638098121426
Trimmed Mean ( 2 / 40 )-0.8312567218840347.7259980443493-0.0174172726804285
Trimmed Mean ( 3 / 40 )-1.1819951553077546.5418036441373-0.0253964191922039
Trimmed Mean ( 4 / 40 )-1.4573505152037345.4627304726741-0.0320559390087599
Trimmed Mean ( 5 / 40 )-2.2695523478416744.5310602695066-0.050965603201588
Trimmed Mean ( 6 / 40 )-3.2453912355821343.527300576408-0.0745599013172239
Trimmed Mean ( 7 / 40 )-2.8350604658472142.719415667803-0.0663646826982223
Trimmed Mean ( 8 / 40 )-2.3082273928153641.9545070095494-0.0550173880553518
Trimmed Mean ( 9 / 40 )-1.6109056410720641.1759871110444-0.0391224535000881
Trimmed Mean ( 10 / 40 )-1.2171817004674640.3763977231560-0.0301458715760917
Trimmed Mean ( 11 / 40 )-0.16550559736988639.6633760804966-0.00417275617269678
Trimmed Mean ( 12 / 40 )0.80082140604879738.94482992073070.0205629709432243
Trimmed Mean ( 13 / 40 )2.1463371163403538.31697204232690.0560153112821492
Trimmed Mean ( 14 / 40 )3.5691459054786737.61433363091470.094887920666106
Trimmed Mean ( 15 / 40 )4.3346668071202336.98888215665520.117188369974580
Trimmed Mean ( 16 / 40 )5.1480526663812236.34482006269620.141644742153094
Trimmed Mean ( 17 / 40 )6.2264021254657835.69594191997320.174428850747930
Trimmed Mean ( 18 / 40 )7.3136317078581434.95996942248740.209200174618968
Trimmed Mean ( 19 / 40 )8.0401749647319434.2422682551320.234802639382014
Trimmed Mean ( 20 / 40 )8.58356328628133.54271791761380.255899456548619
Trimmed Mean ( 21 / 40 )8.5325624392047732.89422334068190.259393947406326
Trimmed Mean ( 22 / 40 )8.7551003140566132.42956442489270.269972800107555
Trimmed Mean ( 23 / 40 )9.1590165227412631.9172770211520.286961087459668
Trimmed Mean ( 24 / 40 )10.157619543414031.5032356524110.322430992660167
Trimmed Mean ( 25 / 40 )11.090116688023231.07414712754960.356892069877308
Trimmed Mean ( 26 / 40 )11.958530180539730.66734626113150.389943429689453
Trimmed Mean ( 27 / 40 )12.620307318167930.29170124943460.416625900745785
Trimmed Mean ( 28 / 40 )13.310719558037929.87077593185490.445610103614449
Trimmed Mean ( 29 / 40 )13.972202746191529.44173874636320.474571249563766
Trimmed Mean ( 30 / 40 )14.533036291620329.04334076850750.500391342974528
Trimmed Mean ( 31 / 40 )14.533036291620328.60837217668670.50799941366337
Trimmed Mean ( 32 / 40 )15.376824249503128.16676432923750.545920861543255
Trimmed Mean ( 33 / 40 )15.972104814655227.66523129536180.577334945951925
Trimmed Mean ( 34 / 40 )16.526418472943627.20674037823440.607438386340647
Trimmed Mean ( 35 / 40 )16.733579240548826.76585075532980.625183910405564
Trimmed Mean ( 36 / 40 )16.680556186439926.2722108002230.634912543648528
Trimmed Mean ( 37 / 40 )16.997813629769925.78053222383320.659327491077008
Trimmed Mean ( 38 / 40 )16.890559466773625.34026894196290.66655012641966
Trimmed Mean ( 39 / 40 )16.762829033609424.77269622919800.676665506189517
Trimmed Mean ( 40 / 40 )16.383411899326424.12047213001430.679232637363664
Median49.7591290429804
Midrange20.953667034015
Midmean - Weighted Average at Xnp8.46687130395737
Midmean - Weighted Average at X(n+1)p14.5330362916203
Midmean - Empirical Distribution Function14.5330362916203
Midmean - Empirical Distribution Function - Averaging14.5330362916203
Midmean - Empirical Distribution Function - Interpolation14.5330362916203
Midmean - Closest Observation8.02313027235234
Midmean - True Basic - Statistics Graphics Toolkit14.5330362916203
Midmean - MS Excel (old versions)14.5330362916203
Number of observations121



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')