Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 24 Oct 2009 04:10:39 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/24/t1256379343q863c2jegk1u7l4.htm/, Retrieved Fri, 03 May 2024 12:12:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50049, Retrieved Fri, 03 May 2024 12:12:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact136
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-10-24 10:10:39] [c4328af89eba9af53ee195d6fed304d9] [Current]
Feedback Forum

Post a new message
Dataseries X:
69,78206203
64,19822724
59,43536404
53,80982368
64,13934426
64,37601297
67,2
58,96084337
60,57206538
61,12573099
59,2679558
58,69734284
66,94053208
62,82089552
59,70385675
60,11963406
62,46715328
56,2804878
61,62393162
59,53793103
64,12837345
63,24287653
60,98208361
60,10222489
58,62831858
58,16274309
57,57653061
50,66896849
47,48563218
51,86721992
55,22606383
56,1206517
48,70980392
51,86528497
49,68446602
46,84115523
49,17371253
48,61561119
46,91392582
49,36257968
50,08178439
49,2609017
52,50601443
52,1339076
55,53719008
53,90199637
55,03133705
56,58369408
56,71466845
53,21407795
49,0327381
53,03166069
51,26201923
52,68386714
53,38838269
51,87606595
60,54860088
71,66123779
72,58706468
78,50655903




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50049&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50049&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50049&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean57.2660198210.88855385266652464.4485639774633
Geometric Mean56.8748292416914
Harmonic Mean56.4982428704264
Quadratic Mean57.671302873573
Winsorized Mean ( 1 / 20 )57.1685744250.85311346726271767.011689088006
Winsorized Mean ( 2 / 20 )57.15677040733330.84006840013917868.038234026972
Winsorized Mean ( 3 / 20 )57.11931056983330.80314764132000471.1193155917828
Winsorized Mean ( 4 / 20 )56.95345261650.75922583173446375.0151670766905
Winsorized Mean ( 5 / 20 )56.95874147150.74942327853868776.003432376113
Winsorized Mean ( 6 / 20 )56.71638700350.69372778299333181.7559688308536
Winsorized Mean ( 7 / 20 )56.70581740483330.68800254556200482.4209412750245
Winsorized Mean ( 8 / 20 )56.71152340483330.68407802204120382.9021275023765
Winsorized Mean ( 9 / 20 )56.75816073433330.67509047939601884.0748943535881
Winsorized Mean ( 10 / 20 )56.67679764266670.63682457504564888.9990742562095
Winsorized Mean ( 11 / 20 )56.70708487583330.60487102549305393.7507046723047
Winsorized Mean ( 12 / 20 )56.75494657583330.57315506989090099.0219742566991
Winsorized Mean ( 13 / 20 )56.70295612650.522201149860153108.584510282456
Winsorized Mean ( 14 / 20 )56.58716080116670.503967163635833112.283428136315
Winsorized Mean ( 15 / 20 )56.55346046366670.498169198751915113.522595546558
Winsorized Mean ( 16 / 20 )56.51288004233330.471050812362615119.971940519295
Winsorized Mean ( 17 / 20 )56.61166203583330.453680747146026124.783038275177
Winsorized Mean ( 18 / 20 )56.53632780283330.426879790464006132.440862898147
Winsorized Mean ( 19 / 20 )56.64094952316670.409437851443429138.338332236468
Winsorized Mean ( 20 / 20 )56.56896589650.381596980126827148.242698036286
Trimmed Mean ( 1 / 20 )57.07954267241380.82186428698739169.4512994130009
Trimmed Mean ( 2 / 20 )56.98415150892860.78308853653193372.7684659531533
Trimmed Mean ( 3 / 20 )56.88825212092590.7436208627048276.5016891995238
Trimmed Mean ( 4 / 20 )56.79938348673080.71281848460316679.6828150694655
Trimmed Mean ( 5 / 20 )56.75316274780.6921682259554781.9933083022668
Trimmed Mean ( 6 / 20 )56.7017680668750.66919060729394284.7318648062984
Trimmed Mean ( 7 / 20 )56.69859003717390.6574386442316286.2416448054104
Trimmed Mean ( 8 / 20 )56.69718210840910.64336879243612788.125477603171
Trimmed Mean ( 9 / 20 )56.6946211626190.62560569159758690.6235699643973
Trimmed Mean ( 10 / 20 )56.6840312340.60423356774249793.8114567943977
Trimmed Mean ( 11 / 20 )56.685173380.58607904293774496.719331740414
Trimmed Mean ( 12 / 20 )56.68185345638890.56981118428011499.4747997584488
Trimmed Mean ( 13 / 20 )56.67110446823530.555522111967437102.014129136154
Trimmed Mean ( 14 / 20 )56.66651047906250.548667310755242103.280274527493
Trimmed Mean ( 15 / 20 )56.67784614733330.542139057310512104.544849486598
Trimmed Mean ( 16 / 20 )56.69561553071430.53218309093984106.534041565637
Trimmed Mean ( 17 / 20 )56.72197161076920.523684199273076108.313314951081
Trimmed Mean ( 18 / 20 )56.73819360708330.513999025790018110.385799895003
Trimmed Mean ( 19 / 20 )56.7687793350.505260971170145112.355362029107
Trimmed Mean ( 20 / 20 )56.78896298950.49432913923084114.880872848932
Median56.649181265
Midrange62.67385713
Midmean - Weighted Average at Xnp56.522664656129
Midmean - Weighted Average at X(n+1)p56.6778461473333
Midmean - Empirical Distribution Function56.522664656129
Midmean - Empirical Distribution Function - Averaging56.6778461473333
Midmean - Empirical Distribution Function - Interpolation56.6778461473333
Midmean - Closest Observation56.522664656129
Midmean - True Basic - Statistics Graphics Toolkit56.6778461473333
Midmean - MS Excel (old versions)56.6665104790625
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 57.266019821 & 0.888553852666524 & 64.4485639774633 \tabularnewline
Geometric Mean & 56.8748292416914 &  &  \tabularnewline
Harmonic Mean & 56.4982428704264 &  &  \tabularnewline
Quadratic Mean & 57.671302873573 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 57.168574425 & 0.853113467262717 & 67.011689088006 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 57.1567704073333 & 0.840068400139178 & 68.038234026972 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 57.1193105698333 & 0.803147641320004 & 71.1193155917828 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 56.9534526165 & 0.759225831734463 & 75.0151670766905 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 56.9587414715 & 0.749423278538687 & 76.003432376113 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 56.7163870035 & 0.693727782993331 & 81.7559688308536 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 56.7058174048333 & 0.688002545562004 & 82.4209412750245 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 56.7115234048333 & 0.684078022041203 & 82.9021275023765 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 56.7581607343333 & 0.675090479396018 & 84.0748943535881 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 56.6767976426667 & 0.636824575045648 & 88.9990742562095 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 56.7070848758333 & 0.604871025493053 & 93.7507046723047 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 56.7549465758333 & 0.573155069890900 & 99.0219742566991 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 56.7029561265 & 0.522201149860153 & 108.584510282456 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 56.5871608011667 & 0.503967163635833 & 112.283428136315 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 56.5534604636667 & 0.498169198751915 & 113.522595546558 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 56.5128800423333 & 0.471050812362615 & 119.971940519295 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 56.6116620358333 & 0.453680747146026 & 124.783038275177 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 56.5363278028333 & 0.426879790464006 & 132.440862898147 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 56.6409495231667 & 0.409437851443429 & 138.338332236468 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 56.5689658965 & 0.381596980126827 & 148.242698036286 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 57.0795426724138 & 0.821864286987391 & 69.4512994130009 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 56.9841515089286 & 0.783088536531933 & 72.7684659531533 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 56.8882521209259 & 0.74362086270482 & 76.5016891995238 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 56.7993834867308 & 0.712818484603166 & 79.6828150694655 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 56.7531627478 & 0.69216822595547 & 81.9933083022668 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 56.701768066875 & 0.669190607293942 & 84.7318648062984 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 56.6985900371739 & 0.65743864423162 & 86.2416448054104 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 56.6971821084091 & 0.643368792436127 & 88.125477603171 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 56.694621162619 & 0.625605691597586 & 90.6235699643973 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 56.684031234 & 0.604233567742497 & 93.8114567943977 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 56.68517338 & 0.586079042937744 & 96.719331740414 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 56.6818534563889 & 0.569811184280114 & 99.4747997584488 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 56.6711044682353 & 0.555522111967437 & 102.014129136154 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 56.6665104790625 & 0.548667310755242 & 103.280274527493 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 56.6778461473333 & 0.542139057310512 & 104.544849486598 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 56.6956155307143 & 0.53218309093984 & 106.534041565637 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 56.7219716107692 & 0.523684199273076 & 108.313314951081 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 56.7381936070833 & 0.513999025790018 & 110.385799895003 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 56.768779335 & 0.505260971170145 & 112.355362029107 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 56.7889629895 & 0.49432913923084 & 114.880872848932 \tabularnewline
Median & 56.649181265 &  &  \tabularnewline
Midrange & 62.67385713 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 56.522664656129 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 56.6778461473333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 56.522664656129 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 56.6778461473333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 56.6778461473333 &  &  \tabularnewline
Midmean - Closest Observation & 56.522664656129 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 56.6778461473333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 56.6665104790625 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50049&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]57.266019821[/C][C]0.888553852666524[/C][C]64.4485639774633[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]56.8748292416914[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]56.4982428704264[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]57.671302873573[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]57.168574425[/C][C]0.853113467262717[/C][C]67.011689088006[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]57.1567704073333[/C][C]0.840068400139178[/C][C]68.038234026972[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]57.1193105698333[/C][C]0.803147641320004[/C][C]71.1193155917828[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]56.9534526165[/C][C]0.759225831734463[/C][C]75.0151670766905[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]56.9587414715[/C][C]0.749423278538687[/C][C]76.003432376113[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]56.7163870035[/C][C]0.693727782993331[/C][C]81.7559688308536[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]56.7058174048333[/C][C]0.688002545562004[/C][C]82.4209412750245[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]56.7115234048333[/C][C]0.684078022041203[/C][C]82.9021275023765[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]56.7581607343333[/C][C]0.675090479396018[/C][C]84.0748943535881[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]56.6767976426667[/C][C]0.636824575045648[/C][C]88.9990742562095[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]56.7070848758333[/C][C]0.604871025493053[/C][C]93.7507046723047[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]56.7549465758333[/C][C]0.573155069890900[/C][C]99.0219742566991[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]56.7029561265[/C][C]0.522201149860153[/C][C]108.584510282456[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]56.5871608011667[/C][C]0.503967163635833[/C][C]112.283428136315[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]56.5534604636667[/C][C]0.498169198751915[/C][C]113.522595546558[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]56.5128800423333[/C][C]0.471050812362615[/C][C]119.971940519295[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]56.6116620358333[/C][C]0.453680747146026[/C][C]124.783038275177[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]56.5363278028333[/C][C]0.426879790464006[/C][C]132.440862898147[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]56.6409495231667[/C][C]0.409437851443429[/C][C]138.338332236468[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]56.5689658965[/C][C]0.381596980126827[/C][C]148.242698036286[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]57.0795426724138[/C][C]0.821864286987391[/C][C]69.4512994130009[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]56.9841515089286[/C][C]0.783088536531933[/C][C]72.7684659531533[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]56.8882521209259[/C][C]0.74362086270482[/C][C]76.5016891995238[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]56.7993834867308[/C][C]0.712818484603166[/C][C]79.6828150694655[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]56.7531627478[/C][C]0.69216822595547[/C][C]81.9933083022668[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]56.701768066875[/C][C]0.669190607293942[/C][C]84.7318648062984[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]56.6985900371739[/C][C]0.65743864423162[/C][C]86.2416448054104[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]56.6971821084091[/C][C]0.643368792436127[/C][C]88.125477603171[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]56.694621162619[/C][C]0.625605691597586[/C][C]90.6235699643973[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]56.684031234[/C][C]0.604233567742497[/C][C]93.8114567943977[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]56.68517338[/C][C]0.586079042937744[/C][C]96.719331740414[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]56.6818534563889[/C][C]0.569811184280114[/C][C]99.4747997584488[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]56.6711044682353[/C][C]0.555522111967437[/C][C]102.014129136154[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]56.6665104790625[/C][C]0.548667310755242[/C][C]103.280274527493[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]56.6778461473333[/C][C]0.542139057310512[/C][C]104.544849486598[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]56.6956155307143[/C][C]0.53218309093984[/C][C]106.534041565637[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]56.7219716107692[/C][C]0.523684199273076[/C][C]108.313314951081[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]56.7381936070833[/C][C]0.513999025790018[/C][C]110.385799895003[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]56.768779335[/C][C]0.505260971170145[/C][C]112.355362029107[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]56.7889629895[/C][C]0.49432913923084[/C][C]114.880872848932[/C][/ROW]
[ROW][C]Median[/C][C]56.649181265[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]62.67385713[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]56.522664656129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]56.6778461473333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]56.522664656129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]56.6778461473333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]56.6778461473333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]56.522664656129[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]56.6778461473333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]56.6665104790625[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50049&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50049&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 Mean57.2660198210.88855385266652464.4485639774633
Geometric Mean56.8748292416914
Harmonic Mean56.4982428704264
Quadratic Mean57.671302873573
Winsorized Mean ( 1 / 20 )57.1685744250.85311346726271767.011689088006
Winsorized Mean ( 2 / 20 )57.15677040733330.84006840013917868.038234026972
Winsorized Mean ( 3 / 20 )57.11931056983330.80314764132000471.1193155917828
Winsorized Mean ( 4 / 20 )56.95345261650.75922583173446375.0151670766905
Winsorized Mean ( 5 / 20 )56.95874147150.74942327853868776.003432376113
Winsorized Mean ( 6 / 20 )56.71638700350.69372778299333181.7559688308536
Winsorized Mean ( 7 / 20 )56.70581740483330.68800254556200482.4209412750245
Winsorized Mean ( 8 / 20 )56.71152340483330.68407802204120382.9021275023765
Winsorized Mean ( 9 / 20 )56.75816073433330.67509047939601884.0748943535881
Winsorized Mean ( 10 / 20 )56.67679764266670.63682457504564888.9990742562095
Winsorized Mean ( 11 / 20 )56.70708487583330.60487102549305393.7507046723047
Winsorized Mean ( 12 / 20 )56.75494657583330.57315506989090099.0219742566991
Winsorized Mean ( 13 / 20 )56.70295612650.522201149860153108.584510282456
Winsorized Mean ( 14 / 20 )56.58716080116670.503967163635833112.283428136315
Winsorized Mean ( 15 / 20 )56.55346046366670.498169198751915113.522595546558
Winsorized Mean ( 16 / 20 )56.51288004233330.471050812362615119.971940519295
Winsorized Mean ( 17 / 20 )56.61166203583330.453680747146026124.783038275177
Winsorized Mean ( 18 / 20 )56.53632780283330.426879790464006132.440862898147
Winsorized Mean ( 19 / 20 )56.64094952316670.409437851443429138.338332236468
Winsorized Mean ( 20 / 20 )56.56896589650.381596980126827148.242698036286
Trimmed Mean ( 1 / 20 )57.07954267241380.82186428698739169.4512994130009
Trimmed Mean ( 2 / 20 )56.98415150892860.78308853653193372.7684659531533
Trimmed Mean ( 3 / 20 )56.88825212092590.7436208627048276.5016891995238
Trimmed Mean ( 4 / 20 )56.79938348673080.71281848460316679.6828150694655
Trimmed Mean ( 5 / 20 )56.75316274780.6921682259554781.9933083022668
Trimmed Mean ( 6 / 20 )56.7017680668750.66919060729394284.7318648062984
Trimmed Mean ( 7 / 20 )56.69859003717390.6574386442316286.2416448054104
Trimmed Mean ( 8 / 20 )56.69718210840910.64336879243612788.125477603171
Trimmed Mean ( 9 / 20 )56.6946211626190.62560569159758690.6235699643973
Trimmed Mean ( 10 / 20 )56.6840312340.60423356774249793.8114567943977
Trimmed Mean ( 11 / 20 )56.685173380.58607904293774496.719331740414
Trimmed Mean ( 12 / 20 )56.68185345638890.56981118428011499.4747997584488
Trimmed Mean ( 13 / 20 )56.67110446823530.555522111967437102.014129136154
Trimmed Mean ( 14 / 20 )56.66651047906250.548667310755242103.280274527493
Trimmed Mean ( 15 / 20 )56.67784614733330.542139057310512104.544849486598
Trimmed Mean ( 16 / 20 )56.69561553071430.53218309093984106.534041565637
Trimmed Mean ( 17 / 20 )56.72197161076920.523684199273076108.313314951081
Trimmed Mean ( 18 / 20 )56.73819360708330.513999025790018110.385799895003
Trimmed Mean ( 19 / 20 )56.7687793350.505260971170145112.355362029107
Trimmed Mean ( 20 / 20 )56.78896298950.49432913923084114.880872848932
Median56.649181265
Midrange62.67385713
Midmean - Weighted Average at Xnp56.522664656129
Midmean - Weighted Average at X(n+1)p56.6778461473333
Midmean - Empirical Distribution Function56.522664656129
Midmean - Empirical Distribution Function - Averaging56.6778461473333
Midmean - Empirical Distribution Function - Interpolation56.6778461473333
Midmean - Closest Observation56.522664656129
Midmean - True Basic - Statistics Graphics Toolkit56.6778461473333
Midmean - MS Excel (old versions)56.6665104790625
Number of observations60



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')