Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationSat, 24 Oct 2009 13:16:39 -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/t1256411841pi8owrasfq3m0b7.htm/, Retrieved Fri, 03 May 2024 08:43:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=50222, Retrieved Fri, 03 May 2024 08:43:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2009-10-24 19:16:39] [4ed6a647410123598b51b3bdc215cd7e] [Current]
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Dataseries X:
8.82
8.8
8.82
8.58
8.54
8.42
8.43
8.44
8.09
7.69
7.56
7.54
7.4
7.39
7.37
7.31
7.35
7.26
7.37
7.35
7.33
7.32
7.31
7.33
7.32
7.27
7.48
7.7
7.77
7.8
7.84
7.81
7.78
7.82
7.8
7.81
7.8
7.66
7.41
7.35
7.39
7.32
7.32
7.3
7.29
7.26
7.22
7.21
7.21
7.21
7.2
7.19
7.18
7.12
7.12
7.07
7.08
7.05
7.06
7.07
7.08
7.08
7.09
7.07
7.06
6.99
6.99
6.99
6.98
6.96
6.95
6.91
6.91
6.87
6.91
6.89
6.88
6.9
6.91
6.85
6.86
6.82
6.8
6.83
6.84
6.89
7.14
7.21
7.25
7.31
7.3
7.48
7.49
7.4
7.44
7.42
7.14
7.24
7.33
7.61
7.66
7.69
7.7
7.68
7.71
7.71
7.72
7.68
7.72
7.74
7.76
7.9
7.97
7.96
7.95
7.97
7.93
7.99
7.96
7.92
7.97
7.98
8
8.04
8.17
8.29
8.26
8.3
8.32
8.28
8.27
8.32




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50222&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]2 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=50222&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50222&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 time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean7.512878787878790.0423582708860616177.365096136419
Geometric Mean7.49761823705715
Harmonic Mean7.48273607809817
Quadratic Mean7.52850522408605
Winsorized Mean ( 1 / 44 )7.51303030303030.0423390721684297177.449101225993
Winsorized Mean ( 2 / 44 )7.512878787878790.0422493192478052177.822481441972
Winsorized Mean ( 3 / 44 )7.508106060606060.0411414924196576182.494742388554
Winsorized Mean ( 4 / 44 )7.507196969696970.0408666402506962183.699881459403
Winsorized Mean ( 5 / 44 )7.503787878787880.0401171558519618187.046856125044
Winsorized Mean ( 6 / 44 )7.503787878787880.0399811328252718187.683223273874
Winsorized Mean ( 7 / 44 )7.503787878787880.0398238851232912188.424305051022
Winsorized Mean ( 8 / 44 )7.498333333333330.0387277678556908193.616460449618
Winsorized Mean ( 9 / 44 )7.498333333333330.0387277678556908193.616460449618
Winsorized Mean ( 10 / 44 )7.497575757575760.0383937742556982195.281029357592
Winsorized Mean ( 11 / 44 )7.497575757575760.0381627753606314196.463063462366
Winsorized Mean ( 12 / 44 )7.496666666666670.0380192353440897197.180890115721
Winsorized Mean ( 13 / 44 )7.495681818181820.0378649170763385197.958490258145
Winsorized Mean ( 14 / 44 )7.494621212121210.0376999496712746198.79658401326
Winsorized Mean ( 15 / 44 )7.488939393939390.0356283047540886210.19634376738
Winsorized Mean ( 16 / 44 )7.480454545454550.0341180245313576219.252276420029
Winsorized Mean ( 17 / 44 )7.476590909090910.0329603518938040226.835894628188
Winsorized Mean ( 18 / 44 )7.47250.0321056071310423232.747506362369
Winsorized Mean ( 19 / 44 )7.47106060606060.0319260396114412234.011505873821
Winsorized Mean ( 20 / 44 )7.469545454545460.0317390294689424235.342591740388
Winsorized Mean ( 21 / 44 )7.47750.0304810257889769245.316547145344
Winsorized Mean ( 22 / 44 )7.479166666666670.0303038131693925246.806123864993
Winsorized Mean ( 23 / 44 )7.479166666666670.0303038131693925246.806123864993
Winsorized Mean ( 24 / 44 )7.479166666666670.0298887678178374250.233355628771
Winsorized Mean ( 25 / 44 )7.479166666666670.0298887678178374250.233355628771
Winsorized Mean ( 26 / 44 )7.477196969696970.0296479291661193252.199636871829
Winsorized Mean ( 27 / 44 )7.475151515151520.0289396391868914258.301475940221
Winsorized Mean ( 28 / 44 )7.47303030303030.0286862347195746260.509278268260
Winsorized Mean ( 29 / 44 )7.468636363636360.0281680568283143265.145601244632
Winsorized Mean ( 30 / 44 )7.457272727272730.0263739042118535282.751945535661
Winsorized Mean ( 31 / 44 )7.459621212121210.0251181352469936296.981489221580
Winsorized Mean ( 32 / 44 )7.457196969696970.0248540301116608300.039749537371
Winsorized Mean ( 33 / 44 )7.462196969696970.0243424547895418306.550717017371
Winsorized Mean ( 34 / 44 )7.459621212121210.0240629151887671310.004883182378
Winsorized Mean ( 35 / 44 )7.470227272727270.0230141077304220324.59339115948
Winsorized Mean ( 36 / 44 )7.472954545454550.0227533767506052328.43276966597
Winsorized Mean ( 37 / 44 )7.470151515151520.0218775176598126341.453341796343
Winsorized Mean ( 38 / 44 )7.470151515151510.0212972705238479350.756286200465
Winsorized Mean ( 39 / 44 )7.467196969696970.0209811152857637355.9008597967
Winsorized Mean ( 40 / 44 )7.461136363636360.0203410795116256366.801396129054
Winsorized Mean ( 41 / 44 )7.454924242424240.0196968395785663378.483269495506
Winsorized Mean ( 42 / 44 )7.458106060606060.0193967346958318384.50317424864
Winsorized Mean ( 43 / 44 )7.461363636363640.0184577004922946404.241234680262
Winsorized Mean ( 44 / 44 )7.464696969696970.0181546417684736411.172914612931
Trimmed Mean ( 1 / 44 )7.50830769230770.041445431281853181.161287507104
Trimmed Mean ( 2 / 44 )7.50343750.0404581959415941185.461494892952
Trimmed Mean ( 3 / 44 )7.498492063492060.0394173545632623190.233265184183
Trimmed Mean ( 4 / 44 )7.495080645161290.038720097464358193.570810405644
Trimmed Mean ( 5 / 44 )7.491803278688520.038036416138059196.963963468479
Trimmed Mean ( 6 / 44 )7.489166666666670.0374783940247463199.826242867336
Trimmed Mean ( 7 / 44 )7.48644067796610.0368904956464198202.936841774113
Trimmed Mean ( 8 / 44 )7.483620689655170.0362695217665091206.333591543671
Trimmed Mean ( 9 / 44 )7.481491228070180.0357847748071415209.069115801089
Trimmed Mean ( 10 / 44 )7.479285714285710.0352443014291986212.212624764621
Trimmed Mean ( 11 / 44 )7.477090909090910.0346949882463871215.509250384874
Trimmed Mean ( 12 / 44 )7.474814814814820.0341158111201888219.101190016597
Trimmed Mean ( 13 / 44 )7.472547169811320.0334884248205071223.138209989363
Trimmed Mean ( 14 / 44 )7.470288461538460.0328066781561688227.706335459440
Trimmed Mean ( 15 / 44 )7.468039215686270.0320632744210933232.915675348907
Trimmed Mean ( 16 / 44 )7.46620.0315100689374753236.946482561337
Trimmed Mean ( 17 / 44 )7.4650.0310826626382651240.166040048642
Trimmed Mean ( 18 / 44 )7.46406250.030740345127059242.809977218824
Trimmed Mean ( 19 / 44 )7.463404255319150.0304509511401074245.095932175629
Trimmed Mean ( 20 / 44 )7.462826086956520.0301387641551654247.615530900178
Trimmed Mean ( 21 / 44 )7.462333333333330.0298008579755667250.406660756264
Trimmed Mean ( 22 / 44 )7.461250.0295511584197615252.485871924753
Trimmed Mean ( 23 / 44 )7.460.0292772024408641254.805766195325
Trimmed Mean ( 24 / 44 )7.458690476190480.028955710220719257.589622887353
Trimmed Mean ( 25 / 44 )7.457317073170730.0286266231427862260.502855540261
Trimmed Mean ( 26 / 44 )7.4558750.0282398709016933264.019443500818
Trimmed Mean ( 27 / 44 )7.454487179487180.0278157245695653267.995434051844
Trimmed Mean ( 28 / 44 )7.453157894736840.0274035536985502271.977787141204
Trimmed Mean ( 29 / 44 )7.451891891891890.0269487945860975276.520416083331
Trimmed Mean ( 30 / 44 )7.450833333333330.0264780225989626281.396894556063
Trimmed Mean ( 31 / 44 )7.450428571428570.0261477215490461284.936052934998
Trimmed Mean ( 32 / 44 )7.449852941176470.0259012210239085287.625549942212
Trimmed Mean ( 33 / 44 )7.449393939393940.0256294909423054290.657116684966
Trimmed Mean ( 34 / 44 )7.448593750.0253554758998943293.766671128861
Trimmed Mean ( 35 / 44 )7.447903225806450.0250511239265381297.308146638341
Trimmed Mean ( 36 / 44 )7.44650.0248018417850813300.239799307130
Trimmed Mean ( 37 / 44 )7.44482758620690.0245137113370344303.700548801011
Trimmed Mean ( 38 / 44 )7.443214285714290.0242700006459489306.683728372982
Trimmed Mean ( 39 / 44 )7.441481481481480.0240317856824928309.651624718949
Trimmed Mean ( 40 / 44 )7.43980769230770.0237643191487041313.066309442886
Trimmed Mean ( 41 / 44 )7.43840.0235144072206547316.333723840005
Trimmed Mean ( 42 / 44 )7.437291666666670.0232846622259452319.407324637056
Trimmed Mean ( 43 / 44 )7.435869565217390.0230092946708898323.168079316437
Trimmed Mean ( 44 / 44 )7.434090909090910.0227852326481578326.267939585509
Median7.38
Midrange7.81
Midmean - Weighted Average at Xnp7.44507246376812
Midmean - Weighted Average at X(n+1)p7.45477611940299
Midmean - Empirical Distribution Function7.44507246376812
Midmean - Empirical Distribution Function - Averaging7.45477611940299
Midmean - Empirical Distribution Function - Interpolation7.45477611940299
Midmean - Closest Observation7.44507246376812
Midmean - True Basic - Statistics Graphics Toolkit7.45477611940299
Midmean - MS Excel (old versions)7.44507246376812
Number of observations132

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 7.51287878787879 & 0.0423582708860616 & 177.365096136419 \tabularnewline
Geometric Mean & 7.49761823705715 &  &  \tabularnewline
Harmonic Mean & 7.48273607809817 &  &  \tabularnewline
Quadratic Mean & 7.52850522408605 &  &  \tabularnewline
Winsorized Mean ( 1 / 44 ) & 7.5130303030303 & 0.0423390721684297 & 177.449101225993 \tabularnewline
Winsorized Mean ( 2 / 44 ) & 7.51287878787879 & 0.0422493192478052 & 177.822481441972 \tabularnewline
Winsorized Mean ( 3 / 44 ) & 7.50810606060606 & 0.0411414924196576 & 182.494742388554 \tabularnewline
Winsorized Mean ( 4 / 44 ) & 7.50719696969697 & 0.0408666402506962 & 183.699881459403 \tabularnewline
Winsorized Mean ( 5 / 44 ) & 7.50378787878788 & 0.0401171558519618 & 187.046856125044 \tabularnewline
Winsorized Mean ( 6 / 44 ) & 7.50378787878788 & 0.0399811328252718 & 187.683223273874 \tabularnewline
Winsorized Mean ( 7 / 44 ) & 7.50378787878788 & 0.0398238851232912 & 188.424305051022 \tabularnewline
Winsorized Mean ( 8 / 44 ) & 7.49833333333333 & 0.0387277678556908 & 193.616460449618 \tabularnewline
Winsorized Mean ( 9 / 44 ) & 7.49833333333333 & 0.0387277678556908 & 193.616460449618 \tabularnewline
Winsorized Mean ( 10 / 44 ) & 7.49757575757576 & 0.0383937742556982 & 195.281029357592 \tabularnewline
Winsorized Mean ( 11 / 44 ) & 7.49757575757576 & 0.0381627753606314 & 196.463063462366 \tabularnewline
Winsorized Mean ( 12 / 44 ) & 7.49666666666667 & 0.0380192353440897 & 197.180890115721 \tabularnewline
Winsorized Mean ( 13 / 44 ) & 7.49568181818182 & 0.0378649170763385 & 197.958490258145 \tabularnewline
Winsorized Mean ( 14 / 44 ) & 7.49462121212121 & 0.0376999496712746 & 198.79658401326 \tabularnewline
Winsorized Mean ( 15 / 44 ) & 7.48893939393939 & 0.0356283047540886 & 210.19634376738 \tabularnewline
Winsorized Mean ( 16 / 44 ) & 7.48045454545455 & 0.0341180245313576 & 219.252276420029 \tabularnewline
Winsorized Mean ( 17 / 44 ) & 7.47659090909091 & 0.0329603518938040 & 226.835894628188 \tabularnewline
Winsorized Mean ( 18 / 44 ) & 7.4725 & 0.0321056071310423 & 232.747506362369 \tabularnewline
Winsorized Mean ( 19 / 44 ) & 7.4710606060606 & 0.0319260396114412 & 234.011505873821 \tabularnewline
Winsorized Mean ( 20 / 44 ) & 7.46954545454546 & 0.0317390294689424 & 235.342591740388 \tabularnewline
Winsorized Mean ( 21 / 44 ) & 7.4775 & 0.0304810257889769 & 245.316547145344 \tabularnewline
Winsorized Mean ( 22 / 44 ) & 7.47916666666667 & 0.0303038131693925 & 246.806123864993 \tabularnewline
Winsorized Mean ( 23 / 44 ) & 7.47916666666667 & 0.0303038131693925 & 246.806123864993 \tabularnewline
Winsorized Mean ( 24 / 44 ) & 7.47916666666667 & 0.0298887678178374 & 250.233355628771 \tabularnewline
Winsorized Mean ( 25 / 44 ) & 7.47916666666667 & 0.0298887678178374 & 250.233355628771 \tabularnewline
Winsorized Mean ( 26 / 44 ) & 7.47719696969697 & 0.0296479291661193 & 252.199636871829 \tabularnewline
Winsorized Mean ( 27 / 44 ) & 7.47515151515152 & 0.0289396391868914 & 258.301475940221 \tabularnewline
Winsorized Mean ( 28 / 44 ) & 7.4730303030303 & 0.0286862347195746 & 260.509278268260 \tabularnewline
Winsorized Mean ( 29 / 44 ) & 7.46863636363636 & 0.0281680568283143 & 265.145601244632 \tabularnewline
Winsorized Mean ( 30 / 44 ) & 7.45727272727273 & 0.0263739042118535 & 282.751945535661 \tabularnewline
Winsorized Mean ( 31 / 44 ) & 7.45962121212121 & 0.0251181352469936 & 296.981489221580 \tabularnewline
Winsorized Mean ( 32 / 44 ) & 7.45719696969697 & 0.0248540301116608 & 300.039749537371 \tabularnewline
Winsorized Mean ( 33 / 44 ) & 7.46219696969697 & 0.0243424547895418 & 306.550717017371 \tabularnewline
Winsorized Mean ( 34 / 44 ) & 7.45962121212121 & 0.0240629151887671 & 310.004883182378 \tabularnewline
Winsorized Mean ( 35 / 44 ) & 7.47022727272727 & 0.0230141077304220 & 324.59339115948 \tabularnewline
Winsorized Mean ( 36 / 44 ) & 7.47295454545455 & 0.0227533767506052 & 328.43276966597 \tabularnewline
Winsorized Mean ( 37 / 44 ) & 7.47015151515152 & 0.0218775176598126 & 341.453341796343 \tabularnewline
Winsorized Mean ( 38 / 44 ) & 7.47015151515151 & 0.0212972705238479 & 350.756286200465 \tabularnewline
Winsorized Mean ( 39 / 44 ) & 7.46719696969697 & 0.0209811152857637 & 355.9008597967 \tabularnewline
Winsorized Mean ( 40 / 44 ) & 7.46113636363636 & 0.0203410795116256 & 366.801396129054 \tabularnewline
Winsorized Mean ( 41 / 44 ) & 7.45492424242424 & 0.0196968395785663 & 378.483269495506 \tabularnewline
Winsorized Mean ( 42 / 44 ) & 7.45810606060606 & 0.0193967346958318 & 384.50317424864 \tabularnewline
Winsorized Mean ( 43 / 44 ) & 7.46136363636364 & 0.0184577004922946 & 404.241234680262 \tabularnewline
Winsorized Mean ( 44 / 44 ) & 7.46469696969697 & 0.0181546417684736 & 411.172914612931 \tabularnewline
Trimmed Mean ( 1 / 44 ) & 7.5083076923077 & 0.041445431281853 & 181.161287507104 \tabularnewline
Trimmed Mean ( 2 / 44 ) & 7.5034375 & 0.0404581959415941 & 185.461494892952 \tabularnewline
Trimmed Mean ( 3 / 44 ) & 7.49849206349206 & 0.0394173545632623 & 190.233265184183 \tabularnewline
Trimmed Mean ( 4 / 44 ) & 7.49508064516129 & 0.038720097464358 & 193.570810405644 \tabularnewline
Trimmed Mean ( 5 / 44 ) & 7.49180327868852 & 0.038036416138059 & 196.963963468479 \tabularnewline
Trimmed Mean ( 6 / 44 ) & 7.48916666666667 & 0.0374783940247463 & 199.826242867336 \tabularnewline
Trimmed Mean ( 7 / 44 ) & 7.4864406779661 & 0.0368904956464198 & 202.936841774113 \tabularnewline
Trimmed Mean ( 8 / 44 ) & 7.48362068965517 & 0.0362695217665091 & 206.333591543671 \tabularnewline
Trimmed Mean ( 9 / 44 ) & 7.48149122807018 & 0.0357847748071415 & 209.069115801089 \tabularnewline
Trimmed Mean ( 10 / 44 ) & 7.47928571428571 & 0.0352443014291986 & 212.212624764621 \tabularnewline
Trimmed Mean ( 11 / 44 ) & 7.47709090909091 & 0.0346949882463871 & 215.509250384874 \tabularnewline
Trimmed Mean ( 12 / 44 ) & 7.47481481481482 & 0.0341158111201888 & 219.101190016597 \tabularnewline
Trimmed Mean ( 13 / 44 ) & 7.47254716981132 & 0.0334884248205071 & 223.138209989363 \tabularnewline
Trimmed Mean ( 14 / 44 ) & 7.47028846153846 & 0.0328066781561688 & 227.706335459440 \tabularnewline
Trimmed Mean ( 15 / 44 ) & 7.46803921568627 & 0.0320632744210933 & 232.915675348907 \tabularnewline
Trimmed Mean ( 16 / 44 ) & 7.4662 & 0.0315100689374753 & 236.946482561337 \tabularnewline
Trimmed Mean ( 17 / 44 ) & 7.465 & 0.0310826626382651 & 240.166040048642 \tabularnewline
Trimmed Mean ( 18 / 44 ) & 7.4640625 & 0.030740345127059 & 242.809977218824 \tabularnewline
Trimmed Mean ( 19 / 44 ) & 7.46340425531915 & 0.0304509511401074 & 245.095932175629 \tabularnewline
Trimmed Mean ( 20 / 44 ) & 7.46282608695652 & 0.0301387641551654 & 247.615530900178 \tabularnewline
Trimmed Mean ( 21 / 44 ) & 7.46233333333333 & 0.0298008579755667 & 250.406660756264 \tabularnewline
Trimmed Mean ( 22 / 44 ) & 7.46125 & 0.0295511584197615 & 252.485871924753 \tabularnewline
Trimmed Mean ( 23 / 44 ) & 7.46 & 0.0292772024408641 & 254.805766195325 \tabularnewline
Trimmed Mean ( 24 / 44 ) & 7.45869047619048 & 0.028955710220719 & 257.589622887353 \tabularnewline
Trimmed Mean ( 25 / 44 ) & 7.45731707317073 & 0.0286266231427862 & 260.502855540261 \tabularnewline
Trimmed Mean ( 26 / 44 ) & 7.455875 & 0.0282398709016933 & 264.019443500818 \tabularnewline
Trimmed Mean ( 27 / 44 ) & 7.45448717948718 & 0.0278157245695653 & 267.995434051844 \tabularnewline
Trimmed Mean ( 28 / 44 ) & 7.45315789473684 & 0.0274035536985502 & 271.977787141204 \tabularnewline
Trimmed Mean ( 29 / 44 ) & 7.45189189189189 & 0.0269487945860975 & 276.520416083331 \tabularnewline
Trimmed Mean ( 30 / 44 ) & 7.45083333333333 & 0.0264780225989626 & 281.396894556063 \tabularnewline
Trimmed Mean ( 31 / 44 ) & 7.45042857142857 & 0.0261477215490461 & 284.936052934998 \tabularnewline
Trimmed Mean ( 32 / 44 ) & 7.44985294117647 & 0.0259012210239085 & 287.625549942212 \tabularnewline
Trimmed Mean ( 33 / 44 ) & 7.44939393939394 & 0.0256294909423054 & 290.657116684966 \tabularnewline
Trimmed Mean ( 34 / 44 ) & 7.44859375 & 0.0253554758998943 & 293.766671128861 \tabularnewline
Trimmed Mean ( 35 / 44 ) & 7.44790322580645 & 0.0250511239265381 & 297.308146638341 \tabularnewline
Trimmed Mean ( 36 / 44 ) & 7.4465 & 0.0248018417850813 & 300.239799307130 \tabularnewline
Trimmed Mean ( 37 / 44 ) & 7.4448275862069 & 0.0245137113370344 & 303.700548801011 \tabularnewline
Trimmed Mean ( 38 / 44 ) & 7.44321428571429 & 0.0242700006459489 & 306.683728372982 \tabularnewline
Trimmed Mean ( 39 / 44 ) & 7.44148148148148 & 0.0240317856824928 & 309.651624718949 \tabularnewline
Trimmed Mean ( 40 / 44 ) & 7.4398076923077 & 0.0237643191487041 & 313.066309442886 \tabularnewline
Trimmed Mean ( 41 / 44 ) & 7.4384 & 0.0235144072206547 & 316.333723840005 \tabularnewline
Trimmed Mean ( 42 / 44 ) & 7.43729166666667 & 0.0232846622259452 & 319.407324637056 \tabularnewline
Trimmed Mean ( 43 / 44 ) & 7.43586956521739 & 0.0230092946708898 & 323.168079316437 \tabularnewline
Trimmed Mean ( 44 / 44 ) & 7.43409090909091 & 0.0227852326481578 & 326.267939585509 \tabularnewline
Median & 7.38 &  &  \tabularnewline
Midrange & 7.81 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 7.44507246376812 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 7.45477611940299 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 7.44507246376812 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 7.45477611940299 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 7.45477611940299 &  &  \tabularnewline
Midmean - Closest Observation & 7.44507246376812 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 7.45477611940299 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 7.44507246376812 &  &  \tabularnewline
Number of observations & 132 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=50222&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]7.51287878787879[/C][C]0.0423582708860616[/C][C]177.365096136419[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]7.49761823705715[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]7.48273607809817[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]7.52850522408605[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 44 )[/C][C]7.5130303030303[/C][C]0.0423390721684297[/C][C]177.449101225993[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 44 )[/C][C]7.51287878787879[/C][C]0.0422493192478052[/C][C]177.822481441972[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 44 )[/C][C]7.50810606060606[/C][C]0.0411414924196576[/C][C]182.494742388554[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 44 )[/C][C]7.50719696969697[/C][C]0.0408666402506962[/C][C]183.699881459403[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 44 )[/C][C]7.50378787878788[/C][C]0.0401171558519618[/C][C]187.046856125044[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 44 )[/C][C]7.50378787878788[/C][C]0.0399811328252718[/C][C]187.683223273874[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 44 )[/C][C]7.50378787878788[/C][C]0.0398238851232912[/C][C]188.424305051022[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 44 )[/C][C]7.49833333333333[/C][C]0.0387277678556908[/C][C]193.616460449618[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 44 )[/C][C]7.49833333333333[/C][C]0.0387277678556908[/C][C]193.616460449618[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 44 )[/C][C]7.49757575757576[/C][C]0.0383937742556982[/C][C]195.281029357592[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 44 )[/C][C]7.49757575757576[/C][C]0.0381627753606314[/C][C]196.463063462366[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 44 )[/C][C]7.49666666666667[/C][C]0.0380192353440897[/C][C]197.180890115721[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 44 )[/C][C]7.49568181818182[/C][C]0.0378649170763385[/C][C]197.958490258145[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 44 )[/C][C]7.49462121212121[/C][C]0.0376999496712746[/C][C]198.79658401326[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 44 )[/C][C]7.48893939393939[/C][C]0.0356283047540886[/C][C]210.19634376738[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 44 )[/C][C]7.48045454545455[/C][C]0.0341180245313576[/C][C]219.252276420029[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 44 )[/C][C]7.47659090909091[/C][C]0.0329603518938040[/C][C]226.835894628188[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 44 )[/C][C]7.4725[/C][C]0.0321056071310423[/C][C]232.747506362369[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 44 )[/C][C]7.4710606060606[/C][C]0.0319260396114412[/C][C]234.011505873821[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 44 )[/C][C]7.46954545454546[/C][C]0.0317390294689424[/C][C]235.342591740388[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 44 )[/C][C]7.4775[/C][C]0.0304810257889769[/C][C]245.316547145344[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 44 )[/C][C]7.47916666666667[/C][C]0.0303038131693925[/C][C]246.806123864993[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 44 )[/C][C]7.47916666666667[/C][C]0.0303038131693925[/C][C]246.806123864993[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 44 )[/C][C]7.47916666666667[/C][C]0.0298887678178374[/C][C]250.233355628771[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 44 )[/C][C]7.47916666666667[/C][C]0.0298887678178374[/C][C]250.233355628771[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 44 )[/C][C]7.47719696969697[/C][C]0.0296479291661193[/C][C]252.199636871829[/C][/ROW]
[ROW][C]Winsorized Mean ( 27 / 44 )[/C][C]7.47515151515152[/C][C]0.0289396391868914[/C][C]258.301475940221[/C][/ROW]
[ROW][C]Winsorized Mean ( 28 / 44 )[/C][C]7.4730303030303[/C][C]0.0286862347195746[/C][C]260.509278268260[/C][/ROW]
[ROW][C]Winsorized Mean ( 29 / 44 )[/C][C]7.46863636363636[/C][C]0.0281680568283143[/C][C]265.145601244632[/C][/ROW]
[ROW][C]Winsorized Mean ( 30 / 44 )[/C][C]7.45727272727273[/C][C]0.0263739042118535[/C][C]282.751945535661[/C][/ROW]
[ROW][C]Winsorized Mean ( 31 / 44 )[/C][C]7.45962121212121[/C][C]0.0251181352469936[/C][C]296.981489221580[/C][/ROW]
[ROW][C]Winsorized Mean ( 32 / 44 )[/C][C]7.45719696969697[/C][C]0.0248540301116608[/C][C]300.039749537371[/C][/ROW]
[ROW][C]Winsorized Mean ( 33 / 44 )[/C][C]7.46219696969697[/C][C]0.0243424547895418[/C][C]306.550717017371[/C][/ROW]
[ROW][C]Winsorized Mean ( 34 / 44 )[/C][C]7.45962121212121[/C][C]0.0240629151887671[/C][C]310.004883182378[/C][/ROW]
[ROW][C]Winsorized Mean ( 35 / 44 )[/C][C]7.47022727272727[/C][C]0.0230141077304220[/C][C]324.59339115948[/C][/ROW]
[ROW][C]Winsorized Mean ( 36 / 44 )[/C][C]7.47295454545455[/C][C]0.0227533767506052[/C][C]328.43276966597[/C][/ROW]
[ROW][C]Winsorized Mean ( 37 / 44 )[/C][C]7.47015151515152[/C][C]0.0218775176598126[/C][C]341.453341796343[/C][/ROW]
[ROW][C]Winsorized Mean ( 38 / 44 )[/C][C]7.47015151515151[/C][C]0.0212972705238479[/C][C]350.756286200465[/C][/ROW]
[ROW][C]Winsorized Mean ( 39 / 44 )[/C][C]7.46719696969697[/C][C]0.0209811152857637[/C][C]355.9008597967[/C][/ROW]
[ROW][C]Winsorized Mean ( 40 / 44 )[/C][C]7.46113636363636[/C][C]0.0203410795116256[/C][C]366.801396129054[/C][/ROW]
[ROW][C]Winsorized Mean ( 41 / 44 )[/C][C]7.45492424242424[/C][C]0.0196968395785663[/C][C]378.483269495506[/C][/ROW]
[ROW][C]Winsorized Mean ( 42 / 44 )[/C][C]7.45810606060606[/C][C]0.0193967346958318[/C][C]384.50317424864[/C][/ROW]
[ROW][C]Winsorized Mean ( 43 / 44 )[/C][C]7.46136363636364[/C][C]0.0184577004922946[/C][C]404.241234680262[/C][/ROW]
[ROW][C]Winsorized Mean ( 44 / 44 )[/C][C]7.46469696969697[/C][C]0.0181546417684736[/C][C]411.172914612931[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 44 )[/C][C]7.5083076923077[/C][C]0.041445431281853[/C][C]181.161287507104[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 44 )[/C][C]7.5034375[/C][C]0.0404581959415941[/C][C]185.461494892952[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 44 )[/C][C]7.49849206349206[/C][C]0.0394173545632623[/C][C]190.233265184183[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 44 )[/C][C]7.49508064516129[/C][C]0.038720097464358[/C][C]193.570810405644[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 44 )[/C][C]7.49180327868852[/C][C]0.038036416138059[/C][C]196.963963468479[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 44 )[/C][C]7.48916666666667[/C][C]0.0374783940247463[/C][C]199.826242867336[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 44 )[/C][C]7.4864406779661[/C][C]0.0368904956464198[/C][C]202.936841774113[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 44 )[/C][C]7.48362068965517[/C][C]0.0362695217665091[/C][C]206.333591543671[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 44 )[/C][C]7.48149122807018[/C][C]0.0357847748071415[/C][C]209.069115801089[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 44 )[/C][C]7.47928571428571[/C][C]0.0352443014291986[/C][C]212.212624764621[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 44 )[/C][C]7.47709090909091[/C][C]0.0346949882463871[/C][C]215.509250384874[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 44 )[/C][C]7.47481481481482[/C][C]0.0341158111201888[/C][C]219.101190016597[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 44 )[/C][C]7.47254716981132[/C][C]0.0334884248205071[/C][C]223.138209989363[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 44 )[/C][C]7.47028846153846[/C][C]0.0328066781561688[/C][C]227.706335459440[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 44 )[/C][C]7.46803921568627[/C][C]0.0320632744210933[/C][C]232.915675348907[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 44 )[/C][C]7.4662[/C][C]0.0315100689374753[/C][C]236.946482561337[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 44 )[/C][C]7.465[/C][C]0.0310826626382651[/C][C]240.166040048642[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 44 )[/C][C]7.4640625[/C][C]0.030740345127059[/C][C]242.809977218824[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 44 )[/C][C]7.46340425531915[/C][C]0.0304509511401074[/C][C]245.095932175629[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 44 )[/C][C]7.46282608695652[/C][C]0.0301387641551654[/C][C]247.615530900178[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 44 )[/C][C]7.46233333333333[/C][C]0.0298008579755667[/C][C]250.406660756264[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 44 )[/C][C]7.46125[/C][C]0.0295511584197615[/C][C]252.485871924753[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 44 )[/C][C]7.46[/C][C]0.0292772024408641[/C][C]254.805766195325[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 44 )[/C][C]7.45869047619048[/C][C]0.028955710220719[/C][C]257.589622887353[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 44 )[/C][C]7.45731707317073[/C][C]0.0286266231427862[/C][C]260.502855540261[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 44 )[/C][C]7.455875[/C][C]0.0282398709016933[/C][C]264.019443500818[/C][/ROW]
[ROW][C]Trimmed Mean ( 27 / 44 )[/C][C]7.45448717948718[/C][C]0.0278157245695653[/C][C]267.995434051844[/C][/ROW]
[ROW][C]Trimmed Mean ( 28 / 44 )[/C][C]7.45315789473684[/C][C]0.0274035536985502[/C][C]271.977787141204[/C][/ROW]
[ROW][C]Trimmed Mean ( 29 / 44 )[/C][C]7.45189189189189[/C][C]0.0269487945860975[/C][C]276.520416083331[/C][/ROW]
[ROW][C]Trimmed Mean ( 30 / 44 )[/C][C]7.45083333333333[/C][C]0.0264780225989626[/C][C]281.396894556063[/C][/ROW]
[ROW][C]Trimmed Mean ( 31 / 44 )[/C][C]7.45042857142857[/C][C]0.0261477215490461[/C][C]284.936052934998[/C][/ROW]
[ROW][C]Trimmed Mean ( 32 / 44 )[/C][C]7.44985294117647[/C][C]0.0259012210239085[/C][C]287.625549942212[/C][/ROW]
[ROW][C]Trimmed Mean ( 33 / 44 )[/C][C]7.44939393939394[/C][C]0.0256294909423054[/C][C]290.657116684966[/C][/ROW]
[ROW][C]Trimmed Mean ( 34 / 44 )[/C][C]7.44859375[/C][C]0.0253554758998943[/C][C]293.766671128861[/C][/ROW]
[ROW][C]Trimmed Mean ( 35 / 44 )[/C][C]7.44790322580645[/C][C]0.0250511239265381[/C][C]297.308146638341[/C][/ROW]
[ROW][C]Trimmed Mean ( 36 / 44 )[/C][C]7.4465[/C][C]0.0248018417850813[/C][C]300.239799307130[/C][/ROW]
[ROW][C]Trimmed Mean ( 37 / 44 )[/C][C]7.4448275862069[/C][C]0.0245137113370344[/C][C]303.700548801011[/C][/ROW]
[ROW][C]Trimmed Mean ( 38 / 44 )[/C][C]7.44321428571429[/C][C]0.0242700006459489[/C][C]306.683728372982[/C][/ROW]
[ROW][C]Trimmed Mean ( 39 / 44 )[/C][C]7.44148148148148[/C][C]0.0240317856824928[/C][C]309.651624718949[/C][/ROW]
[ROW][C]Trimmed Mean ( 40 / 44 )[/C][C]7.4398076923077[/C][C]0.0237643191487041[/C][C]313.066309442886[/C][/ROW]
[ROW][C]Trimmed Mean ( 41 / 44 )[/C][C]7.4384[/C][C]0.0235144072206547[/C][C]316.333723840005[/C][/ROW]
[ROW][C]Trimmed Mean ( 42 / 44 )[/C][C]7.43729166666667[/C][C]0.0232846622259452[/C][C]319.407324637056[/C][/ROW]
[ROW][C]Trimmed Mean ( 43 / 44 )[/C][C]7.43586956521739[/C][C]0.0230092946708898[/C][C]323.168079316437[/C][/ROW]
[ROW][C]Trimmed Mean ( 44 / 44 )[/C][C]7.43409090909091[/C][C]0.0227852326481578[/C][C]326.267939585509[/C][/ROW]
[ROW][C]Median[/C][C]7.38[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]7.81[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]7.44507246376812[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]7.45477611940299[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]7.44507246376812[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]7.45477611940299[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]7.45477611940299[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]7.44507246376812[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]7.45477611940299[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]7.44507246376812[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]132[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=50222&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=50222&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 Mean7.512878787878790.0423582708860616177.365096136419
Geometric Mean7.49761823705715
Harmonic Mean7.48273607809817
Quadratic Mean7.52850522408605
Winsorized Mean ( 1 / 44 )7.51303030303030.0423390721684297177.449101225993
Winsorized Mean ( 2 / 44 )7.512878787878790.0422493192478052177.822481441972
Winsorized Mean ( 3 / 44 )7.508106060606060.0411414924196576182.494742388554
Winsorized Mean ( 4 / 44 )7.507196969696970.0408666402506962183.699881459403
Winsorized Mean ( 5 / 44 )7.503787878787880.0401171558519618187.046856125044
Winsorized Mean ( 6 / 44 )7.503787878787880.0399811328252718187.683223273874
Winsorized Mean ( 7 / 44 )7.503787878787880.0398238851232912188.424305051022
Winsorized Mean ( 8 / 44 )7.498333333333330.0387277678556908193.616460449618
Winsorized Mean ( 9 / 44 )7.498333333333330.0387277678556908193.616460449618
Winsorized Mean ( 10 / 44 )7.497575757575760.0383937742556982195.281029357592
Winsorized Mean ( 11 / 44 )7.497575757575760.0381627753606314196.463063462366
Winsorized Mean ( 12 / 44 )7.496666666666670.0380192353440897197.180890115721
Winsorized Mean ( 13 / 44 )7.495681818181820.0378649170763385197.958490258145
Winsorized Mean ( 14 / 44 )7.494621212121210.0376999496712746198.79658401326
Winsorized Mean ( 15 / 44 )7.488939393939390.0356283047540886210.19634376738
Winsorized Mean ( 16 / 44 )7.480454545454550.0341180245313576219.252276420029
Winsorized Mean ( 17 / 44 )7.476590909090910.0329603518938040226.835894628188
Winsorized Mean ( 18 / 44 )7.47250.0321056071310423232.747506362369
Winsorized Mean ( 19 / 44 )7.47106060606060.0319260396114412234.011505873821
Winsorized Mean ( 20 / 44 )7.469545454545460.0317390294689424235.342591740388
Winsorized Mean ( 21 / 44 )7.47750.0304810257889769245.316547145344
Winsorized Mean ( 22 / 44 )7.479166666666670.0303038131693925246.806123864993
Winsorized Mean ( 23 / 44 )7.479166666666670.0303038131693925246.806123864993
Winsorized Mean ( 24 / 44 )7.479166666666670.0298887678178374250.233355628771
Winsorized Mean ( 25 / 44 )7.479166666666670.0298887678178374250.233355628771
Winsorized Mean ( 26 / 44 )7.477196969696970.0296479291661193252.199636871829
Winsorized Mean ( 27 / 44 )7.475151515151520.0289396391868914258.301475940221
Winsorized Mean ( 28 / 44 )7.47303030303030.0286862347195746260.509278268260
Winsorized Mean ( 29 / 44 )7.468636363636360.0281680568283143265.145601244632
Winsorized Mean ( 30 / 44 )7.457272727272730.0263739042118535282.751945535661
Winsorized Mean ( 31 / 44 )7.459621212121210.0251181352469936296.981489221580
Winsorized Mean ( 32 / 44 )7.457196969696970.0248540301116608300.039749537371
Winsorized Mean ( 33 / 44 )7.462196969696970.0243424547895418306.550717017371
Winsorized Mean ( 34 / 44 )7.459621212121210.0240629151887671310.004883182378
Winsorized Mean ( 35 / 44 )7.470227272727270.0230141077304220324.59339115948
Winsorized Mean ( 36 / 44 )7.472954545454550.0227533767506052328.43276966597
Winsorized Mean ( 37 / 44 )7.470151515151520.0218775176598126341.453341796343
Winsorized Mean ( 38 / 44 )7.470151515151510.0212972705238479350.756286200465
Winsorized Mean ( 39 / 44 )7.467196969696970.0209811152857637355.9008597967
Winsorized Mean ( 40 / 44 )7.461136363636360.0203410795116256366.801396129054
Winsorized Mean ( 41 / 44 )7.454924242424240.0196968395785663378.483269495506
Winsorized Mean ( 42 / 44 )7.458106060606060.0193967346958318384.50317424864
Winsorized Mean ( 43 / 44 )7.461363636363640.0184577004922946404.241234680262
Winsorized Mean ( 44 / 44 )7.464696969696970.0181546417684736411.172914612931
Trimmed Mean ( 1 / 44 )7.50830769230770.041445431281853181.161287507104
Trimmed Mean ( 2 / 44 )7.50343750.0404581959415941185.461494892952
Trimmed Mean ( 3 / 44 )7.498492063492060.0394173545632623190.233265184183
Trimmed Mean ( 4 / 44 )7.495080645161290.038720097464358193.570810405644
Trimmed Mean ( 5 / 44 )7.491803278688520.038036416138059196.963963468479
Trimmed Mean ( 6 / 44 )7.489166666666670.0374783940247463199.826242867336
Trimmed Mean ( 7 / 44 )7.48644067796610.0368904956464198202.936841774113
Trimmed Mean ( 8 / 44 )7.483620689655170.0362695217665091206.333591543671
Trimmed Mean ( 9 / 44 )7.481491228070180.0357847748071415209.069115801089
Trimmed Mean ( 10 / 44 )7.479285714285710.0352443014291986212.212624764621
Trimmed Mean ( 11 / 44 )7.477090909090910.0346949882463871215.509250384874
Trimmed Mean ( 12 / 44 )7.474814814814820.0341158111201888219.101190016597
Trimmed Mean ( 13 / 44 )7.472547169811320.0334884248205071223.138209989363
Trimmed Mean ( 14 / 44 )7.470288461538460.0328066781561688227.706335459440
Trimmed Mean ( 15 / 44 )7.468039215686270.0320632744210933232.915675348907
Trimmed Mean ( 16 / 44 )7.46620.0315100689374753236.946482561337
Trimmed Mean ( 17 / 44 )7.4650.0310826626382651240.166040048642
Trimmed Mean ( 18 / 44 )7.46406250.030740345127059242.809977218824
Trimmed Mean ( 19 / 44 )7.463404255319150.0304509511401074245.095932175629
Trimmed Mean ( 20 / 44 )7.462826086956520.0301387641551654247.615530900178
Trimmed Mean ( 21 / 44 )7.462333333333330.0298008579755667250.406660756264
Trimmed Mean ( 22 / 44 )7.461250.0295511584197615252.485871924753
Trimmed Mean ( 23 / 44 )7.460.0292772024408641254.805766195325
Trimmed Mean ( 24 / 44 )7.458690476190480.028955710220719257.589622887353
Trimmed Mean ( 25 / 44 )7.457317073170730.0286266231427862260.502855540261
Trimmed Mean ( 26 / 44 )7.4558750.0282398709016933264.019443500818
Trimmed Mean ( 27 / 44 )7.454487179487180.0278157245695653267.995434051844
Trimmed Mean ( 28 / 44 )7.453157894736840.0274035536985502271.977787141204
Trimmed Mean ( 29 / 44 )7.451891891891890.0269487945860975276.520416083331
Trimmed Mean ( 30 / 44 )7.450833333333330.0264780225989626281.396894556063
Trimmed Mean ( 31 / 44 )7.450428571428570.0261477215490461284.936052934998
Trimmed Mean ( 32 / 44 )7.449852941176470.0259012210239085287.625549942212
Trimmed Mean ( 33 / 44 )7.449393939393940.0256294909423054290.657116684966
Trimmed Mean ( 34 / 44 )7.448593750.0253554758998943293.766671128861
Trimmed Mean ( 35 / 44 )7.447903225806450.0250511239265381297.308146638341
Trimmed Mean ( 36 / 44 )7.44650.0248018417850813300.239799307130
Trimmed Mean ( 37 / 44 )7.44482758620690.0245137113370344303.700548801011
Trimmed Mean ( 38 / 44 )7.443214285714290.0242700006459489306.683728372982
Trimmed Mean ( 39 / 44 )7.441481481481480.0240317856824928309.651624718949
Trimmed Mean ( 40 / 44 )7.43980769230770.0237643191487041313.066309442886
Trimmed Mean ( 41 / 44 )7.43840.0235144072206547316.333723840005
Trimmed Mean ( 42 / 44 )7.437291666666670.0232846622259452319.407324637056
Trimmed Mean ( 43 / 44 )7.435869565217390.0230092946708898323.168079316437
Trimmed Mean ( 44 / 44 )7.434090909090910.0227852326481578326.267939585509
Median7.38
Midrange7.81
Midmean - Weighted Average at Xnp7.44507246376812
Midmean - Weighted Average at X(n+1)p7.45477611940299
Midmean - Empirical Distribution Function7.44507246376812
Midmean - Empirical Distribution Function - Averaging7.45477611940299
Midmean - Empirical Distribution Function - Interpolation7.45477611940299
Midmean - Closest Observation7.44507246376812
Midmean - True Basic - Statistics Graphics Toolkit7.45477611940299
Midmean - MS Excel (old versions)7.44507246376812
Number of observations132



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')