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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 08 Oct 2012 03:51:15 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Oct/08/t13496827299ay4dgqeeg23wac.htm/, Retrieved Thu, 02 May 2024 07:12:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=173257, Retrieved Thu, 02 May 2024 07:12:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact54
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Prijs eau de toil...] [2012-10-08 07:51:15] [38988f759262636e31810af7a466e7c0] [Current]
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Dataseries X:
52,21
52,53
53,06
53,23
53,25
53,27
53,35
53,6
53,98
54,18
54,27
54,32
54,4
54,73
54,96
55,27
55,27
55,26
55,37
55,53
55,55
55,54
55,6
55,56
55,64
56,13
56,69
56,8
56,93
57
57,01
57,21
57,17
57,36
57,29
57,26
57,29
57,68
58,19
58,34
58,46
58,67
58,72
58,74
58,77
58,84
59,13
59,12
59,12
59,33
59,49
59,67
59,7
59,73
59,74
59,62
59,6
59,98
60,05
60,06
60,1
60,18
60,38
60,52
60,78
60,72
60,72
60,86
60,99
61,11
61,17
61,19




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173257&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173257&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173257&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'Gwilym Jenkins' @ jenkins.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean57.41027777777780.303678089965037189.049785529103
Geometric Mean57.3527106522953
Harmonic Mean57.29463715
Quadratic Mean57.4672745279143
Winsorized Mean ( 1 / 24 )57.41444444444440.302588202126381189.744491163156
Winsorized Mean ( 2 / 24 )57.42750.299109643172028191.99481297556
Winsorized Mean ( 3 / 24 )57.42958333333330.296819502060763193.483187373506
Winsorized Mean ( 4 / 24 )57.42347222222220.295396418068329194.394612493031
Winsorized Mean ( 5 / 24 )57.41930555555560.294218237269506195.158893236652
Winsorized Mean ( 6 / 24 )57.42097222222220.292101899259398196.578565109671
Winsorized Mean ( 7 / 24 )57.44527777777780.287425704642861199.861309722302
Winsorized Mean ( 8 / 24 )57.46527777777780.276175958589069208.074873972945
Winsorized Mean ( 9 / 24 )57.47277777777780.269104120134722213.570783490811
Winsorized Mean ( 10 / 24 )57.45750.262818533913398218.62042659036
Winsorized Mean ( 11 / 24 )57.45291666666670.259748391369896221.186804521343
Winsorized Mean ( 12 / 24 )57.45958333333330.256541600946965223.977643864521
Winsorized Mean ( 13 / 24 )57.51736111111110.246528478695911233.309195819351
Winsorized Mean ( 14 / 24 )57.54847222222220.23756776973329242.240234383773
Winsorized Mean ( 15 / 24 )57.56097222222220.221105148486185260.333025333504
Winsorized Mean ( 16 / 24 )57.56097222222220.22047148223869261.081259298219
Winsorized Mean ( 17 / 24 )57.55388888888890.219492991995274262.212876892799
Winsorized Mean ( 18 / 24 )57.57138888888890.214824263582151267.992953537453
Winsorized Mean ( 19 / 24 )57.60041666666670.206987430679525278.27977997296
Winsorized Mean ( 20 / 24 )57.59763888888890.205833879136297279.825843688004
Winsorized Mean ( 21 / 24 )57.56847222222220.201064718724825286.318119794104
Winsorized Mean ( 22 / 24 )57.52263888888890.194134146973048296.303560119565
Winsorized Mean ( 23 / 24 )57.47152777777780.184063384218868312.237700190489
Winsorized Mean ( 24 / 24 )57.48152777777780.181734025041204316.294803709681
Trimmed Mean ( 1 / 24 )57.43057142857140.298398963532792192.462368999684
Trimmed Mean ( 2 / 24 )57.44764705882350.293346552855667195.835425709226
Trimmed Mean ( 3 / 24 )57.45863636363640.289433808381471198.520817885609
Trimmed Mean ( 4 / 24 )57.469531250.28566186284713201.180271938345
Trimmed Mean ( 5 / 24 )57.48290322580650.28150802514847204.196321563086
Trimmed Mean ( 6 / 24 )57.49816666666670.276723106182501207.782311567239
Trimmed Mean ( 7 / 24 )57.51413793103450.271379041302461211.93286576222
Trimmed Mean ( 8 / 24 )57.52678571428570.265963466286042216.295818811505
Trimmed Mean ( 9 / 24 )57.5370370370370.261909831015912219.682616776388
Trimmed Mean ( 10 / 24 )57.54692307692310.258320591102309222.773271117715
Trimmed Mean ( 11 / 24 )57.55980.254980669935618225.741818054419
Trimmed Mean ( 12 / 24 )57.5743750.251174529304027229.22059477739
Trimmed Mean ( 13 / 24 )57.5893478260870.246778940796552233.364109758314
Trimmed Mean ( 14 / 24 )57.59840909090910.243117078082934236.916343126091
Trimmed Mean ( 15 / 24 )57.60452380952380.240007791777542240.011057069832
Trimmed Mean ( 16 / 24 )57.609750.239035853844307241.008823879297
Trimmed Mean ( 17 / 24 )57.61552631578950.237286011216977242.810463289828
Trimmed Mean ( 18 / 24 )57.62277777777780.234547727945302245.67612861812
Trimmed Mean ( 19 / 24 )57.62882352941180.23134219112602249.106413529296
Trimmed Mean ( 20 / 24 )57.63218750.228243527261772252.503053170493
Trimmed Mean ( 21 / 24 )57.63633333333330.223422430332048257.970219228547
Trimmed Mean ( 22 / 24 )57.64464285714290.217116433142308265.501058684765
Trimmed Mean ( 23 / 24 )57.660.209193322440861275.630212892194
Trimmed Mean ( 24 / 24 )57.68458333333330.19975617308002288.774972226894
Median57.325
Midrange56.7
Midmean - Weighted Average at Xnp57.498947368421
Midmean - Weighted Average at X(n+1)p57.6227777777778
Midmean - Empirical Distribution Function57.498947368421
Midmean - Empirical Distribution Function - Averaging57.6227777777778
Midmean - Empirical Distribution Function - Interpolation57.6227777777778
Midmean - Closest Observation57.498947368421
Midmean - True Basic - Statistics Graphics Toolkit57.6227777777778
Midmean - MS Excel (old versions)57.5553846153846
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 57.4102777777778 & 0.303678089965037 & 189.049785529103 \tabularnewline
Geometric Mean & 57.3527106522953 &  &  \tabularnewline
Harmonic Mean & 57.29463715 &  &  \tabularnewline
Quadratic Mean & 57.4672745279143 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 57.4144444444444 & 0.302588202126381 & 189.744491163156 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 57.4275 & 0.299109643172028 & 191.99481297556 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 57.4295833333333 & 0.296819502060763 & 193.483187373506 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 57.4234722222222 & 0.295396418068329 & 194.394612493031 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 57.4193055555556 & 0.294218237269506 & 195.158893236652 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 57.4209722222222 & 0.292101899259398 & 196.578565109671 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 57.4452777777778 & 0.287425704642861 & 199.861309722302 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 57.4652777777778 & 0.276175958589069 & 208.074873972945 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 57.4727777777778 & 0.269104120134722 & 213.570783490811 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 57.4575 & 0.262818533913398 & 218.62042659036 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 57.4529166666667 & 0.259748391369896 & 221.186804521343 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 57.4595833333333 & 0.256541600946965 & 223.977643864521 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 57.5173611111111 & 0.246528478695911 & 233.309195819351 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 57.5484722222222 & 0.23756776973329 & 242.240234383773 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 57.5609722222222 & 0.221105148486185 & 260.333025333504 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 57.5609722222222 & 0.22047148223869 & 261.081259298219 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 57.5538888888889 & 0.219492991995274 & 262.212876892799 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 57.5713888888889 & 0.214824263582151 & 267.992953537453 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 57.6004166666667 & 0.206987430679525 & 278.27977997296 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 57.5976388888889 & 0.205833879136297 & 279.825843688004 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 57.5684722222222 & 0.201064718724825 & 286.318119794104 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 57.5226388888889 & 0.194134146973048 & 296.303560119565 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 57.4715277777778 & 0.184063384218868 & 312.237700190489 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 57.4815277777778 & 0.181734025041204 & 316.294803709681 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 57.4305714285714 & 0.298398963532792 & 192.462368999684 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 57.4476470588235 & 0.293346552855667 & 195.835425709226 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 57.4586363636364 & 0.289433808381471 & 198.520817885609 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 57.46953125 & 0.28566186284713 & 201.180271938345 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 57.4829032258065 & 0.28150802514847 & 204.196321563086 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 57.4981666666667 & 0.276723106182501 & 207.782311567239 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 57.5141379310345 & 0.271379041302461 & 211.93286576222 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 57.5267857142857 & 0.265963466286042 & 216.295818811505 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 57.537037037037 & 0.261909831015912 & 219.682616776388 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 57.5469230769231 & 0.258320591102309 & 222.773271117715 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 57.5598 & 0.254980669935618 & 225.741818054419 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 57.574375 & 0.251174529304027 & 229.22059477739 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 57.589347826087 & 0.246778940796552 & 233.364109758314 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 57.5984090909091 & 0.243117078082934 & 236.916343126091 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 57.6045238095238 & 0.240007791777542 & 240.011057069832 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 57.60975 & 0.239035853844307 & 241.008823879297 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 57.6155263157895 & 0.237286011216977 & 242.810463289828 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 57.6227777777778 & 0.234547727945302 & 245.67612861812 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 57.6288235294118 & 0.23134219112602 & 249.106413529296 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 57.6321875 & 0.228243527261772 & 252.503053170493 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 57.6363333333333 & 0.223422430332048 & 257.970219228547 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 57.6446428571429 & 0.217116433142308 & 265.501058684765 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 57.66 & 0.209193322440861 & 275.630212892194 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 57.6845833333333 & 0.19975617308002 & 288.774972226894 \tabularnewline
Median & 57.325 &  &  \tabularnewline
Midrange & 56.7 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 57.498947368421 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 57.6227777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 57.498947368421 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 57.6227777777778 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 57.6227777777778 &  &  \tabularnewline
Midmean - Closest Observation & 57.498947368421 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 57.6227777777778 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 57.5553846153846 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=173257&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]57.4102777777778[/C][C]0.303678089965037[/C][C]189.049785529103[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]57.3527106522953[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]57.29463715[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]57.4672745279143[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]57.4144444444444[/C][C]0.302588202126381[/C][C]189.744491163156[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]57.4275[/C][C]0.299109643172028[/C][C]191.99481297556[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]57.4295833333333[/C][C]0.296819502060763[/C][C]193.483187373506[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]57.4234722222222[/C][C]0.295396418068329[/C][C]194.394612493031[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]57.4193055555556[/C][C]0.294218237269506[/C][C]195.158893236652[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]57.4209722222222[/C][C]0.292101899259398[/C][C]196.578565109671[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]57.4452777777778[/C][C]0.287425704642861[/C][C]199.861309722302[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]57.4652777777778[/C][C]0.276175958589069[/C][C]208.074873972945[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]57.4727777777778[/C][C]0.269104120134722[/C][C]213.570783490811[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]57.4575[/C][C]0.262818533913398[/C][C]218.62042659036[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]57.4529166666667[/C][C]0.259748391369896[/C][C]221.186804521343[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]57.4595833333333[/C][C]0.256541600946965[/C][C]223.977643864521[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]57.5173611111111[/C][C]0.246528478695911[/C][C]233.309195819351[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]57.5484722222222[/C][C]0.23756776973329[/C][C]242.240234383773[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]57.5609722222222[/C][C]0.221105148486185[/C][C]260.333025333504[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]57.5609722222222[/C][C]0.22047148223869[/C][C]261.081259298219[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]57.5538888888889[/C][C]0.219492991995274[/C][C]262.212876892799[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]57.5713888888889[/C][C]0.214824263582151[/C][C]267.992953537453[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]57.6004166666667[/C][C]0.206987430679525[/C][C]278.27977997296[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]57.5976388888889[/C][C]0.205833879136297[/C][C]279.825843688004[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]57.5684722222222[/C][C]0.201064718724825[/C][C]286.318119794104[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]57.5226388888889[/C][C]0.194134146973048[/C][C]296.303560119565[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]57.4715277777778[/C][C]0.184063384218868[/C][C]312.237700190489[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]57.4815277777778[/C][C]0.181734025041204[/C][C]316.294803709681[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]57.4305714285714[/C][C]0.298398963532792[/C][C]192.462368999684[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]57.4476470588235[/C][C]0.293346552855667[/C][C]195.835425709226[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]57.4586363636364[/C][C]0.289433808381471[/C][C]198.520817885609[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]57.46953125[/C][C]0.28566186284713[/C][C]201.180271938345[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]57.4829032258065[/C][C]0.28150802514847[/C][C]204.196321563086[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]57.4981666666667[/C][C]0.276723106182501[/C][C]207.782311567239[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]57.5141379310345[/C][C]0.271379041302461[/C][C]211.93286576222[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]57.5267857142857[/C][C]0.265963466286042[/C][C]216.295818811505[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]57.537037037037[/C][C]0.261909831015912[/C][C]219.682616776388[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]57.5469230769231[/C][C]0.258320591102309[/C][C]222.773271117715[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]57.5598[/C][C]0.254980669935618[/C][C]225.741818054419[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]57.574375[/C][C]0.251174529304027[/C][C]229.22059477739[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]57.589347826087[/C][C]0.246778940796552[/C][C]233.364109758314[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]57.5984090909091[/C][C]0.243117078082934[/C][C]236.916343126091[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]57.6045238095238[/C][C]0.240007791777542[/C][C]240.011057069832[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]57.60975[/C][C]0.239035853844307[/C][C]241.008823879297[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]57.6155263157895[/C][C]0.237286011216977[/C][C]242.810463289828[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]57.6227777777778[/C][C]0.234547727945302[/C][C]245.67612861812[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]57.6288235294118[/C][C]0.23134219112602[/C][C]249.106413529296[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]57.6321875[/C][C]0.228243527261772[/C][C]252.503053170493[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]57.6363333333333[/C][C]0.223422430332048[/C][C]257.970219228547[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]57.6446428571429[/C][C]0.217116433142308[/C][C]265.501058684765[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]57.66[/C][C]0.209193322440861[/C][C]275.630212892194[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]57.6845833333333[/C][C]0.19975617308002[/C][C]288.774972226894[/C][/ROW]
[ROW][C]Median[/C][C]57.325[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]56.7[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]57.498947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]57.6227777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]57.498947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]57.6227777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]57.6227777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]57.498947368421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]57.6227777777778[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]57.5553846153846[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=173257&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=173257&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 Mean57.41027777777780.303678089965037189.049785529103
Geometric Mean57.3527106522953
Harmonic Mean57.29463715
Quadratic Mean57.4672745279143
Winsorized Mean ( 1 / 24 )57.41444444444440.302588202126381189.744491163156
Winsorized Mean ( 2 / 24 )57.42750.299109643172028191.99481297556
Winsorized Mean ( 3 / 24 )57.42958333333330.296819502060763193.483187373506
Winsorized Mean ( 4 / 24 )57.42347222222220.295396418068329194.394612493031
Winsorized Mean ( 5 / 24 )57.41930555555560.294218237269506195.158893236652
Winsorized Mean ( 6 / 24 )57.42097222222220.292101899259398196.578565109671
Winsorized Mean ( 7 / 24 )57.44527777777780.287425704642861199.861309722302
Winsorized Mean ( 8 / 24 )57.46527777777780.276175958589069208.074873972945
Winsorized Mean ( 9 / 24 )57.47277777777780.269104120134722213.570783490811
Winsorized Mean ( 10 / 24 )57.45750.262818533913398218.62042659036
Winsorized Mean ( 11 / 24 )57.45291666666670.259748391369896221.186804521343
Winsorized Mean ( 12 / 24 )57.45958333333330.256541600946965223.977643864521
Winsorized Mean ( 13 / 24 )57.51736111111110.246528478695911233.309195819351
Winsorized Mean ( 14 / 24 )57.54847222222220.23756776973329242.240234383773
Winsorized Mean ( 15 / 24 )57.56097222222220.221105148486185260.333025333504
Winsorized Mean ( 16 / 24 )57.56097222222220.22047148223869261.081259298219
Winsorized Mean ( 17 / 24 )57.55388888888890.219492991995274262.212876892799
Winsorized Mean ( 18 / 24 )57.57138888888890.214824263582151267.992953537453
Winsorized Mean ( 19 / 24 )57.60041666666670.206987430679525278.27977997296
Winsorized Mean ( 20 / 24 )57.59763888888890.205833879136297279.825843688004
Winsorized Mean ( 21 / 24 )57.56847222222220.201064718724825286.318119794104
Winsorized Mean ( 22 / 24 )57.52263888888890.194134146973048296.303560119565
Winsorized Mean ( 23 / 24 )57.47152777777780.184063384218868312.237700190489
Winsorized Mean ( 24 / 24 )57.48152777777780.181734025041204316.294803709681
Trimmed Mean ( 1 / 24 )57.43057142857140.298398963532792192.462368999684
Trimmed Mean ( 2 / 24 )57.44764705882350.293346552855667195.835425709226
Trimmed Mean ( 3 / 24 )57.45863636363640.289433808381471198.520817885609
Trimmed Mean ( 4 / 24 )57.469531250.28566186284713201.180271938345
Trimmed Mean ( 5 / 24 )57.48290322580650.28150802514847204.196321563086
Trimmed Mean ( 6 / 24 )57.49816666666670.276723106182501207.782311567239
Trimmed Mean ( 7 / 24 )57.51413793103450.271379041302461211.93286576222
Trimmed Mean ( 8 / 24 )57.52678571428570.265963466286042216.295818811505
Trimmed Mean ( 9 / 24 )57.5370370370370.261909831015912219.682616776388
Trimmed Mean ( 10 / 24 )57.54692307692310.258320591102309222.773271117715
Trimmed Mean ( 11 / 24 )57.55980.254980669935618225.741818054419
Trimmed Mean ( 12 / 24 )57.5743750.251174529304027229.22059477739
Trimmed Mean ( 13 / 24 )57.5893478260870.246778940796552233.364109758314
Trimmed Mean ( 14 / 24 )57.59840909090910.243117078082934236.916343126091
Trimmed Mean ( 15 / 24 )57.60452380952380.240007791777542240.011057069832
Trimmed Mean ( 16 / 24 )57.609750.239035853844307241.008823879297
Trimmed Mean ( 17 / 24 )57.61552631578950.237286011216977242.810463289828
Trimmed Mean ( 18 / 24 )57.62277777777780.234547727945302245.67612861812
Trimmed Mean ( 19 / 24 )57.62882352941180.23134219112602249.106413529296
Trimmed Mean ( 20 / 24 )57.63218750.228243527261772252.503053170493
Trimmed Mean ( 21 / 24 )57.63633333333330.223422430332048257.970219228547
Trimmed Mean ( 22 / 24 )57.64464285714290.217116433142308265.501058684765
Trimmed Mean ( 23 / 24 )57.660.209193322440861275.630212892194
Trimmed Mean ( 24 / 24 )57.68458333333330.19975617308002288.774972226894
Median57.325
Midrange56.7
Midmean - Weighted Average at Xnp57.498947368421
Midmean - Weighted Average at X(n+1)p57.6227777777778
Midmean - Empirical Distribution Function57.498947368421
Midmean - Empirical Distribution Function - Averaging57.6227777777778
Midmean - Empirical Distribution Function - Interpolation57.6227777777778
Midmean - Closest Observation57.498947368421
Midmean - True Basic - Statistics Graphics Toolkit57.6227777777778
Midmean - MS Excel (old versions)57.5553846153846
Number of observations72



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')