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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 computationSun, 17 Oct 2010 10:44:05 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Oct/17/t1287312190gzz190wc7z4zfam.htm/, Retrieved Fri, 03 May 2024 18:45:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=84015, Retrieved Fri, 03 May 2024 18:45:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [] [Opdracht 5 oefeni...] [1970-01-01 00:00:00] [fce79e8682e68cbd9028e3d984a957c2]
- RM D    [Central Tendency] [Opdracht 5 oefeni...] [2010-10-17 10:44:05] [93b6d34f85f9cfe38e2fbbaaab7aeb02] [Current]
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Dataseries X:
0,74
0,73
0,76
0,8
0,83
0,81
0,83
0,88
0,89
0,93
0,91
0,9
0,86
0,88
0,93
0,98
0,97
1,03
1,06
1,06
1,08
1,09
1,04
1
1,01
1,02
1,04
1,06
1,06
1,06
1,06
1,06
1,02
0,98
0,99
0,99
0,94
0,96
0,98
1,01
1,01
1,02
1,04
1,03
1,05
1,08
1,17
1,11
1,11
1,11
1,2
1,21
1,31
1,37
1,37
1,26
1,23
1,17
1,06
0,95
0,92
0,92
0,9
0,93
0,93
0,97
0,96
0,99
0,98
0,96
1
0,99
1,03
1,02
1,07
1,13
1,15
1,16




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=84015&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=84015&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=84015&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.014102564102560.014439737666960570.2299853011128
Geometric Mean1.00626132334733
Harmonic Mean0.998430026892108
Quadratic Mean1.02198775646236
Winsorized Mean ( 1 / 26 )1.014230769230770.014407511858784470.3959697671449
Winsorized Mean ( 2 / 26 )1.013205128205130.013821194867445073.3080705338776
Winsorized Mean ( 3 / 26 )1.012820512820510.012966435622168478.1109429247402
Winsorized Mean ( 4 / 26 )1.011794871794870.012492746599814680.9905863142928
Winsorized Mean ( 5 / 26 )1.011794871794870.01194774892133184.6849794431533
Winsorized Mean ( 6 / 26 )1.011025641025640.011784768870975685.790875671365
Winsorized Mean ( 7 / 26 )1.011025641025640.010728679022418994.2357991056471
Winsorized Mean ( 8 / 26 )1.013076923076920.010369959194225497.6934338990518
Winsorized Mean ( 9 / 26 )1.011923076923080.010147197845684899.724386211057
Winsorized Mean ( 10 / 26 )1.011923076923080.0096940505016459104.385991877314
Winsorized Mean ( 11 / 26 )1.010512820512820.00896007616587881112.779490018287
Winsorized Mean ( 12 / 26 )1.007435897435900.00845043116026645119.217100089853
Winsorized Mean ( 13 / 26 )1.009102564102560.00818164148101545123.337421524039
Winsorized Mean ( 14 / 26 )1.010897435897440.00790634889787747127.858945886997
Winsorized Mean ( 15 / 26 )1.007051282051280.00730868539910127137.788292566966
Winsorized Mean ( 16 / 26 )1.007051282051280.0067001547547969150.302689849110
Winsorized Mean ( 17 / 26 )1.007051282051280.0067001547547969150.302689849110
Winsorized Mean ( 18 / 26 )1.004743589743590.0063835775160883157.395063694515
Winsorized Mean ( 19 / 26 )1.002307692307690.00607129107539029165.089711539363
Winsorized Mean ( 20 / 26 )1.004871794871790.00568264848736533176.831594828715
Winsorized Mean ( 21 / 26 )1.007564102564100.00529259089635065190.372564646710
Winsorized Mean ( 22 / 26 )1.010384615384620.00490482954887392205.997905802167
Winsorized Mean ( 23 / 26 )1.010384615384620.00490482954887392205.997905802167
Winsorized Mean ( 24 / 26 )1.010384615384620.00490482954887392205.997905802167
Winsorized Mean ( 25 / 26 )1.013589743589740.00448839239589327225.824672663902
Winsorized Mean ( 26 / 26 )1.013589743589740.00448839239589327225.824672663902
Trimmed Mean ( 1 / 26 )1.013157894736840.013539041048106374.8323231414199
Trimmed Mean ( 2 / 26 )1.012027027027030.012490618070778981.0229743069808
Trimmed Mean ( 3 / 26 )1.011388888888890.011621821179387087.0249914602659
Trimmed Mean ( 4 / 26 )1.010857142857140.010995468400551791.9339773471065
Trimmed Mean ( 5 / 26 )1.010588235294120.010429499832998496.897094920762
Trimmed Mean ( 6 / 26 )1.010303030303030.00993209977393165101.720990857817
Trimmed Mean ( 7 / 26 )1.010156250.00937927729806133107.700862006585
Trimmed Mean ( 8 / 26 )1.010.00900378908427672112.174995498702
Trimmed Mean ( 9 / 26 )1.00950.00863714550565612116.878892376992
Trimmed Mean ( 10 / 26 )1.009137931034480.0082434394628562122.417097327095
Trimmed Mean ( 11 / 26 )1.008750.00786684023764785128.228102964706
Trimmed Mean ( 12 / 26 )1.008518518518520.00757172739365253133.195302219144
Trimmed Mean ( 13 / 26 )1.008653846153850.00731755902930403137.840206292095
Trimmed Mean ( 14 / 26 )1.00860.00705668014677423142.928399618772
Trimmed Mean ( 15 / 26 )1.008333333333330.0067852921179044148.605736615618
Trimmed Mean ( 16 / 26 )1.008478260869570.00657154891927982153.461272716218
Trimmed Mean ( 17 / 26 )1.008636363636360.00642562678716392156.970891252392
Trimmed Mean ( 18 / 26 )1.008809523809520.00623021729507331161.922044774789
Trimmed Mean ( 19 / 26 )1.009250.0060382063477026167.144006329627
Trimmed Mean ( 20 / 26 )1.010.00584289333810359172.859564868903
Trimmed Mean ( 21 / 26 )1.010555555555560.00567568532250253178.049961922480
Trimmed Mean ( 22 / 26 )1.010882352941180.00554302000510317182.370323760425
Trimmed Mean ( 23 / 26 )1.01093750.00545064688007675185.471105034375
Trimmed Mean ( 24 / 26 )1.0110.00530343631823832190.631119020551
Trimmed Mean ( 25 / 26 )1.011071428571430.00507455749665408199.243269829553
Trimmed Mean ( 26 / 26 )1.010769230769230.0048650425541052207.761642273062
Median1.01
Midrange1.05
Midmean - Weighted Average at Xnp1.00372093023256
Midmean - Weighted Average at X(n+1)p1.00372093023256
Midmean - Empirical Distribution Function1.00372093023256
Midmean - Empirical Distribution Function - Averaging1.00372093023256
Midmean - Empirical Distribution Function - Interpolation1.01128205128205
Midmean - Closest Observation1.00372093023256
Midmean - True Basic - Statistics Graphics Toolkit1.00372093023256
Midmean - MS Excel (old versions)1.00372093023256
Number of observations78

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.01410256410256 & 0.0144397376669605 & 70.2299853011128 \tabularnewline
Geometric Mean & 1.00626132334733 &  &  \tabularnewline
Harmonic Mean & 0.998430026892108 &  &  \tabularnewline
Quadratic Mean & 1.02198775646236 &  &  \tabularnewline
Winsorized Mean ( 1 / 26 ) & 1.01423076923077 & 0.0144075118587844 & 70.3959697671449 \tabularnewline
Winsorized Mean ( 2 / 26 ) & 1.01320512820513 & 0.0138211948674450 & 73.3080705338776 \tabularnewline
Winsorized Mean ( 3 / 26 ) & 1.01282051282051 & 0.0129664356221684 & 78.1109429247402 \tabularnewline
Winsorized Mean ( 4 / 26 ) & 1.01179487179487 & 0.0124927465998146 & 80.9905863142928 \tabularnewline
Winsorized Mean ( 5 / 26 ) & 1.01179487179487 & 0.011947748921331 & 84.6849794431533 \tabularnewline
Winsorized Mean ( 6 / 26 ) & 1.01102564102564 & 0.0117847688709756 & 85.790875671365 \tabularnewline
Winsorized Mean ( 7 / 26 ) & 1.01102564102564 & 0.0107286790224189 & 94.2357991056471 \tabularnewline
Winsorized Mean ( 8 / 26 ) & 1.01307692307692 & 0.0103699591942254 & 97.6934338990518 \tabularnewline
Winsorized Mean ( 9 / 26 ) & 1.01192307692308 & 0.0101471978456848 & 99.724386211057 \tabularnewline
Winsorized Mean ( 10 / 26 ) & 1.01192307692308 & 0.0096940505016459 & 104.385991877314 \tabularnewline
Winsorized Mean ( 11 / 26 ) & 1.01051282051282 & 0.00896007616587881 & 112.779490018287 \tabularnewline
Winsorized Mean ( 12 / 26 ) & 1.00743589743590 & 0.00845043116026645 & 119.217100089853 \tabularnewline
Winsorized Mean ( 13 / 26 ) & 1.00910256410256 & 0.00818164148101545 & 123.337421524039 \tabularnewline
Winsorized Mean ( 14 / 26 ) & 1.01089743589744 & 0.00790634889787747 & 127.858945886997 \tabularnewline
Winsorized Mean ( 15 / 26 ) & 1.00705128205128 & 0.00730868539910127 & 137.788292566966 \tabularnewline
Winsorized Mean ( 16 / 26 ) & 1.00705128205128 & 0.0067001547547969 & 150.302689849110 \tabularnewline
Winsorized Mean ( 17 / 26 ) & 1.00705128205128 & 0.0067001547547969 & 150.302689849110 \tabularnewline
Winsorized Mean ( 18 / 26 ) & 1.00474358974359 & 0.0063835775160883 & 157.395063694515 \tabularnewline
Winsorized Mean ( 19 / 26 ) & 1.00230769230769 & 0.00607129107539029 & 165.089711539363 \tabularnewline
Winsorized Mean ( 20 / 26 ) & 1.00487179487179 & 0.00568264848736533 & 176.831594828715 \tabularnewline
Winsorized Mean ( 21 / 26 ) & 1.00756410256410 & 0.00529259089635065 & 190.372564646710 \tabularnewline
Winsorized Mean ( 22 / 26 ) & 1.01038461538462 & 0.00490482954887392 & 205.997905802167 \tabularnewline
Winsorized Mean ( 23 / 26 ) & 1.01038461538462 & 0.00490482954887392 & 205.997905802167 \tabularnewline
Winsorized Mean ( 24 / 26 ) & 1.01038461538462 & 0.00490482954887392 & 205.997905802167 \tabularnewline
Winsorized Mean ( 25 / 26 ) & 1.01358974358974 & 0.00448839239589327 & 225.824672663902 \tabularnewline
Winsorized Mean ( 26 / 26 ) & 1.01358974358974 & 0.00448839239589327 & 225.824672663902 \tabularnewline
Trimmed Mean ( 1 / 26 ) & 1.01315789473684 & 0.0135390410481063 & 74.8323231414199 \tabularnewline
Trimmed Mean ( 2 / 26 ) & 1.01202702702703 & 0.0124906180707789 & 81.0229743069808 \tabularnewline
Trimmed Mean ( 3 / 26 ) & 1.01138888888889 & 0.0116218211793870 & 87.0249914602659 \tabularnewline
Trimmed Mean ( 4 / 26 ) & 1.01085714285714 & 0.0109954684005517 & 91.9339773471065 \tabularnewline
Trimmed Mean ( 5 / 26 ) & 1.01058823529412 & 0.0104294998329984 & 96.897094920762 \tabularnewline
Trimmed Mean ( 6 / 26 ) & 1.01030303030303 & 0.00993209977393165 & 101.720990857817 \tabularnewline
Trimmed Mean ( 7 / 26 ) & 1.01015625 & 0.00937927729806133 & 107.700862006585 \tabularnewline
Trimmed Mean ( 8 / 26 ) & 1.01 & 0.00900378908427672 & 112.174995498702 \tabularnewline
Trimmed Mean ( 9 / 26 ) & 1.0095 & 0.00863714550565612 & 116.878892376992 \tabularnewline
Trimmed Mean ( 10 / 26 ) & 1.00913793103448 & 0.0082434394628562 & 122.417097327095 \tabularnewline
Trimmed Mean ( 11 / 26 ) & 1.00875 & 0.00786684023764785 & 128.228102964706 \tabularnewline
Trimmed Mean ( 12 / 26 ) & 1.00851851851852 & 0.00757172739365253 & 133.195302219144 \tabularnewline
Trimmed Mean ( 13 / 26 ) & 1.00865384615385 & 0.00731755902930403 & 137.840206292095 \tabularnewline
Trimmed Mean ( 14 / 26 ) & 1.0086 & 0.00705668014677423 & 142.928399618772 \tabularnewline
Trimmed Mean ( 15 / 26 ) & 1.00833333333333 & 0.0067852921179044 & 148.605736615618 \tabularnewline
Trimmed Mean ( 16 / 26 ) & 1.00847826086957 & 0.00657154891927982 & 153.461272716218 \tabularnewline
Trimmed Mean ( 17 / 26 ) & 1.00863636363636 & 0.00642562678716392 & 156.970891252392 \tabularnewline
Trimmed Mean ( 18 / 26 ) & 1.00880952380952 & 0.00623021729507331 & 161.922044774789 \tabularnewline
Trimmed Mean ( 19 / 26 ) & 1.00925 & 0.0060382063477026 & 167.144006329627 \tabularnewline
Trimmed Mean ( 20 / 26 ) & 1.01 & 0.00584289333810359 & 172.859564868903 \tabularnewline
Trimmed Mean ( 21 / 26 ) & 1.01055555555556 & 0.00567568532250253 & 178.049961922480 \tabularnewline
Trimmed Mean ( 22 / 26 ) & 1.01088235294118 & 0.00554302000510317 & 182.370323760425 \tabularnewline
Trimmed Mean ( 23 / 26 ) & 1.0109375 & 0.00545064688007675 & 185.471105034375 \tabularnewline
Trimmed Mean ( 24 / 26 ) & 1.011 & 0.00530343631823832 & 190.631119020551 \tabularnewline
Trimmed Mean ( 25 / 26 ) & 1.01107142857143 & 0.00507455749665408 & 199.243269829553 \tabularnewline
Trimmed Mean ( 26 / 26 ) & 1.01076923076923 & 0.0048650425541052 & 207.761642273062 \tabularnewline
Median & 1.01 &  &  \tabularnewline
Midrange & 1.05 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.00372093023256 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.00372093023256 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.00372093023256 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.00372093023256 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.01128205128205 &  &  \tabularnewline
Midmean - Closest Observation & 1.00372093023256 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.00372093023256 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.00372093023256 &  &  \tabularnewline
Number of observations & 78 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=84015&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]1.01410256410256[/C][C]0.0144397376669605[/C][C]70.2299853011128[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.00626132334733[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.998430026892108[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.02198775646236[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 26 )[/C][C]1.01423076923077[/C][C]0.0144075118587844[/C][C]70.3959697671449[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 26 )[/C][C]1.01320512820513[/C][C]0.0138211948674450[/C][C]73.3080705338776[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 26 )[/C][C]1.01282051282051[/C][C]0.0129664356221684[/C][C]78.1109429247402[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 26 )[/C][C]1.01179487179487[/C][C]0.0124927465998146[/C][C]80.9905863142928[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 26 )[/C][C]1.01179487179487[/C][C]0.011947748921331[/C][C]84.6849794431533[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 26 )[/C][C]1.01102564102564[/C][C]0.0117847688709756[/C][C]85.790875671365[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 26 )[/C][C]1.01102564102564[/C][C]0.0107286790224189[/C][C]94.2357991056471[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 26 )[/C][C]1.01307692307692[/C][C]0.0103699591942254[/C][C]97.6934338990518[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 26 )[/C][C]1.01192307692308[/C][C]0.0101471978456848[/C][C]99.724386211057[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 26 )[/C][C]1.01192307692308[/C][C]0.0096940505016459[/C][C]104.385991877314[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 26 )[/C][C]1.01051282051282[/C][C]0.00896007616587881[/C][C]112.779490018287[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 26 )[/C][C]1.00743589743590[/C][C]0.00845043116026645[/C][C]119.217100089853[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 26 )[/C][C]1.00910256410256[/C][C]0.00818164148101545[/C][C]123.337421524039[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 26 )[/C][C]1.01089743589744[/C][C]0.00790634889787747[/C][C]127.858945886997[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 26 )[/C][C]1.00705128205128[/C][C]0.00730868539910127[/C][C]137.788292566966[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 26 )[/C][C]1.00705128205128[/C][C]0.0067001547547969[/C][C]150.302689849110[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 26 )[/C][C]1.00705128205128[/C][C]0.0067001547547969[/C][C]150.302689849110[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 26 )[/C][C]1.00474358974359[/C][C]0.0063835775160883[/C][C]157.395063694515[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 26 )[/C][C]1.00230769230769[/C][C]0.00607129107539029[/C][C]165.089711539363[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 26 )[/C][C]1.00487179487179[/C][C]0.00568264848736533[/C][C]176.831594828715[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 26 )[/C][C]1.00756410256410[/C][C]0.00529259089635065[/C][C]190.372564646710[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 26 )[/C][C]1.01038461538462[/C][C]0.00490482954887392[/C][C]205.997905802167[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 26 )[/C][C]1.01038461538462[/C][C]0.00490482954887392[/C][C]205.997905802167[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 26 )[/C][C]1.01038461538462[/C][C]0.00490482954887392[/C][C]205.997905802167[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 26 )[/C][C]1.01358974358974[/C][C]0.00448839239589327[/C][C]225.824672663902[/C][/ROW]
[ROW][C]Winsorized Mean ( 26 / 26 )[/C][C]1.01358974358974[/C][C]0.00448839239589327[/C][C]225.824672663902[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 26 )[/C][C]1.01315789473684[/C][C]0.0135390410481063[/C][C]74.8323231414199[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 26 )[/C][C]1.01202702702703[/C][C]0.0124906180707789[/C][C]81.0229743069808[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 26 )[/C][C]1.01138888888889[/C][C]0.0116218211793870[/C][C]87.0249914602659[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 26 )[/C][C]1.01085714285714[/C][C]0.0109954684005517[/C][C]91.9339773471065[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 26 )[/C][C]1.01058823529412[/C][C]0.0104294998329984[/C][C]96.897094920762[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 26 )[/C][C]1.01030303030303[/C][C]0.00993209977393165[/C][C]101.720990857817[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 26 )[/C][C]1.01015625[/C][C]0.00937927729806133[/C][C]107.700862006585[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 26 )[/C][C]1.01[/C][C]0.00900378908427672[/C][C]112.174995498702[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 26 )[/C][C]1.0095[/C][C]0.00863714550565612[/C][C]116.878892376992[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 26 )[/C][C]1.00913793103448[/C][C]0.0082434394628562[/C][C]122.417097327095[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 26 )[/C][C]1.00875[/C][C]0.00786684023764785[/C][C]128.228102964706[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 26 )[/C][C]1.00851851851852[/C][C]0.00757172739365253[/C][C]133.195302219144[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 26 )[/C][C]1.00865384615385[/C][C]0.00731755902930403[/C][C]137.840206292095[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 26 )[/C][C]1.0086[/C][C]0.00705668014677423[/C][C]142.928399618772[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 26 )[/C][C]1.00833333333333[/C][C]0.0067852921179044[/C][C]148.605736615618[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 26 )[/C][C]1.00847826086957[/C][C]0.00657154891927982[/C][C]153.461272716218[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 26 )[/C][C]1.00863636363636[/C][C]0.00642562678716392[/C][C]156.970891252392[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 26 )[/C][C]1.00880952380952[/C][C]0.00623021729507331[/C][C]161.922044774789[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 26 )[/C][C]1.00925[/C][C]0.0060382063477026[/C][C]167.144006329627[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 26 )[/C][C]1.01[/C][C]0.00584289333810359[/C][C]172.859564868903[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 26 )[/C][C]1.01055555555556[/C][C]0.00567568532250253[/C][C]178.049961922480[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 26 )[/C][C]1.01088235294118[/C][C]0.00554302000510317[/C][C]182.370323760425[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 26 )[/C][C]1.0109375[/C][C]0.00545064688007675[/C][C]185.471105034375[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 26 )[/C][C]1.011[/C][C]0.00530343631823832[/C][C]190.631119020551[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 26 )[/C][C]1.01107142857143[/C][C]0.00507455749665408[/C][C]199.243269829553[/C][/ROW]
[ROW][C]Trimmed Mean ( 26 / 26 )[/C][C]1.01076923076923[/C][C]0.0048650425541052[/C][C]207.761642273062[/C][/ROW]
[ROW][C]Median[/C][C]1.01[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.05[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.00372093023256[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.00372093023256[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.00372093023256[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.00372093023256[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.01128205128205[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.00372093023256[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.00372093023256[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.00372093023256[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]78[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=84015&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=84015&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 Mean1.014102564102560.014439737666960570.2299853011128
Geometric Mean1.00626132334733
Harmonic Mean0.998430026892108
Quadratic Mean1.02198775646236
Winsorized Mean ( 1 / 26 )1.014230769230770.014407511858784470.3959697671449
Winsorized Mean ( 2 / 26 )1.013205128205130.013821194867445073.3080705338776
Winsorized Mean ( 3 / 26 )1.012820512820510.012966435622168478.1109429247402
Winsorized Mean ( 4 / 26 )1.011794871794870.012492746599814680.9905863142928
Winsorized Mean ( 5 / 26 )1.011794871794870.01194774892133184.6849794431533
Winsorized Mean ( 6 / 26 )1.011025641025640.011784768870975685.790875671365
Winsorized Mean ( 7 / 26 )1.011025641025640.010728679022418994.2357991056471
Winsorized Mean ( 8 / 26 )1.013076923076920.010369959194225497.6934338990518
Winsorized Mean ( 9 / 26 )1.011923076923080.010147197845684899.724386211057
Winsorized Mean ( 10 / 26 )1.011923076923080.0096940505016459104.385991877314
Winsorized Mean ( 11 / 26 )1.010512820512820.00896007616587881112.779490018287
Winsorized Mean ( 12 / 26 )1.007435897435900.00845043116026645119.217100089853
Winsorized Mean ( 13 / 26 )1.009102564102560.00818164148101545123.337421524039
Winsorized Mean ( 14 / 26 )1.010897435897440.00790634889787747127.858945886997
Winsorized Mean ( 15 / 26 )1.007051282051280.00730868539910127137.788292566966
Winsorized Mean ( 16 / 26 )1.007051282051280.0067001547547969150.302689849110
Winsorized Mean ( 17 / 26 )1.007051282051280.0067001547547969150.302689849110
Winsorized Mean ( 18 / 26 )1.004743589743590.0063835775160883157.395063694515
Winsorized Mean ( 19 / 26 )1.002307692307690.00607129107539029165.089711539363
Winsorized Mean ( 20 / 26 )1.004871794871790.00568264848736533176.831594828715
Winsorized Mean ( 21 / 26 )1.007564102564100.00529259089635065190.372564646710
Winsorized Mean ( 22 / 26 )1.010384615384620.00490482954887392205.997905802167
Winsorized Mean ( 23 / 26 )1.010384615384620.00490482954887392205.997905802167
Winsorized Mean ( 24 / 26 )1.010384615384620.00490482954887392205.997905802167
Winsorized Mean ( 25 / 26 )1.013589743589740.00448839239589327225.824672663902
Winsorized Mean ( 26 / 26 )1.013589743589740.00448839239589327225.824672663902
Trimmed Mean ( 1 / 26 )1.013157894736840.013539041048106374.8323231414199
Trimmed Mean ( 2 / 26 )1.012027027027030.012490618070778981.0229743069808
Trimmed Mean ( 3 / 26 )1.011388888888890.011621821179387087.0249914602659
Trimmed Mean ( 4 / 26 )1.010857142857140.010995468400551791.9339773471065
Trimmed Mean ( 5 / 26 )1.010588235294120.010429499832998496.897094920762
Trimmed Mean ( 6 / 26 )1.010303030303030.00993209977393165101.720990857817
Trimmed Mean ( 7 / 26 )1.010156250.00937927729806133107.700862006585
Trimmed Mean ( 8 / 26 )1.010.00900378908427672112.174995498702
Trimmed Mean ( 9 / 26 )1.00950.00863714550565612116.878892376992
Trimmed Mean ( 10 / 26 )1.009137931034480.0082434394628562122.417097327095
Trimmed Mean ( 11 / 26 )1.008750.00786684023764785128.228102964706
Trimmed Mean ( 12 / 26 )1.008518518518520.00757172739365253133.195302219144
Trimmed Mean ( 13 / 26 )1.008653846153850.00731755902930403137.840206292095
Trimmed Mean ( 14 / 26 )1.00860.00705668014677423142.928399618772
Trimmed Mean ( 15 / 26 )1.008333333333330.0067852921179044148.605736615618
Trimmed Mean ( 16 / 26 )1.008478260869570.00657154891927982153.461272716218
Trimmed Mean ( 17 / 26 )1.008636363636360.00642562678716392156.970891252392
Trimmed Mean ( 18 / 26 )1.008809523809520.00623021729507331161.922044774789
Trimmed Mean ( 19 / 26 )1.009250.0060382063477026167.144006329627
Trimmed Mean ( 20 / 26 )1.010.00584289333810359172.859564868903
Trimmed Mean ( 21 / 26 )1.010555555555560.00567568532250253178.049961922480
Trimmed Mean ( 22 / 26 )1.010882352941180.00554302000510317182.370323760425
Trimmed Mean ( 23 / 26 )1.01093750.00545064688007675185.471105034375
Trimmed Mean ( 24 / 26 )1.0110.00530343631823832190.631119020551
Trimmed Mean ( 25 / 26 )1.011071428571430.00507455749665408199.243269829553
Trimmed Mean ( 26 / 26 )1.010769230769230.0048650425541052207.761642273062
Median1.01
Midrange1.05
Midmean - Weighted Average at Xnp1.00372093023256
Midmean - Weighted Average at X(n+1)p1.00372093023256
Midmean - Empirical Distribution Function1.00372093023256
Midmean - Empirical Distribution Function - Averaging1.00372093023256
Midmean - Empirical Distribution Function - Interpolation1.01128205128205
Midmean - Closest Observation1.00372093023256
Midmean - True Basic - Statistics Graphics Toolkit1.00372093023256
Midmean - MS Excel (old versions)1.00372093023256
Number of observations78



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')