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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 computationFri, 12 Oct 2012 05:36:12 -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/12/t1350034723tsomhx2xl0104xy.htm/, Retrieved Mon, 13 May 2024 19:20:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=175303, Retrieved Mon, 13 May 2024 19:20:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2012-10-12 09:36:12] [41b2be8ffca33ab0c963750c05621031] [Current]
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Dataseries X:
0,43
0,45
0,44
0,44
0,44
0,48
0,47
0,47
0,47
0,49
0,49
0,46
0,45
0,44
0,42
0,43
0,43
0,47
0,47
0,47
0,47
0,48
0,48
0,48
0,49
0,49
0,47
0,5
0,51
0,5
0,49
0,5
0,51
0,51
0,5
0,53
0,5
0,49
0,46
0,46
0,47
0,49
0,5
0,5
0,51
0,5
0,52
0,5
0,48
0,47
0,43
0,42
0,45
0,5
0,52
0,52
0,51
0,52
0,52
0,51
0,51
0,51
0,48
0,49
0,47
0,51
0,5
0,51
0,51
0,52
0,51
0,52




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175303&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=175303&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175303&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'George Udny Yule' @ yule.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.4834722222222220.00335182501278966144.241486467051
Geometric Mean0.48262641117379
Harmonic Mean0.481759791946577
Quadratic Mean0.484296454205021
Winsorized Mean ( 1 / 24 )0.4833333333333330.00332745961364495145.255957833815
Winsorized Mean ( 2 / 24 )0.4836111111111110.00325798378680261148.438771570968
Winsorized Mean ( 3 / 24 )0.4836111111111110.00325798378680261148.438771570968
Winsorized Mean ( 4 / 24 )0.4836111111111110.00325798378680261148.438771570968
Winsorized Mean ( 5 / 24 )0.4836111111111110.00325798378680261148.438771570968
Winsorized Mean ( 6 / 24 )0.4844444444444440.00307629185103973157.476750549761
Winsorized Mean ( 7 / 24 )0.4844444444444440.00307629185103973157.476750549761
Winsorized Mean ( 8 / 24 )0.4833333333333330.00291373091688732165.881252291364
Winsorized Mean ( 9 / 24 )0.4833333333333330.00291373091688732165.881252291364
Winsorized Mean ( 10 / 24 )0.4847222222222220.00263873444898539183.694961199526
Winsorized Mean ( 11 / 24 )0.4847222222222220.00263873444898539183.694961199526
Winsorized Mean ( 12 / 24 )0.4847222222222220.00263873444898539183.694961199526
Winsorized Mean ( 13 / 24 )0.4865277777777780.00232493224548509209.265357613149
Winsorized Mean ( 14 / 24 )0.4865277777777780.00232493224548509209.265357613149
Winsorized Mean ( 15 / 24 )0.4865277777777780.00232493224548509209.265357613149
Winsorized Mean ( 16 / 24 )0.488750.00199703908367399244.737323368172
Winsorized Mean ( 17 / 24 )0.488750.00199703908367399244.737323368172
Winsorized Mean ( 18 / 24 )0.488750.00199703908367399244.737323368172
Winsorized Mean ( 19 / 24 )0.488750.00199703908367399244.737323368172
Winsorized Mean ( 20 / 24 )0.4859722222222220.00161492115998958300.926283129114
Winsorized Mean ( 21 / 24 )0.4859722222222220.00161492115998958300.926283129114
Winsorized Mean ( 22 / 24 )0.4859722222222220.00161492115998958300.926283129114
Winsorized Mean ( 23 / 24 )0.4859722222222220.00161492115998958300.926283129114
Winsorized Mean ( 24 / 24 )0.4859722222222220.00161492115998958300.926283129114
Trimmed Mean ( 1 / 24 )0.4837142857142860.0032569176486742148.519040974583
Trimmed Mean ( 2 / 24 )0.4841176470588240.00317222426153646152.611419352912
Trimmed Mean ( 3 / 24 )0.4843939393939390.00311495967772986155.505685308569
Trimmed Mean ( 4 / 24 )0.48468750.00304536427239621159.155837084353
Trimmed Mean ( 5 / 24 )0.4850.00296060865295989163.817666179932
Trimmed Mean ( 6 / 24 )0.4853333333333330.00285691416894842169.880264030465
Trimmed Mean ( 7 / 24 )0.485517241379310.00278458740735964174.358772181506
Trimmed Mean ( 8 / 24 )0.4857142857142860.00269507900345786180.222652134168
Trimmed Mean ( 9 / 24 )0.4861111111111110.00262249403416594185.362141830654
Trimmed Mean ( 10 / 24 )0.4865384615384620.00253012938497661192.297858136199
Trimmed Mean ( 11 / 24 )0.48680.00248160580006954196.16330683397
Trimmed Mean ( 12 / 24 )0.4870833333333330.00241813357289446201.429457327414
Trimmed Mean ( 13 / 24 )0.4873913043478260.00233508800708671208.725025724364
Trimmed Mean ( 14 / 24 )0.48750.00230187440856617211.783926258454
Trimmed Mean ( 15 / 24 )0.4876190476190480.00225570701720051216.171268653594
Trimmed Mean ( 16 / 24 )0.487750.00219227957696772222.485309412333
Trimmed Mean ( 17 / 24 )0.4876315789473680.00218081022066046223.601106748156
Trimmed Mean ( 18 / 24 )0.48750.00215932823181156225.764658108978
Trimmed Mean ( 19 / 24 )0.4873529411764710.00212400017495542229.450518377052
Trimmed Mean ( 20 / 24 )0.48718750.00206908771972952235.460050994691
Trimmed Mean ( 21 / 24 )0.4873333333333330.00208626230888063233.5915916512
Trimmed Mean ( 22 / 24 )0.48750.00209717623201965232.455428664915
Trimmed Mean ( 23 / 24 )0.4876923076923080.00209818179953629232.435677308845
Trimmed Mean ( 24 / 24 )0.4879166666666670.00208333333333334234.2
Median0.49
Midrange0.475
Midmean - Weighted Average at Xnp0.491458333333334
Midmean - Weighted Average at X(n+1)p0.491458333333334
Midmean - Empirical Distribution Function0.491458333333334
Midmean - Empirical Distribution Function - Averaging0.491458333333334
Midmean - Empirical Distribution Function - Interpolation0.491458333333334
Midmean - Closest Observation0.491458333333334
Midmean - True Basic - Statistics Graphics Toolkit0.491458333333334
Midmean - MS Excel (old versions)0.491458333333334
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.483472222222222 & 0.00335182501278966 & 144.241486467051 \tabularnewline
Geometric Mean & 0.48262641117379 &  &  \tabularnewline
Harmonic Mean & 0.481759791946577 &  &  \tabularnewline
Quadratic Mean & 0.484296454205021 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 0.483333333333333 & 0.00332745961364495 & 145.255957833815 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 0.483611111111111 & 0.00325798378680261 & 148.438771570968 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 0.483611111111111 & 0.00325798378680261 & 148.438771570968 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 0.483611111111111 & 0.00325798378680261 & 148.438771570968 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 0.483611111111111 & 0.00325798378680261 & 148.438771570968 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 0.484444444444444 & 0.00307629185103973 & 157.476750549761 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 0.484444444444444 & 0.00307629185103973 & 157.476750549761 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 0.483333333333333 & 0.00291373091688732 & 165.881252291364 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 0.483333333333333 & 0.00291373091688732 & 165.881252291364 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 0.484722222222222 & 0.00263873444898539 & 183.694961199526 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 0.484722222222222 & 0.00263873444898539 & 183.694961199526 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 0.484722222222222 & 0.00263873444898539 & 183.694961199526 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 0.486527777777778 & 0.00232493224548509 & 209.265357613149 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 0.486527777777778 & 0.00232493224548509 & 209.265357613149 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 0.486527777777778 & 0.00232493224548509 & 209.265357613149 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 0.48875 & 0.00199703908367399 & 244.737323368172 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 0.48875 & 0.00199703908367399 & 244.737323368172 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 0.48875 & 0.00199703908367399 & 244.737323368172 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 0.48875 & 0.00199703908367399 & 244.737323368172 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 0.485972222222222 & 0.00161492115998958 & 300.926283129114 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 0.485972222222222 & 0.00161492115998958 & 300.926283129114 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 0.485972222222222 & 0.00161492115998958 & 300.926283129114 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 0.485972222222222 & 0.00161492115998958 & 300.926283129114 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 0.485972222222222 & 0.00161492115998958 & 300.926283129114 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 0.483714285714286 & 0.0032569176486742 & 148.519040974583 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 0.484117647058824 & 0.00317222426153646 & 152.611419352912 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 0.484393939393939 & 0.00311495967772986 & 155.505685308569 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 0.4846875 & 0.00304536427239621 & 159.155837084353 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 0.485 & 0.00296060865295989 & 163.817666179932 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 0.485333333333333 & 0.00285691416894842 & 169.880264030465 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 0.48551724137931 & 0.00278458740735964 & 174.358772181506 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 0.485714285714286 & 0.00269507900345786 & 180.222652134168 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 0.486111111111111 & 0.00262249403416594 & 185.362141830654 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 0.486538461538462 & 0.00253012938497661 & 192.297858136199 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 0.4868 & 0.00248160580006954 & 196.16330683397 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 0.487083333333333 & 0.00241813357289446 & 201.429457327414 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 0.487391304347826 & 0.00233508800708671 & 208.725025724364 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 0.4875 & 0.00230187440856617 & 211.783926258454 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 0.487619047619048 & 0.00225570701720051 & 216.171268653594 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 0.48775 & 0.00219227957696772 & 222.485309412333 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 0.487631578947368 & 0.00218081022066046 & 223.601106748156 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 0.4875 & 0.00215932823181156 & 225.764658108978 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 0.487352941176471 & 0.00212400017495542 & 229.450518377052 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 0.4871875 & 0.00206908771972952 & 235.460050994691 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 0.487333333333333 & 0.00208626230888063 & 233.5915916512 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 0.4875 & 0.00209717623201965 & 232.455428664915 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 0.487692307692308 & 0.00209818179953629 & 232.435677308845 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 0.487916666666667 & 0.00208333333333334 & 234.2 \tabularnewline
Median & 0.49 &  &  \tabularnewline
Midrange & 0.475 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.491458333333334 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.491458333333334 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.491458333333334 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.491458333333334 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.491458333333334 &  &  \tabularnewline
Midmean - Closest Observation & 0.491458333333334 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.491458333333334 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.491458333333334 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=175303&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]0.483472222222222[/C][C]0.00335182501278966[/C][C]144.241486467051[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.48262641117379[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.481759791946577[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.484296454205021[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]0.483333333333333[/C][C]0.00332745961364495[/C][C]145.255957833815[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]0.483611111111111[/C][C]0.00325798378680261[/C][C]148.438771570968[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]0.483611111111111[/C][C]0.00325798378680261[/C][C]148.438771570968[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]0.483611111111111[/C][C]0.00325798378680261[/C][C]148.438771570968[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]0.483611111111111[/C][C]0.00325798378680261[/C][C]148.438771570968[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]0.484444444444444[/C][C]0.00307629185103973[/C][C]157.476750549761[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]0.484444444444444[/C][C]0.00307629185103973[/C][C]157.476750549761[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]0.483333333333333[/C][C]0.00291373091688732[/C][C]165.881252291364[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]0.483333333333333[/C][C]0.00291373091688732[/C][C]165.881252291364[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]0.484722222222222[/C][C]0.00263873444898539[/C][C]183.694961199526[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]0.484722222222222[/C][C]0.00263873444898539[/C][C]183.694961199526[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]0.484722222222222[/C][C]0.00263873444898539[/C][C]183.694961199526[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]0.486527777777778[/C][C]0.00232493224548509[/C][C]209.265357613149[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]0.486527777777778[/C][C]0.00232493224548509[/C][C]209.265357613149[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]0.486527777777778[/C][C]0.00232493224548509[/C][C]209.265357613149[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]0.48875[/C][C]0.00199703908367399[/C][C]244.737323368172[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]0.48875[/C][C]0.00199703908367399[/C][C]244.737323368172[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]0.48875[/C][C]0.00199703908367399[/C][C]244.737323368172[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]0.48875[/C][C]0.00199703908367399[/C][C]244.737323368172[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]0.485972222222222[/C][C]0.00161492115998958[/C][C]300.926283129114[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]0.485972222222222[/C][C]0.00161492115998958[/C][C]300.926283129114[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]0.485972222222222[/C][C]0.00161492115998958[/C][C]300.926283129114[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]0.485972222222222[/C][C]0.00161492115998958[/C][C]300.926283129114[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]0.485972222222222[/C][C]0.00161492115998958[/C][C]300.926283129114[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]0.483714285714286[/C][C]0.0032569176486742[/C][C]148.519040974583[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]0.484117647058824[/C][C]0.00317222426153646[/C][C]152.611419352912[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]0.484393939393939[/C][C]0.00311495967772986[/C][C]155.505685308569[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]0.4846875[/C][C]0.00304536427239621[/C][C]159.155837084353[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]0.485[/C][C]0.00296060865295989[/C][C]163.817666179932[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]0.485333333333333[/C][C]0.00285691416894842[/C][C]169.880264030465[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]0.48551724137931[/C][C]0.00278458740735964[/C][C]174.358772181506[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]0.485714285714286[/C][C]0.00269507900345786[/C][C]180.222652134168[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]0.486111111111111[/C][C]0.00262249403416594[/C][C]185.362141830654[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]0.486538461538462[/C][C]0.00253012938497661[/C][C]192.297858136199[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]0.4868[/C][C]0.00248160580006954[/C][C]196.16330683397[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]0.487083333333333[/C][C]0.00241813357289446[/C][C]201.429457327414[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]0.487391304347826[/C][C]0.00233508800708671[/C][C]208.725025724364[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]0.4875[/C][C]0.00230187440856617[/C][C]211.783926258454[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]0.487619047619048[/C][C]0.00225570701720051[/C][C]216.171268653594[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]0.48775[/C][C]0.00219227957696772[/C][C]222.485309412333[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]0.487631578947368[/C][C]0.00218081022066046[/C][C]223.601106748156[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]0.4875[/C][C]0.00215932823181156[/C][C]225.764658108978[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]0.487352941176471[/C][C]0.00212400017495542[/C][C]229.450518377052[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]0.4871875[/C][C]0.00206908771972952[/C][C]235.460050994691[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]0.487333333333333[/C][C]0.00208626230888063[/C][C]233.5915916512[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]0.4875[/C][C]0.00209717623201965[/C][C]232.455428664915[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]0.487692307692308[/C][C]0.00209818179953629[/C][C]232.435677308845[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]0.487916666666667[/C][C]0.00208333333333334[/C][C]234.2[/C][/ROW]
[ROW][C]Median[/C][C]0.49[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.475[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.491458333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.491458333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.491458333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.491458333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.491458333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.491458333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.491458333333334[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.491458333333334[/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=175303&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=175303&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 Mean0.4834722222222220.00335182501278966144.241486467051
Geometric Mean0.48262641117379
Harmonic Mean0.481759791946577
Quadratic Mean0.484296454205021
Winsorized Mean ( 1 / 24 )0.4833333333333330.00332745961364495145.255957833815
Winsorized Mean ( 2 / 24 )0.4836111111111110.00325798378680261148.438771570968
Winsorized Mean ( 3 / 24 )0.4836111111111110.00325798378680261148.438771570968
Winsorized Mean ( 4 / 24 )0.4836111111111110.00325798378680261148.438771570968
Winsorized Mean ( 5 / 24 )0.4836111111111110.00325798378680261148.438771570968
Winsorized Mean ( 6 / 24 )0.4844444444444440.00307629185103973157.476750549761
Winsorized Mean ( 7 / 24 )0.4844444444444440.00307629185103973157.476750549761
Winsorized Mean ( 8 / 24 )0.4833333333333330.00291373091688732165.881252291364
Winsorized Mean ( 9 / 24 )0.4833333333333330.00291373091688732165.881252291364
Winsorized Mean ( 10 / 24 )0.4847222222222220.00263873444898539183.694961199526
Winsorized Mean ( 11 / 24 )0.4847222222222220.00263873444898539183.694961199526
Winsorized Mean ( 12 / 24 )0.4847222222222220.00263873444898539183.694961199526
Winsorized Mean ( 13 / 24 )0.4865277777777780.00232493224548509209.265357613149
Winsorized Mean ( 14 / 24 )0.4865277777777780.00232493224548509209.265357613149
Winsorized Mean ( 15 / 24 )0.4865277777777780.00232493224548509209.265357613149
Winsorized Mean ( 16 / 24 )0.488750.00199703908367399244.737323368172
Winsorized Mean ( 17 / 24 )0.488750.00199703908367399244.737323368172
Winsorized Mean ( 18 / 24 )0.488750.00199703908367399244.737323368172
Winsorized Mean ( 19 / 24 )0.488750.00199703908367399244.737323368172
Winsorized Mean ( 20 / 24 )0.4859722222222220.00161492115998958300.926283129114
Winsorized Mean ( 21 / 24 )0.4859722222222220.00161492115998958300.926283129114
Winsorized Mean ( 22 / 24 )0.4859722222222220.00161492115998958300.926283129114
Winsorized Mean ( 23 / 24 )0.4859722222222220.00161492115998958300.926283129114
Winsorized Mean ( 24 / 24 )0.4859722222222220.00161492115998958300.926283129114
Trimmed Mean ( 1 / 24 )0.4837142857142860.0032569176486742148.519040974583
Trimmed Mean ( 2 / 24 )0.4841176470588240.00317222426153646152.611419352912
Trimmed Mean ( 3 / 24 )0.4843939393939390.00311495967772986155.505685308569
Trimmed Mean ( 4 / 24 )0.48468750.00304536427239621159.155837084353
Trimmed Mean ( 5 / 24 )0.4850.00296060865295989163.817666179932
Trimmed Mean ( 6 / 24 )0.4853333333333330.00285691416894842169.880264030465
Trimmed Mean ( 7 / 24 )0.485517241379310.00278458740735964174.358772181506
Trimmed Mean ( 8 / 24 )0.4857142857142860.00269507900345786180.222652134168
Trimmed Mean ( 9 / 24 )0.4861111111111110.00262249403416594185.362141830654
Trimmed Mean ( 10 / 24 )0.4865384615384620.00253012938497661192.297858136199
Trimmed Mean ( 11 / 24 )0.48680.00248160580006954196.16330683397
Trimmed Mean ( 12 / 24 )0.4870833333333330.00241813357289446201.429457327414
Trimmed Mean ( 13 / 24 )0.4873913043478260.00233508800708671208.725025724364
Trimmed Mean ( 14 / 24 )0.48750.00230187440856617211.783926258454
Trimmed Mean ( 15 / 24 )0.4876190476190480.00225570701720051216.171268653594
Trimmed Mean ( 16 / 24 )0.487750.00219227957696772222.485309412333
Trimmed Mean ( 17 / 24 )0.4876315789473680.00218081022066046223.601106748156
Trimmed Mean ( 18 / 24 )0.48750.00215932823181156225.764658108978
Trimmed Mean ( 19 / 24 )0.4873529411764710.00212400017495542229.450518377052
Trimmed Mean ( 20 / 24 )0.48718750.00206908771972952235.460050994691
Trimmed Mean ( 21 / 24 )0.4873333333333330.00208626230888063233.5915916512
Trimmed Mean ( 22 / 24 )0.48750.00209717623201965232.455428664915
Trimmed Mean ( 23 / 24 )0.4876923076923080.00209818179953629232.435677308845
Trimmed Mean ( 24 / 24 )0.4879166666666670.00208333333333334234.2
Median0.49
Midrange0.475
Midmean - Weighted Average at Xnp0.491458333333334
Midmean - Weighted Average at X(n+1)p0.491458333333334
Midmean - Empirical Distribution Function0.491458333333334
Midmean - Empirical Distribution Function - Averaging0.491458333333334
Midmean - Empirical Distribution Function - Interpolation0.491458333333334
Midmean - Closest Observation0.491458333333334
Midmean - True Basic - Statistics Graphics Toolkit0.491458333333334
Midmean - MS Excel (old versions)0.491458333333334
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')