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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationThu, 22 Oct 2009 14:37:51 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/22/t125624524194fq2t9l1shg35d.htm/, Retrieved Thu, 02 May 2024 15:18:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49823, Retrieved Thu, 02 May 2024 15:18:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact126

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
F RMPD    [Univariate Data Series] [] [2009-10-14 08:30:28] [74be16979710d4c4e7c6647856088456]
- RMPD        [Central Tendency] [] [2009-10-22 20:37:51] [17416e80e7873ecccac25c455c5f767e] [Current]
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Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0,64
0,69
0,73
0,68
0,67
0,60
0,61
0,64
0,59
0,58
0,54
0,55
0,57
0,59
0,57
0,53
0,54
0,53
0,48
0,47
0,48
0,46
0,46
0,51
0,53
0,53
0,51
0,55
0,52
0,50
0,48
0,47
0,46
0,44
0,45
0,43
0,40
0,38
0,38
0,37
0,35
0,33
0,32
0,29
0,28
0,27
0,31
0,35
0,47
0,58
0,70
0,68
0,71
0,67
0,63
0,56
0,49
0,51
0,47
0,49

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49823&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49823&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49823&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.50950.014916765299677134.1561987310366
Geometric Mean0.495535763267674
Harmonic Mean0.480402813428653
Quadratic Mean0.522224408978873
Winsorized Mean ( 1 / 20 )0.5093333333333330.014792093373331234.4328095069773
Winsorized Mean ( 2 / 20 )0.5093333333333330.014630798462609134.8124085390829
Winsorized Mean ( 3 / 20 )0.5098333333333330.01427631214677835.7118370690989
Winsorized Mean ( 4 / 20 )0.5098333333333330.013980397225806536.4677287131892
Winsorized Mean ( 5 / 20 )0.5106666666666670.013791970698340437.0263741009917
Winsorized Mean ( 6 / 20 )0.5116666666666670.013155237118862038.8945225421318
Winsorized Mean ( 7 / 20 )0.5116666666666670.013155237118862038.8945225421318
Winsorized Mean ( 8 / 20 )0.5103333333333330.011827304105777743.1487453750371
Winsorized Mean ( 9 / 20 )0.5118333333333330.011531072408285544.3873141378909
Winsorized Mean ( 10 / 20 )0.5101666666666670.011223189438283945.4564782562088
Winsorized Mean ( 11 / 20 )0.5101666666666670.0098677459708962651.7004256262111
Winsorized Mean ( 12 / 20 )0.5141666666666670.0084448749766351260.8850537265783
Winsorized Mean ( 13 / 20 )0.5141666666666670.0077178041528416366.6208492058398
Winsorized Mean ( 14 / 20 )0.51650.0073485653313676570.2858281459782
Winsorized Mean ( 15 / 20 )0.51650.0065562537532371478.7797451776449
Winsorized Mean ( 16 / 20 )0.51650.0065562537532371478.7797451776449
Winsorized Mean ( 17 / 20 )0.5136666666666670.006101619062093984.1853058080605
Winsorized Mean ( 18 / 20 )0.5166666666666670.0056681619828347891.1524173499837
Winsorized Mean ( 19 / 20 )0.51350.0051739514890748199.2471616875987
Winsorized Mean ( 20 / 20 )0.5101666666666670.00467890847927578109.035401937512
Trimmed Mean ( 1 / 20 )0.5098275862068960.014359677065558435.5041122359023
Trimmed Mean ( 2 / 20 )0.5103571428571430.013826297843579436.9120605263208
Trimmed Mean ( 3 / 20 )0.5109259259259260.013273630796793938.491798796252
Trimmed Mean ( 4 / 20 )0.5113461538461540.012760199381157740.0735238197949
Trimmed Mean ( 5 / 20 )0.51180.012234744770195941.8316858760106
Trimmed Mean ( 6 / 20 )0.5120833333333330.011634803245955844.0130634363181
Trimmed Mean ( 7 / 20 )0.5121739130434780.011081224245129546.2199754931042
Trimmed Mean ( 8 / 20 )0.5122727272727270.010357579551278449.458729690326
Trimmed Mean ( 9 / 20 )0.5126190476190480.0098305003329195452.1457738933625
Trimmed Mean ( 10 / 20 )0.512750.0092194575456421255.6160704099525
Trimmed Mean ( 11 / 20 )0.5131578947368420.008484822556805160.4795081218608
Trimmed Mean ( 12 / 20 )0.5136111111111110.0079197640835652364.8518195355006
Trimmed Mean ( 13 / 20 )0.5135294117647060.0075864871067267167.6900131167922
Trimmed Mean ( 14 / 20 )0.51343750.0073315680533544670.0310624225991
Trimmed Mean ( 15 / 20 )0.5130.0070653761562909872.6075991783151
Trimmed Mean ( 16 / 20 )0.51250.0069126255167187874.1397026007665
Trimmed Mean ( 17 / 20 )0.5119230769230770.0066568468111753776.9017361288338
Trimmed Mean ( 18 / 20 )0.5116666666666670.0064174430172169979.7306131575996
Trimmed Mean ( 19 / 20 )0.5109090909090910.0061689450889458482.8195231992891
Trimmed Mean ( 20 / 20 )0.51050.0059592917276079885.6645425890085
Median0.51
Midrange0.5
Midmean - Weighted Average at Xnp0.510967741935484
Midmean - Weighted Average at X(n+1)p0.513
Midmean - Empirical Distribution Function0.510967741935484
Midmean - Empirical Distribution Function - Averaging0.513
Midmean - Empirical Distribution Function - Interpolation0.513
Midmean - Closest Observation0.510967741935484
Midmean - True Basic - Statistics Graphics Toolkit0.513
Midmean - MS Excel (old versions)0.515757575757576
Number of observations60

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 0.5095 & 0.0149167652996771 & 34.1561987310366 \tabularnewline
Geometric Mean & 0.495535763267674 &  &  \tabularnewline
Harmonic Mean & 0.480402813428653 &  &  \tabularnewline
Quadratic Mean & 0.522224408978873 &  &  \tabularnewline
Winsorized Mean ( 1 / 20 ) & 0.509333333333333 & 0.0147920933733312 & 34.4328095069773 \tabularnewline
Winsorized Mean ( 2 / 20 ) & 0.509333333333333 & 0.0146307984626091 & 34.8124085390829 \tabularnewline
Winsorized Mean ( 3 / 20 ) & 0.509833333333333 & 0.014276312146778 & 35.7118370690989 \tabularnewline
Winsorized Mean ( 4 / 20 ) & 0.509833333333333 & 0.0139803972258065 & 36.4677287131892 \tabularnewline
Winsorized Mean ( 5 / 20 ) & 0.510666666666667 & 0.0137919706983404 & 37.0263741009917 \tabularnewline
Winsorized Mean ( 6 / 20 ) & 0.511666666666667 & 0.0131552371188620 & 38.8945225421318 \tabularnewline
Winsorized Mean ( 7 / 20 ) & 0.511666666666667 & 0.0131552371188620 & 38.8945225421318 \tabularnewline
Winsorized Mean ( 8 / 20 ) & 0.510333333333333 & 0.0118273041057777 & 43.1487453750371 \tabularnewline
Winsorized Mean ( 9 / 20 ) & 0.511833333333333 & 0.0115310724082855 & 44.3873141378909 \tabularnewline
Winsorized Mean ( 10 / 20 ) & 0.510166666666667 & 0.0112231894382839 & 45.4564782562088 \tabularnewline
Winsorized Mean ( 11 / 20 ) & 0.510166666666667 & 0.00986774597089626 & 51.7004256262111 \tabularnewline
Winsorized Mean ( 12 / 20 ) & 0.514166666666667 & 0.00844487497663512 & 60.8850537265783 \tabularnewline
Winsorized Mean ( 13 / 20 ) & 0.514166666666667 & 0.00771780415284163 & 66.6208492058398 \tabularnewline
Winsorized Mean ( 14 / 20 ) & 0.5165 & 0.00734856533136765 & 70.2858281459782 \tabularnewline
Winsorized Mean ( 15 / 20 ) & 0.5165 & 0.00655625375323714 & 78.7797451776449 \tabularnewline
Winsorized Mean ( 16 / 20 ) & 0.5165 & 0.00655625375323714 & 78.7797451776449 \tabularnewline
Winsorized Mean ( 17 / 20 ) & 0.513666666666667 & 0.0061016190620939 & 84.1853058080605 \tabularnewline
Winsorized Mean ( 18 / 20 ) & 0.516666666666667 & 0.00566816198283478 & 91.1524173499837 \tabularnewline
Winsorized Mean ( 19 / 20 ) & 0.5135 & 0.00517395148907481 & 99.2471616875987 \tabularnewline
Winsorized Mean ( 20 / 20 ) & 0.510166666666667 & 0.00467890847927578 & 109.035401937512 \tabularnewline
Trimmed Mean ( 1 / 20 ) & 0.509827586206896 & 0.0143596770655584 & 35.5041122359023 \tabularnewline
Trimmed Mean ( 2 / 20 ) & 0.510357142857143 & 0.0138262978435794 & 36.9120605263208 \tabularnewline
Trimmed Mean ( 3 / 20 ) & 0.510925925925926 & 0.0132736307967939 & 38.491798796252 \tabularnewline
Trimmed Mean ( 4 / 20 ) & 0.511346153846154 & 0.0127601993811577 & 40.0735238197949 \tabularnewline
Trimmed Mean ( 5 / 20 ) & 0.5118 & 0.0122347447701959 & 41.8316858760106 \tabularnewline
Trimmed Mean ( 6 / 20 ) & 0.512083333333333 & 0.0116348032459558 & 44.0130634363181 \tabularnewline
Trimmed Mean ( 7 / 20 ) & 0.512173913043478 & 0.0110812242451295 & 46.2199754931042 \tabularnewline
Trimmed Mean ( 8 / 20 ) & 0.512272727272727 & 0.0103575795512784 & 49.458729690326 \tabularnewline
Trimmed Mean ( 9 / 20 ) & 0.512619047619048 & 0.00983050033291954 & 52.1457738933625 \tabularnewline
Trimmed Mean ( 10 / 20 ) & 0.51275 & 0.00921945754564212 & 55.6160704099525 \tabularnewline
Trimmed Mean ( 11 / 20 ) & 0.513157894736842 & 0.0084848225568051 & 60.4795081218608 \tabularnewline
Trimmed Mean ( 12 / 20 ) & 0.513611111111111 & 0.00791976408356523 & 64.8518195355006 \tabularnewline
Trimmed Mean ( 13 / 20 ) & 0.513529411764706 & 0.00758648710672671 & 67.6900131167922 \tabularnewline
Trimmed Mean ( 14 / 20 ) & 0.5134375 & 0.00733156805335446 & 70.0310624225991 \tabularnewline
Trimmed Mean ( 15 / 20 ) & 0.513 & 0.00706537615629098 & 72.6075991783151 \tabularnewline
Trimmed Mean ( 16 / 20 ) & 0.5125 & 0.00691262551671878 & 74.1397026007665 \tabularnewline
Trimmed Mean ( 17 / 20 ) & 0.511923076923077 & 0.00665684681117537 & 76.9017361288338 \tabularnewline
Trimmed Mean ( 18 / 20 ) & 0.511666666666667 & 0.00641744301721699 & 79.7306131575996 \tabularnewline
Trimmed Mean ( 19 / 20 ) & 0.510909090909091 & 0.00616894508894584 & 82.8195231992891 \tabularnewline
Trimmed Mean ( 20 / 20 ) & 0.5105 & 0.00595929172760798 & 85.6645425890085 \tabularnewline
Median & 0.51 &  &  \tabularnewline
Midrange & 0.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 0.510967741935484 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 0.513 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 0.510967741935484 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 0.513 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 0.513 &  &  \tabularnewline
Midmean - Closest Observation & 0.510967741935484 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 0.513 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 0.515757575757576 &  &  \tabularnewline
Number of observations & 60 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=49823&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]0.5095[/C][C]0.0149167652996771[/C][C]34.1561987310366[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]0.495535763267674[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]0.480402813428653[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]0.522224408978873[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 20 )[/C][C]0.509333333333333[/C][C]0.0147920933733312[/C][C]34.4328095069773[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 20 )[/C][C]0.509333333333333[/C][C]0.0146307984626091[/C][C]34.8124085390829[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 20 )[/C][C]0.509833333333333[/C][C]0.014276312146778[/C][C]35.7118370690989[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 20 )[/C][C]0.509833333333333[/C][C]0.0139803972258065[/C][C]36.4677287131892[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 20 )[/C][C]0.510666666666667[/C][C]0.0137919706983404[/C][C]37.0263741009917[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 20 )[/C][C]0.511666666666667[/C][C]0.0131552371188620[/C][C]38.8945225421318[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 20 )[/C][C]0.511666666666667[/C][C]0.0131552371188620[/C][C]38.8945225421318[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 20 )[/C][C]0.510333333333333[/C][C]0.0118273041057777[/C][C]43.1487453750371[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 20 )[/C][C]0.511833333333333[/C][C]0.0115310724082855[/C][C]44.3873141378909[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 20 )[/C][C]0.510166666666667[/C][C]0.0112231894382839[/C][C]45.4564782562088[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 20 )[/C][C]0.510166666666667[/C][C]0.00986774597089626[/C][C]51.7004256262111[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 20 )[/C][C]0.514166666666667[/C][C]0.00844487497663512[/C][C]60.8850537265783[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 20 )[/C][C]0.514166666666667[/C][C]0.00771780415284163[/C][C]66.6208492058398[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 20 )[/C][C]0.5165[/C][C]0.00734856533136765[/C][C]70.2858281459782[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 20 )[/C][C]0.5165[/C][C]0.00655625375323714[/C][C]78.7797451776449[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 20 )[/C][C]0.5165[/C][C]0.00655625375323714[/C][C]78.7797451776449[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 20 )[/C][C]0.513666666666667[/C][C]0.0061016190620939[/C][C]84.1853058080605[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 20 )[/C][C]0.516666666666667[/C][C]0.00566816198283478[/C][C]91.1524173499837[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 20 )[/C][C]0.5135[/C][C]0.00517395148907481[/C][C]99.2471616875987[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 20 )[/C][C]0.510166666666667[/C][C]0.00467890847927578[/C][C]109.035401937512[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 20 )[/C][C]0.509827586206896[/C][C]0.0143596770655584[/C][C]35.5041122359023[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 20 )[/C][C]0.510357142857143[/C][C]0.0138262978435794[/C][C]36.9120605263208[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 20 )[/C][C]0.510925925925926[/C][C]0.0132736307967939[/C][C]38.491798796252[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 20 )[/C][C]0.511346153846154[/C][C]0.0127601993811577[/C][C]40.0735238197949[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 20 )[/C][C]0.5118[/C][C]0.0122347447701959[/C][C]41.8316858760106[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 20 )[/C][C]0.512083333333333[/C][C]0.0116348032459558[/C][C]44.0130634363181[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 20 )[/C][C]0.512173913043478[/C][C]0.0110812242451295[/C][C]46.2199754931042[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 20 )[/C][C]0.512272727272727[/C][C]0.0103575795512784[/C][C]49.458729690326[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 20 )[/C][C]0.512619047619048[/C][C]0.00983050033291954[/C][C]52.1457738933625[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 20 )[/C][C]0.51275[/C][C]0.00921945754564212[/C][C]55.6160704099525[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 20 )[/C][C]0.513157894736842[/C][C]0.0084848225568051[/C][C]60.4795081218608[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 20 )[/C][C]0.513611111111111[/C][C]0.00791976408356523[/C][C]64.8518195355006[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 20 )[/C][C]0.513529411764706[/C][C]0.00758648710672671[/C][C]67.6900131167922[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 20 )[/C][C]0.5134375[/C][C]0.00733156805335446[/C][C]70.0310624225991[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 20 )[/C][C]0.513[/C][C]0.00706537615629098[/C][C]72.6075991783151[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 20 )[/C][C]0.5125[/C][C]0.00691262551671878[/C][C]74.1397026007665[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 20 )[/C][C]0.511923076923077[/C][C]0.00665684681117537[/C][C]76.9017361288338[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 20 )[/C][C]0.511666666666667[/C][C]0.00641744301721699[/C][C]79.7306131575996[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 20 )[/C][C]0.510909090909091[/C][C]0.00616894508894584[/C][C]82.8195231992891[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 20 )[/C][C]0.5105[/C][C]0.00595929172760798[/C][C]85.6645425890085[/C][/ROW]
[ROW][C]Median[/C][C]0.51[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]0.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]0.510967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]0.513[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]0.510967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]0.513[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]0.513[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]0.510967741935484[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]0.513[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]0.515757575757576[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]60[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=49823&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49823&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean0.50950.014916765299677134.1561987310366
Geometric Mean0.495535763267674
Harmonic Mean0.480402813428653
Quadratic Mean0.522224408978873
Winsorized Mean ( 1 / 20 )0.5093333333333330.014792093373331234.4328095069773
Winsorized Mean ( 2 / 20 )0.5093333333333330.014630798462609134.8124085390829
Winsorized Mean ( 3 / 20 )0.5098333333333330.01427631214677835.7118370690989
Winsorized Mean ( 4 / 20 )0.5098333333333330.013980397225806536.4677287131892
Winsorized Mean ( 5 / 20 )0.5106666666666670.013791970698340437.0263741009917
Winsorized Mean ( 6 / 20 )0.5116666666666670.013155237118862038.8945225421318
Winsorized Mean ( 7 / 20 )0.5116666666666670.013155237118862038.8945225421318
Winsorized Mean ( 8 / 20 )0.5103333333333330.011827304105777743.1487453750371
Winsorized Mean ( 9 / 20 )0.5118333333333330.011531072408285544.3873141378909
Winsorized Mean ( 10 / 20 )0.5101666666666670.011223189438283945.4564782562088
Winsorized Mean ( 11 / 20 )0.5101666666666670.0098677459708962651.7004256262111
Winsorized Mean ( 12 / 20 )0.5141666666666670.0084448749766351260.8850537265783
Winsorized Mean ( 13 / 20 )0.5141666666666670.0077178041528416366.6208492058398
Winsorized Mean ( 14 / 20 )0.51650.0073485653313676570.2858281459782
Winsorized Mean ( 15 / 20 )0.51650.0065562537532371478.7797451776449
Winsorized Mean ( 16 / 20 )0.51650.0065562537532371478.7797451776449
Winsorized Mean ( 17 / 20 )0.5136666666666670.006101619062093984.1853058080605
Winsorized Mean ( 18 / 20 )0.5166666666666670.0056681619828347891.1524173499837
Winsorized Mean ( 19 / 20 )0.51350.0051739514890748199.2471616875987
Winsorized Mean ( 20 / 20 )0.5101666666666670.00467890847927578109.035401937512
Trimmed Mean ( 1 / 20 )0.5098275862068960.014359677065558435.5041122359023
Trimmed Mean ( 2 / 20 )0.5103571428571430.013826297843579436.9120605263208
Trimmed Mean ( 3 / 20 )0.5109259259259260.013273630796793938.491798796252
Trimmed Mean ( 4 / 20 )0.5113461538461540.012760199381157740.0735238197949
Trimmed Mean ( 5 / 20 )0.51180.012234744770195941.8316858760106
Trimmed Mean ( 6 / 20 )0.5120833333333330.011634803245955844.0130634363181
Trimmed Mean ( 7 / 20 )0.5121739130434780.011081224245129546.2199754931042
Trimmed Mean ( 8 / 20 )0.5122727272727270.010357579551278449.458729690326
Trimmed Mean ( 9 / 20 )0.5126190476190480.0098305003329195452.1457738933625
Trimmed Mean ( 10 / 20 )0.512750.0092194575456421255.6160704099525
Trimmed Mean ( 11 / 20 )0.5131578947368420.008484822556805160.4795081218608
Trimmed Mean ( 12 / 20 )0.5136111111111110.0079197640835652364.8518195355006
Trimmed Mean ( 13 / 20 )0.5135294117647060.0075864871067267167.6900131167922
Trimmed Mean ( 14 / 20 )0.51343750.0073315680533544670.0310624225991
Trimmed Mean ( 15 / 20 )0.5130.0070653761562909872.6075991783151
Trimmed Mean ( 16 / 20 )0.51250.0069126255167187874.1397026007665
Trimmed Mean ( 17 / 20 )0.5119230769230770.0066568468111753776.9017361288338
Trimmed Mean ( 18 / 20 )0.5116666666666670.0064174430172169979.7306131575996
Trimmed Mean ( 19 / 20 )0.5109090909090910.0061689450889458482.8195231992891
Trimmed Mean ( 20 / 20 )0.51050.0059592917276079885.6645425890085
Median0.51
Midrange0.5
Midmean - Weighted Average at Xnp0.510967741935484
Midmean - Weighted Average at X(n+1)p0.513
Midmean - Empirical Distribution Function0.510967741935484
Midmean - Empirical Distribution Function - Averaging0.513
Midmean - Empirical Distribution Function - Interpolation0.513
Midmean - Closest Observation0.510967741935484
Midmean - True Basic - Statistics Graphics Toolkit0.513
Midmean - MS Excel (old versions)0.515757575757576
Number of observations60


Figures (Output of Computation)

Input Parameters & R Code

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')