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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 computationMon, 24 Feb 2014 13:38:28 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Feb/24/t13932671344tjsogiejfijoya.htm/, Retrieved Thu, 16 May 2024 17:39:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=234007, Retrieved Thu, 16 May 2024 17:39:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2014-02-24 18:38:28] [a3f6f3ab25c27d7686091f6989fa462a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0,978
0,973
0,96
0,978
0,985
1,035
1,015
1,05
1,022
1,042
1,058
1,056
1,013
1,098
1,097
1,139
1,182
1,189
1,191
1,168
1,168
1,177
1,184
1,2
1,251
1,171
1,288
1,313
1,363
1,377
1,342
1,334
1,348
1,327
1,349
1,361
1,393
1,38
1,348
1,421
1,432
1,457
1,453
1,428
1,383
1,408
1,458
1,474
1,491
1,476
1,446
1,444
1,451
1,472
1,449
1,415
1,39
1,394
1,418
1,426
1,437
1,406
1,387
1,404
1,421

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234007&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234007&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234007&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean1.279138461538460.020885803019072161.2443993831793
Geometric Mean1.26754486278997
Harmonic Mean1.2553326636179
Quadratic Mean1.29000506856488
Winsorized Mean ( 1 / 21 )1.279107692307690.020803581457991661.4849753101686
Winsorized Mean ( 2 / 21 )1.27920.020759395463259561.6202915091607
Winsorized Mean ( 3 / 21 )1.279107692307690.020745923175466761.655857948048
Winsorized Mean ( 4 / 21 )1.278676923076920.02052752734009262.290840094489
Winsorized Mean ( 5 / 21 )1.280753846153850.02005137668841263.8736115757086
Winsorized Mean ( 6 / 21 )1.280569230769230.019962657075519664.1482356744787
Winsorized Mean ( 7 / 21 )1.281107692307690.019778158153398164.7738622763305
Winsorized Mean ( 8 / 21 )1.282461538461540.019422083942629766.031098529373
Winsorized Mean ( 9 / 21 )1.283015384615380.019175009932648366.9108067803846
Winsorized Mean ( 10 / 21 )1.283938461538460.018894289391179467.9537840749839
Winsorized Mean ( 11 / 21 )1.283769230769230.018543734288458469.2292723137351
Winsorized Mean ( 12 / 21 )1.283215384615380.018354855419087969.9114950957837
Winsorized Mean ( 13 / 21 )1.290215384615380.016802450775735276.7873331001577
Winsorized Mean ( 14 / 21 )1.290.016708775331451577.2049401832453
Winsorized Mean ( 15 / 21 )1.298307692307690.014919220358137887.0224891878829
Winsorized Mean ( 16 / 21 )1.305446153846150.01376530670341494.8359656615851
Winsorized Mean ( 17 / 21 )1.304661538461540.013662998828304495.4886664967566
Winsorized Mean ( 18 / 21 )1.304661538461540.013426281576901697.1722163719594
Winsorized Mean ( 19 / 21 )1.304369230769230.0128946092125959101.156166058533
Winsorized Mean ( 20 / 21 )1.305292307692310.0125809632419253103.751380764114
Winsorized Mean ( 21 / 21 )1.305292307692310.0124015298970321105.252522755655
Trimmed Mean ( 1 / 21 )1.280841269841270.020663249882923161.9864385853364
Trimmed Mean ( 2 / 21 )1.282688524590160.020477116922979762.6400937893124
Trimmed Mean ( 3 / 21 )1.284610169491530.020262955996340163.3969777027375
Trimmed Mean ( 4 / 21 )1.286701754385960.019991037542489864.3639306689886
Trimmed Mean ( 5 / 21 )1.289072727272730.019720092721206165.3684922021952
Trimmed Mean ( 6 / 21 )1.291113207547170.019522077494667666.1360558526537
Trimmed Mean ( 7 / 21 )1.293352941176470.019277556258955367.0911252340738
Trimmed Mean ( 8 / 21 )1.295673469387760.018997994607628568.2005388541108
Trimmed Mean ( 9 / 21 )1.297957446808510.018714317448523669.3563871820988
Trimmed Mean ( 10 / 21 )1.300355555555560.018388324017080270.7163716686583
Trimmed Mean ( 11 / 21 )1.302837209302330.018011960165572172.3317838439682
Trimmed Mean ( 12 / 21 )1.305585365853660.017577076798841974.2777300682717
Trimmed Mean ( 13 / 21 )1.308692307692310.017014487509692576.916351841147
Trimmed Mean ( 14 / 21 )1.311189189189190.01666102777752278.6979775016137
Trimmed Mean ( 15 / 21 )1.3140.016162047045652481.3015824225969
Trimmed Mean ( 16 / 21 )1.316060606060610.015949371804976282.5148866145308
Trimmed Mean ( 17 / 21 )1.317451612903230.015917586048525482.7670482752174
Trimmed Mean ( 18 / 21 )1.319137931034480.015815494377625383.4079478982783
Trimmed Mean ( 19 / 21 )1.321074074074070.015647007662547284.4298221465185
Trimmed Mean ( 20 / 21 )1.323360.015461013334621285.5933548053192
Trimmed Mean ( 21 / 21 )1.325913043478260.015171211691999887.3966477033243
Median1.348
Midrange1.2255
Midmean - Weighted Average at Xnp1.31278125
Midmean - Weighted Average at X(n+1)p1.31914705882353
Midmean - Empirical Distribution Function1.31914705882353
Midmean - Empirical Distribution Function - Averaging1.31914705882353
Midmean - Empirical Distribution Function - Interpolation1.31914705882353
Midmean - Closest Observation1.314
Midmean - True Basic - Statistics Graphics Toolkit1.31914705882353
Midmean - MS Excel (old versions)1.31914705882353
Number of observations65

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 1.27913846153846 & 0.0208858030190721 & 61.2443993831793 \tabularnewline
Geometric Mean & 1.26754486278997 &  &  \tabularnewline
Harmonic Mean & 1.2553326636179 &  &  \tabularnewline
Quadratic Mean & 1.29000506856488 &  &  \tabularnewline
Winsorized Mean ( 1 / 21 ) & 1.27910769230769 & 0.0208035814579916 & 61.4849753101686 \tabularnewline
Winsorized Mean ( 2 / 21 ) & 1.2792 & 0.0207593954632595 & 61.6202915091607 \tabularnewline
Winsorized Mean ( 3 / 21 ) & 1.27910769230769 & 0.0207459231754667 & 61.655857948048 \tabularnewline
Winsorized Mean ( 4 / 21 ) & 1.27867692307692 & 0.020527527340092 & 62.290840094489 \tabularnewline
Winsorized Mean ( 5 / 21 ) & 1.28075384615385 & 0.020051376688412 & 63.8736115757086 \tabularnewline
Winsorized Mean ( 6 / 21 ) & 1.28056923076923 & 0.0199626570755196 & 64.1482356744787 \tabularnewline
Winsorized Mean ( 7 / 21 ) & 1.28110769230769 & 0.0197781581533981 & 64.7738622763305 \tabularnewline
Winsorized Mean ( 8 / 21 ) & 1.28246153846154 & 0.0194220839426297 & 66.031098529373 \tabularnewline
Winsorized Mean ( 9 / 21 ) & 1.28301538461538 & 0.0191750099326483 & 66.9108067803846 \tabularnewline
Winsorized Mean ( 10 / 21 ) & 1.28393846153846 & 0.0188942893911794 & 67.9537840749839 \tabularnewline
Winsorized Mean ( 11 / 21 ) & 1.28376923076923 & 0.0185437342884584 & 69.2292723137351 \tabularnewline
Winsorized Mean ( 12 / 21 ) & 1.28321538461538 & 0.0183548554190879 & 69.9114950957837 \tabularnewline
Winsorized Mean ( 13 / 21 ) & 1.29021538461538 & 0.0168024507757352 & 76.7873331001577 \tabularnewline
Winsorized Mean ( 14 / 21 ) & 1.29 & 0.0167087753314515 & 77.2049401832453 \tabularnewline
Winsorized Mean ( 15 / 21 ) & 1.29830769230769 & 0.0149192203581378 & 87.0224891878829 \tabularnewline
Winsorized Mean ( 16 / 21 ) & 1.30544615384615 & 0.013765306703414 & 94.8359656615851 \tabularnewline
Winsorized Mean ( 17 / 21 ) & 1.30466153846154 & 0.0136629988283044 & 95.4886664967566 \tabularnewline
Winsorized Mean ( 18 / 21 ) & 1.30466153846154 & 0.0134262815769016 & 97.1722163719594 \tabularnewline
Winsorized Mean ( 19 / 21 ) & 1.30436923076923 & 0.0128946092125959 & 101.156166058533 \tabularnewline
Winsorized Mean ( 20 / 21 ) & 1.30529230769231 & 0.0125809632419253 & 103.751380764114 \tabularnewline
Winsorized Mean ( 21 / 21 ) & 1.30529230769231 & 0.0124015298970321 & 105.252522755655 \tabularnewline
Trimmed Mean ( 1 / 21 ) & 1.28084126984127 & 0.0206632498829231 & 61.9864385853364 \tabularnewline
Trimmed Mean ( 2 / 21 ) & 1.28268852459016 & 0.0204771169229797 & 62.6400937893124 \tabularnewline
Trimmed Mean ( 3 / 21 ) & 1.28461016949153 & 0.0202629559963401 & 63.3969777027375 \tabularnewline
Trimmed Mean ( 4 / 21 ) & 1.28670175438596 & 0.0199910375424898 & 64.3639306689886 \tabularnewline
Trimmed Mean ( 5 / 21 ) & 1.28907272727273 & 0.0197200927212061 & 65.3684922021952 \tabularnewline
Trimmed Mean ( 6 / 21 ) & 1.29111320754717 & 0.0195220774946676 & 66.1360558526537 \tabularnewline
Trimmed Mean ( 7 / 21 ) & 1.29335294117647 & 0.0192775562589553 & 67.0911252340738 \tabularnewline
Trimmed Mean ( 8 / 21 ) & 1.29567346938776 & 0.0189979946076285 & 68.2005388541108 \tabularnewline
Trimmed Mean ( 9 / 21 ) & 1.29795744680851 & 0.0187143174485236 & 69.3563871820988 \tabularnewline
Trimmed Mean ( 10 / 21 ) & 1.30035555555556 & 0.0183883240170802 & 70.7163716686583 \tabularnewline
Trimmed Mean ( 11 / 21 ) & 1.30283720930233 & 0.0180119601655721 & 72.3317838439682 \tabularnewline
Trimmed Mean ( 12 / 21 ) & 1.30558536585366 & 0.0175770767988419 & 74.2777300682717 \tabularnewline
Trimmed Mean ( 13 / 21 ) & 1.30869230769231 & 0.0170144875096925 & 76.916351841147 \tabularnewline
Trimmed Mean ( 14 / 21 ) & 1.31118918918919 & 0.016661027777522 & 78.6979775016137 \tabularnewline
Trimmed Mean ( 15 / 21 ) & 1.314 & 0.0161620470456524 & 81.3015824225969 \tabularnewline
Trimmed Mean ( 16 / 21 ) & 1.31606060606061 & 0.0159493718049762 & 82.5148866145308 \tabularnewline
Trimmed Mean ( 17 / 21 ) & 1.31745161290323 & 0.0159175860485254 & 82.7670482752174 \tabularnewline
Trimmed Mean ( 18 / 21 ) & 1.31913793103448 & 0.0158154943776253 & 83.4079478982783 \tabularnewline
Trimmed Mean ( 19 / 21 ) & 1.32107407407407 & 0.0156470076625472 & 84.4298221465185 \tabularnewline
Trimmed Mean ( 20 / 21 ) & 1.32336 & 0.0154610133346212 & 85.5933548053192 \tabularnewline
Trimmed Mean ( 21 / 21 ) & 1.32591304347826 & 0.0151712116919998 & 87.3966477033243 \tabularnewline
Median & 1.348 &  &  \tabularnewline
Midrange & 1.2255 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 1.31278125 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 1.31914705882353 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 1.31914705882353 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 1.31914705882353 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 1.31914705882353 &  &  \tabularnewline
Midmean - Closest Observation & 1.314 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 1.31914705882353 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 1.31914705882353 &  &  \tabularnewline
Number of observations & 65 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=234007&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]1.27913846153846[/C][C]0.0208858030190721[/C][C]61.2443993831793[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]1.26754486278997[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]1.2553326636179[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]1.29000506856488[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 21 )[/C][C]1.27910769230769[/C][C]0.0208035814579916[/C][C]61.4849753101686[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 21 )[/C][C]1.2792[/C][C]0.0207593954632595[/C][C]61.6202915091607[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 21 )[/C][C]1.27910769230769[/C][C]0.0207459231754667[/C][C]61.655857948048[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 21 )[/C][C]1.27867692307692[/C][C]0.020527527340092[/C][C]62.290840094489[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 21 )[/C][C]1.28075384615385[/C][C]0.020051376688412[/C][C]63.8736115757086[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 21 )[/C][C]1.28056923076923[/C][C]0.0199626570755196[/C][C]64.1482356744787[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 21 )[/C][C]1.28110769230769[/C][C]0.0197781581533981[/C][C]64.7738622763305[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 21 )[/C][C]1.28246153846154[/C][C]0.0194220839426297[/C][C]66.031098529373[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 21 )[/C][C]1.28301538461538[/C][C]0.0191750099326483[/C][C]66.9108067803846[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 21 )[/C][C]1.28393846153846[/C][C]0.0188942893911794[/C][C]67.9537840749839[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 21 )[/C][C]1.28376923076923[/C][C]0.0185437342884584[/C][C]69.2292723137351[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 21 )[/C][C]1.28321538461538[/C][C]0.0183548554190879[/C][C]69.9114950957837[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 21 )[/C][C]1.29021538461538[/C][C]0.0168024507757352[/C][C]76.7873331001577[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 21 )[/C][C]1.29[/C][C]0.0167087753314515[/C][C]77.2049401832453[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 21 )[/C][C]1.29830769230769[/C][C]0.0149192203581378[/C][C]87.0224891878829[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 21 )[/C][C]1.30544615384615[/C][C]0.013765306703414[/C][C]94.8359656615851[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 21 )[/C][C]1.30466153846154[/C][C]0.0136629988283044[/C][C]95.4886664967566[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 21 )[/C][C]1.30466153846154[/C][C]0.0134262815769016[/C][C]97.1722163719594[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 21 )[/C][C]1.30436923076923[/C][C]0.0128946092125959[/C][C]101.156166058533[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 21 )[/C][C]1.30529230769231[/C][C]0.0125809632419253[/C][C]103.751380764114[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 21 )[/C][C]1.30529230769231[/C][C]0.0124015298970321[/C][C]105.252522755655[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 21 )[/C][C]1.28084126984127[/C][C]0.0206632498829231[/C][C]61.9864385853364[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 21 )[/C][C]1.28268852459016[/C][C]0.0204771169229797[/C][C]62.6400937893124[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 21 )[/C][C]1.28461016949153[/C][C]0.0202629559963401[/C][C]63.3969777027375[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 21 )[/C][C]1.28670175438596[/C][C]0.0199910375424898[/C][C]64.3639306689886[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 21 )[/C][C]1.28907272727273[/C][C]0.0197200927212061[/C][C]65.3684922021952[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 21 )[/C][C]1.29111320754717[/C][C]0.0195220774946676[/C][C]66.1360558526537[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 21 )[/C][C]1.29335294117647[/C][C]0.0192775562589553[/C][C]67.0911252340738[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 21 )[/C][C]1.29567346938776[/C][C]0.0189979946076285[/C][C]68.2005388541108[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 21 )[/C][C]1.29795744680851[/C][C]0.0187143174485236[/C][C]69.3563871820988[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 21 )[/C][C]1.30035555555556[/C][C]0.0183883240170802[/C][C]70.7163716686583[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 21 )[/C][C]1.30283720930233[/C][C]0.0180119601655721[/C][C]72.3317838439682[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 21 )[/C][C]1.30558536585366[/C][C]0.0175770767988419[/C][C]74.2777300682717[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 21 )[/C][C]1.30869230769231[/C][C]0.0170144875096925[/C][C]76.916351841147[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 21 )[/C][C]1.31118918918919[/C][C]0.016661027777522[/C][C]78.6979775016137[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 21 )[/C][C]1.314[/C][C]0.0161620470456524[/C][C]81.3015824225969[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 21 )[/C][C]1.31606060606061[/C][C]0.0159493718049762[/C][C]82.5148866145308[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 21 )[/C][C]1.31745161290323[/C][C]0.0159175860485254[/C][C]82.7670482752174[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 21 )[/C][C]1.31913793103448[/C][C]0.0158154943776253[/C][C]83.4079478982783[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 21 )[/C][C]1.32107407407407[/C][C]0.0156470076625472[/C][C]84.4298221465185[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 21 )[/C][C]1.32336[/C][C]0.0154610133346212[/C][C]85.5933548053192[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 21 )[/C][C]1.32591304347826[/C][C]0.0151712116919998[/C][C]87.3966477033243[/C][/ROW]
[ROW][C]Median[/C][C]1.348[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]1.2255[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]1.31278125[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]1.31914705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]1.31914705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]1.31914705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]1.31914705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]1.314[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]1.31914705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]1.31914705882353[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]65[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=234007&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=234007&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 Mean1.279138461538460.020885803019072161.2443993831793
Geometric Mean1.26754486278997
Harmonic Mean1.2553326636179
Quadratic Mean1.29000506856488
Winsorized Mean ( 1 / 21 )1.279107692307690.020803581457991661.4849753101686
Winsorized Mean ( 2 / 21 )1.27920.020759395463259561.6202915091607
Winsorized Mean ( 3 / 21 )1.279107692307690.020745923175466761.655857948048
Winsorized Mean ( 4 / 21 )1.278676923076920.02052752734009262.290840094489
Winsorized Mean ( 5 / 21 )1.280753846153850.02005137668841263.8736115757086
Winsorized Mean ( 6 / 21 )1.280569230769230.019962657075519664.1482356744787
Winsorized Mean ( 7 / 21 )1.281107692307690.019778158153398164.7738622763305
Winsorized Mean ( 8 / 21 )1.282461538461540.019422083942629766.031098529373
Winsorized Mean ( 9 / 21 )1.283015384615380.019175009932648366.9108067803846
Winsorized Mean ( 10 / 21 )1.283938461538460.018894289391179467.9537840749839
Winsorized Mean ( 11 / 21 )1.283769230769230.018543734288458469.2292723137351
Winsorized Mean ( 12 / 21 )1.283215384615380.018354855419087969.9114950957837
Winsorized Mean ( 13 / 21 )1.290215384615380.016802450775735276.7873331001577
Winsorized Mean ( 14 / 21 )1.290.016708775331451577.2049401832453
Winsorized Mean ( 15 / 21 )1.298307692307690.014919220358137887.0224891878829
Winsorized Mean ( 16 / 21 )1.305446153846150.01376530670341494.8359656615851
Winsorized Mean ( 17 / 21 )1.304661538461540.013662998828304495.4886664967566
Winsorized Mean ( 18 / 21 )1.304661538461540.013426281576901697.1722163719594
Winsorized Mean ( 19 / 21 )1.304369230769230.0128946092125959101.156166058533
Winsorized Mean ( 20 / 21 )1.305292307692310.0125809632419253103.751380764114
Winsorized Mean ( 21 / 21 )1.305292307692310.0124015298970321105.252522755655
Trimmed Mean ( 1 / 21 )1.280841269841270.020663249882923161.9864385853364
Trimmed Mean ( 2 / 21 )1.282688524590160.020477116922979762.6400937893124
Trimmed Mean ( 3 / 21 )1.284610169491530.020262955996340163.3969777027375
Trimmed Mean ( 4 / 21 )1.286701754385960.019991037542489864.3639306689886
Trimmed Mean ( 5 / 21 )1.289072727272730.019720092721206165.3684922021952
Trimmed Mean ( 6 / 21 )1.291113207547170.019522077494667666.1360558526537
Trimmed Mean ( 7 / 21 )1.293352941176470.019277556258955367.0911252340738
Trimmed Mean ( 8 / 21 )1.295673469387760.018997994607628568.2005388541108
Trimmed Mean ( 9 / 21 )1.297957446808510.018714317448523669.3563871820988
Trimmed Mean ( 10 / 21 )1.300355555555560.018388324017080270.7163716686583
Trimmed Mean ( 11 / 21 )1.302837209302330.018011960165572172.3317838439682
Trimmed Mean ( 12 / 21 )1.305585365853660.017577076798841974.2777300682717
Trimmed Mean ( 13 / 21 )1.308692307692310.017014487509692576.916351841147
Trimmed Mean ( 14 / 21 )1.311189189189190.01666102777752278.6979775016137
Trimmed Mean ( 15 / 21 )1.3140.016162047045652481.3015824225969
Trimmed Mean ( 16 / 21 )1.316060606060610.015949371804976282.5148866145308
Trimmed Mean ( 17 / 21 )1.317451612903230.015917586048525482.7670482752174
Trimmed Mean ( 18 / 21 )1.319137931034480.015815494377625383.4079478982783
Trimmed Mean ( 19 / 21 )1.321074074074070.015647007662547284.4298221465185
Trimmed Mean ( 20 / 21 )1.323360.015461013334621285.5933548053192
Trimmed Mean ( 21 / 21 )1.325913043478260.015171211691999887.3966477033243
Median1.348
Midrange1.2255
Midmean - Weighted Average at Xnp1.31278125
Midmean - Weighted Average at X(n+1)p1.31914705882353
Midmean - Empirical Distribution Function1.31914705882353
Midmean - Empirical Distribution Function - Averaging1.31914705882353
Midmean - Empirical Distribution Function - Interpolation1.31914705882353
Midmean - Closest Observation1.314
Midmean - True Basic - Statistics Graphics Toolkit1.31914705882353
Midmean - MS Excel (old versions)1.31914705882353
Number of observations65


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')