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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 10 Dec 2010 14:17:35 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/10/t1291990540fnbgg1gc08naeph.htm/, Retrieved Mon, 29 Apr 2024 14:14:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=107710, Retrieved Mon, 29 Apr 2024 14:14:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [Classiscal Decomp...] [2010-12-10 12:54:42] [05ab9592748364013445d860bb938e43]
- RMP     [Central Tendency] [Central Tendency:...] [2010-12-10 14:17:35] [60147a93d53c93401a082f47876e6cb5] [Current]
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Dataseries X:
4143
4429
5219
4929
5761
5592
4163
4962
5208
4755
4491
5732
5731
5040
6102
4904
5369
5578
4619
4731
5011
5299
4146
4625
4736
4219
5116
4205
4121
5103
4300
4578
3809
5657
4248
3830
4736
4839
4411
4570
4104
4801
3953
3828
4440
4026
4109
4785
3224
3552
3940
3913
3681
4309
3830
4143
4087
3818
3380
3430
3458
3970
5260
5024
5634
6549
4676




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=107710&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=107710&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107710&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean4581.2089552238887.054518332246552.6245971259015
Geometric Mean4527.52601444762
Harmonic Mean4474.7490542078
Quadratic Mean4635.47794473444
Winsorized Mean ( 1 / 22 )4576.8656716417984.47071728404754.1828673746348
Winsorized Mean ( 2 / 22 )4568.1791044776181.629098860706655.9626305843807
Winsorized Mean ( 3 / 22 )4568.1343283582181.08165444883556.3399249732976
Winsorized Mean ( 4 / 22 )4573.6865671641879.942901969374657.211915685977
Winsorized Mean ( 5 / 22 )4577.7910447761276.966874926572559.4774186836012
Winsorized Mean ( 6 / 22 )4587.1940298507574.609955886095961.4823313507092
Winsorized Mean ( 7 / 22 )4583.7462686567273.539220078614962.3306347790553
Winsorized Mean ( 8 / 22 )4583.2686567164273.00526173886562.7799770530304
Winsorized Mean ( 9 / 22 )4555.4626865671667.487420568822467.5009156991204
Winsorized Mean ( 10 / 22 )4545.0149253731365.62327378802669.2591920978262
Winsorized Mean ( 11 / 22 )4552.2388059701562.329714071560973.034809701577
Winsorized Mean ( 12 / 22 )4549.7313432835860.334652371902675.4082631526416
Winsorized Mean ( 13 / 22 )4550.1194029850759.592189857305776.3542909545763
Winsorized Mean ( 14 / 22 )4534.4477611940355.925850160984681.0796393464107
Winsorized Mean ( 15 / 22 )4544.0746268656753.588926982870484.7950291730637
Winsorized Mean ( 16 / 22 )4543.5970149253749.153692726839292.4365345280447
Winsorized Mean ( 17 / 22 )4543.8507462686647.931511394815194.7988205262432
Winsorized Mean ( 18 / 22 )4541.7014925373147.216827212500196.1881973157008
Winsorized Mean ( 19 / 22 )4531.2089552238844.6818166452707101.410580308253
Winsorized Mean ( 20 / 22 )4527.9253731343342.346048689753106.926750269146
Winsorized Mean ( 21 / 22 )4520.0895522388141.230945087521109.628570061734
Winsorized Mean ( 22 / 22 )4499.7313432835838.147335014945117.956636853419
Trimmed Mean ( 1 / 22 )4571.8153846153881.73615765042855.9338182272805
Trimmed Mean ( 2 / 22 )4566.4444444444478.432576860928558.2212726803732
Trimmed Mean ( 3 / 22 )4565.4918032786976.304493643863159.832541771226
Trimmed Mean ( 4 / 22 )4564.4915254237373.967778430784361.7091877336153
Trimmed Mean ( 5 / 22 )4561.7894736842171.539330266390763.7661752870413
Trimmed Mean ( 6 / 22 )4557.8909090909169.534642059055765.5484917175514
Trimmed Mean ( 7 / 22 )4551.7169811320867.72071573128267.213066666239
Trimmed Mean ( 8 / 22 )4545.7058823529465.729411413751169.1578668450079
Trimmed Mean ( 9 / 22 )4539.2857142857163.333402703148571.6728538266277
Trimmed Mean ( 10 / 22 )4536.7234042553261.744352995659473.4759242610291
Trimmed Mean ( 11 / 22 )4535.4888888888960.141840947444475.4132034776301
Trimmed Mean ( 12 / 22 )4533.1162790697758.823319831832177.0632513096733
Trimmed Mean ( 13 / 22 )4530.8536585365957.523362814446578.765451754825
Trimmed Mean ( 14 / 22 )4528.3076923076955.918066553966380.9811206175635
Trimmed Mean ( 15 / 22 )4527.5135135135154.640850606367982.8594991342589
Trimmed Mean ( 16 / 22 )4525.453.405004014432184.7373777703876
Trimmed Mean ( 17 / 22 )4523.0909090909152.735840474229885.7688218944986
Trimmed Mean ( 18 / 22 )4520.4516129032351.951649123848687.0126683009971
Trimmed Mean ( 19 / 22 )4517.7241379310350.853549424240388.8379314537595
Trimmed Mean ( 20 / 22 )4515.9629629629649.857988683457590.5765170679925
Trimmed Mean ( 21 / 22 )4514.3648.909436035731792.3003895751721
Trimmed Mean ( 22 / 22 )4513.565217391347.580546481789894.86156740799
Median4570
Midrange4886.5
Midmean - Weighted Average at Xnp4510.26470588235
Midmean - Weighted Average at X(n+1)p4525.4
Midmean - Empirical Distribution Function4525.4
Midmean - Empirical Distribution Function - Averaging4525.4
Midmean - Empirical Distribution Function - Interpolation4523.09090909091
Midmean - Closest Observation4510.26470588235
Midmean - True Basic - Statistics Graphics Toolkit4525.4
Midmean - MS Excel (old versions)4525.4
Number of observations67

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 4581.20895522388 & 87.0545183322465 & 52.6245971259015 \tabularnewline
Geometric Mean & 4527.52601444762 &  &  \tabularnewline
Harmonic Mean & 4474.7490542078 &  &  \tabularnewline
Quadratic Mean & 4635.47794473444 &  &  \tabularnewline
Winsorized Mean ( 1 / 22 ) & 4576.86567164179 & 84.470717284047 & 54.1828673746348 \tabularnewline
Winsorized Mean ( 2 / 22 ) & 4568.17910447761 & 81.6290988607066 & 55.9626305843807 \tabularnewline
Winsorized Mean ( 3 / 22 ) & 4568.13432835821 & 81.081654448835 & 56.3399249732976 \tabularnewline
Winsorized Mean ( 4 / 22 ) & 4573.68656716418 & 79.9429019693746 & 57.211915685977 \tabularnewline
Winsorized Mean ( 5 / 22 ) & 4577.79104477612 & 76.9668749265725 & 59.4774186836012 \tabularnewline
Winsorized Mean ( 6 / 22 ) & 4587.19402985075 & 74.6099558860959 & 61.4823313507092 \tabularnewline
Winsorized Mean ( 7 / 22 ) & 4583.74626865672 & 73.5392200786149 & 62.3306347790553 \tabularnewline
Winsorized Mean ( 8 / 22 ) & 4583.26865671642 & 73.005261738865 & 62.7799770530304 \tabularnewline
Winsorized Mean ( 9 / 22 ) & 4555.46268656716 & 67.4874205688224 & 67.5009156991204 \tabularnewline
Winsorized Mean ( 10 / 22 ) & 4545.01492537313 & 65.623273788026 & 69.2591920978262 \tabularnewline
Winsorized Mean ( 11 / 22 ) & 4552.23880597015 & 62.3297140715609 & 73.034809701577 \tabularnewline
Winsorized Mean ( 12 / 22 ) & 4549.73134328358 & 60.3346523719026 & 75.4082631526416 \tabularnewline
Winsorized Mean ( 13 / 22 ) & 4550.11940298507 & 59.5921898573057 & 76.3542909545763 \tabularnewline
Winsorized Mean ( 14 / 22 ) & 4534.44776119403 & 55.9258501609846 & 81.0796393464107 \tabularnewline
Winsorized Mean ( 15 / 22 ) & 4544.07462686567 & 53.5889269828704 & 84.7950291730637 \tabularnewline
Winsorized Mean ( 16 / 22 ) & 4543.59701492537 & 49.1536927268392 & 92.4365345280447 \tabularnewline
Winsorized Mean ( 17 / 22 ) & 4543.85074626866 & 47.9315113948151 & 94.7988205262432 \tabularnewline
Winsorized Mean ( 18 / 22 ) & 4541.70149253731 & 47.2168272125001 & 96.1881973157008 \tabularnewline
Winsorized Mean ( 19 / 22 ) & 4531.20895522388 & 44.6818166452707 & 101.410580308253 \tabularnewline
Winsorized Mean ( 20 / 22 ) & 4527.92537313433 & 42.346048689753 & 106.926750269146 \tabularnewline
Winsorized Mean ( 21 / 22 ) & 4520.08955223881 & 41.230945087521 & 109.628570061734 \tabularnewline
Winsorized Mean ( 22 / 22 ) & 4499.73134328358 & 38.147335014945 & 117.956636853419 \tabularnewline
Trimmed Mean ( 1 / 22 ) & 4571.81538461538 & 81.736157650428 & 55.9338182272805 \tabularnewline
Trimmed Mean ( 2 / 22 ) & 4566.44444444444 & 78.4325768609285 & 58.2212726803732 \tabularnewline
Trimmed Mean ( 3 / 22 ) & 4565.49180327869 & 76.3044936438631 & 59.832541771226 \tabularnewline
Trimmed Mean ( 4 / 22 ) & 4564.49152542373 & 73.9677784307843 & 61.7091877336153 \tabularnewline
Trimmed Mean ( 5 / 22 ) & 4561.78947368421 & 71.5393302663907 & 63.7661752870413 \tabularnewline
Trimmed Mean ( 6 / 22 ) & 4557.89090909091 & 69.5346420590557 & 65.5484917175514 \tabularnewline
Trimmed Mean ( 7 / 22 ) & 4551.71698113208 & 67.720715731282 & 67.213066666239 \tabularnewline
Trimmed Mean ( 8 / 22 ) & 4545.70588235294 & 65.7294114137511 & 69.1578668450079 \tabularnewline
Trimmed Mean ( 9 / 22 ) & 4539.28571428571 & 63.3334027031485 & 71.6728538266277 \tabularnewline
Trimmed Mean ( 10 / 22 ) & 4536.72340425532 & 61.7443529956594 & 73.4759242610291 \tabularnewline
Trimmed Mean ( 11 / 22 ) & 4535.48888888889 & 60.1418409474444 & 75.4132034776301 \tabularnewline
Trimmed Mean ( 12 / 22 ) & 4533.11627906977 & 58.8233198318321 & 77.0632513096733 \tabularnewline
Trimmed Mean ( 13 / 22 ) & 4530.85365853659 & 57.5233628144465 & 78.765451754825 \tabularnewline
Trimmed Mean ( 14 / 22 ) & 4528.30769230769 & 55.9180665539663 & 80.9811206175635 \tabularnewline
Trimmed Mean ( 15 / 22 ) & 4527.51351351351 & 54.6408506063679 & 82.8594991342589 \tabularnewline
Trimmed Mean ( 16 / 22 ) & 4525.4 & 53.4050040144321 & 84.7373777703876 \tabularnewline
Trimmed Mean ( 17 / 22 ) & 4523.09090909091 & 52.7358404742298 & 85.7688218944986 \tabularnewline
Trimmed Mean ( 18 / 22 ) & 4520.45161290323 & 51.9516491238486 & 87.0126683009971 \tabularnewline
Trimmed Mean ( 19 / 22 ) & 4517.72413793103 & 50.8535494242403 & 88.8379314537595 \tabularnewline
Trimmed Mean ( 20 / 22 ) & 4515.96296296296 & 49.8579886834575 & 90.5765170679925 \tabularnewline
Trimmed Mean ( 21 / 22 ) & 4514.36 & 48.9094360357317 & 92.3003895751721 \tabularnewline
Trimmed Mean ( 22 / 22 ) & 4513.5652173913 & 47.5805464817898 & 94.86156740799 \tabularnewline
Median & 4570 &  &  \tabularnewline
Midrange & 4886.5 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 4510.26470588235 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 4525.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 4525.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 4525.4 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 4523.09090909091 &  &  \tabularnewline
Midmean - Closest Observation & 4510.26470588235 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 4525.4 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 4525.4 &  &  \tabularnewline
Number of observations & 67 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107710&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]4581.20895522388[/C][C]87.0545183322465[/C][C]52.6245971259015[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]4527.52601444762[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]4474.7490542078[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]4635.47794473444[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 22 )[/C][C]4576.86567164179[/C][C]84.470717284047[/C][C]54.1828673746348[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 22 )[/C][C]4568.17910447761[/C][C]81.6290988607066[/C][C]55.9626305843807[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 22 )[/C][C]4568.13432835821[/C][C]81.081654448835[/C][C]56.3399249732976[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 22 )[/C][C]4573.68656716418[/C][C]79.9429019693746[/C][C]57.211915685977[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 22 )[/C][C]4577.79104477612[/C][C]76.9668749265725[/C][C]59.4774186836012[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 22 )[/C][C]4587.19402985075[/C][C]74.6099558860959[/C][C]61.4823313507092[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 22 )[/C][C]4583.74626865672[/C][C]73.5392200786149[/C][C]62.3306347790553[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 22 )[/C][C]4583.26865671642[/C][C]73.005261738865[/C][C]62.7799770530304[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 22 )[/C][C]4555.46268656716[/C][C]67.4874205688224[/C][C]67.5009156991204[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 22 )[/C][C]4545.01492537313[/C][C]65.623273788026[/C][C]69.2591920978262[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 22 )[/C][C]4552.23880597015[/C][C]62.3297140715609[/C][C]73.034809701577[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 22 )[/C][C]4549.73134328358[/C][C]60.3346523719026[/C][C]75.4082631526416[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 22 )[/C][C]4550.11940298507[/C][C]59.5921898573057[/C][C]76.3542909545763[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 22 )[/C][C]4534.44776119403[/C][C]55.9258501609846[/C][C]81.0796393464107[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 22 )[/C][C]4544.07462686567[/C][C]53.5889269828704[/C][C]84.7950291730637[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 22 )[/C][C]4543.59701492537[/C][C]49.1536927268392[/C][C]92.4365345280447[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 22 )[/C][C]4543.85074626866[/C][C]47.9315113948151[/C][C]94.7988205262432[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 22 )[/C][C]4541.70149253731[/C][C]47.2168272125001[/C][C]96.1881973157008[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 22 )[/C][C]4531.20895522388[/C][C]44.6818166452707[/C][C]101.410580308253[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 22 )[/C][C]4527.92537313433[/C][C]42.346048689753[/C][C]106.926750269146[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 22 )[/C][C]4520.08955223881[/C][C]41.230945087521[/C][C]109.628570061734[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 22 )[/C][C]4499.73134328358[/C][C]38.147335014945[/C][C]117.956636853419[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 22 )[/C][C]4571.81538461538[/C][C]81.736157650428[/C][C]55.9338182272805[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 22 )[/C][C]4566.44444444444[/C][C]78.4325768609285[/C][C]58.2212726803732[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 22 )[/C][C]4565.49180327869[/C][C]76.3044936438631[/C][C]59.832541771226[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 22 )[/C][C]4564.49152542373[/C][C]73.9677784307843[/C][C]61.7091877336153[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 22 )[/C][C]4561.78947368421[/C][C]71.5393302663907[/C][C]63.7661752870413[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 22 )[/C][C]4557.89090909091[/C][C]69.5346420590557[/C][C]65.5484917175514[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 22 )[/C][C]4551.71698113208[/C][C]67.720715731282[/C][C]67.213066666239[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 22 )[/C][C]4545.70588235294[/C][C]65.7294114137511[/C][C]69.1578668450079[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 22 )[/C][C]4539.28571428571[/C][C]63.3334027031485[/C][C]71.6728538266277[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 22 )[/C][C]4536.72340425532[/C][C]61.7443529956594[/C][C]73.4759242610291[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 22 )[/C][C]4535.48888888889[/C][C]60.1418409474444[/C][C]75.4132034776301[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 22 )[/C][C]4533.11627906977[/C][C]58.8233198318321[/C][C]77.0632513096733[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 22 )[/C][C]4530.85365853659[/C][C]57.5233628144465[/C][C]78.765451754825[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 22 )[/C][C]4528.30769230769[/C][C]55.9180665539663[/C][C]80.9811206175635[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 22 )[/C][C]4527.51351351351[/C][C]54.6408506063679[/C][C]82.8594991342589[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 22 )[/C][C]4525.4[/C][C]53.4050040144321[/C][C]84.7373777703876[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 22 )[/C][C]4523.09090909091[/C][C]52.7358404742298[/C][C]85.7688218944986[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 22 )[/C][C]4520.45161290323[/C][C]51.9516491238486[/C][C]87.0126683009971[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 22 )[/C][C]4517.72413793103[/C][C]50.8535494242403[/C][C]88.8379314537595[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 22 )[/C][C]4515.96296296296[/C][C]49.8579886834575[/C][C]90.5765170679925[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 22 )[/C][C]4514.36[/C][C]48.9094360357317[/C][C]92.3003895751721[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 22 )[/C][C]4513.5652173913[/C][C]47.5805464817898[/C][C]94.86156740799[/C][/ROW]
[ROW][C]Median[/C][C]4570[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]4886.5[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]4510.26470588235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]4525.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]4525.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]4525.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]4523.09090909091[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]4510.26470588235[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]4525.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]4525.4[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]67[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107710&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107710&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 Mean4581.2089552238887.054518332246552.6245971259015
Geometric Mean4527.52601444762
Harmonic Mean4474.7490542078
Quadratic Mean4635.47794473444
Winsorized Mean ( 1 / 22 )4576.8656716417984.47071728404754.1828673746348
Winsorized Mean ( 2 / 22 )4568.1791044776181.629098860706655.9626305843807
Winsorized Mean ( 3 / 22 )4568.1343283582181.08165444883556.3399249732976
Winsorized Mean ( 4 / 22 )4573.6865671641879.942901969374657.211915685977
Winsorized Mean ( 5 / 22 )4577.7910447761276.966874926572559.4774186836012
Winsorized Mean ( 6 / 22 )4587.1940298507574.609955886095961.4823313507092
Winsorized Mean ( 7 / 22 )4583.7462686567273.539220078614962.3306347790553
Winsorized Mean ( 8 / 22 )4583.2686567164273.00526173886562.7799770530304
Winsorized Mean ( 9 / 22 )4555.4626865671667.487420568822467.5009156991204
Winsorized Mean ( 10 / 22 )4545.0149253731365.62327378802669.2591920978262
Winsorized Mean ( 11 / 22 )4552.2388059701562.329714071560973.034809701577
Winsorized Mean ( 12 / 22 )4549.7313432835860.334652371902675.4082631526416
Winsorized Mean ( 13 / 22 )4550.1194029850759.592189857305776.3542909545763
Winsorized Mean ( 14 / 22 )4534.4477611940355.925850160984681.0796393464107
Winsorized Mean ( 15 / 22 )4544.0746268656753.588926982870484.7950291730637
Winsorized Mean ( 16 / 22 )4543.5970149253749.153692726839292.4365345280447
Winsorized Mean ( 17 / 22 )4543.8507462686647.931511394815194.7988205262432
Winsorized Mean ( 18 / 22 )4541.7014925373147.216827212500196.1881973157008
Winsorized Mean ( 19 / 22 )4531.2089552238844.6818166452707101.410580308253
Winsorized Mean ( 20 / 22 )4527.9253731343342.346048689753106.926750269146
Winsorized Mean ( 21 / 22 )4520.0895522388141.230945087521109.628570061734
Winsorized Mean ( 22 / 22 )4499.7313432835838.147335014945117.956636853419
Trimmed Mean ( 1 / 22 )4571.8153846153881.73615765042855.9338182272805
Trimmed Mean ( 2 / 22 )4566.4444444444478.432576860928558.2212726803732
Trimmed Mean ( 3 / 22 )4565.4918032786976.304493643863159.832541771226
Trimmed Mean ( 4 / 22 )4564.4915254237373.967778430784361.7091877336153
Trimmed Mean ( 5 / 22 )4561.7894736842171.539330266390763.7661752870413
Trimmed Mean ( 6 / 22 )4557.8909090909169.534642059055765.5484917175514
Trimmed Mean ( 7 / 22 )4551.7169811320867.72071573128267.213066666239
Trimmed Mean ( 8 / 22 )4545.7058823529465.729411413751169.1578668450079
Trimmed Mean ( 9 / 22 )4539.2857142857163.333402703148571.6728538266277
Trimmed Mean ( 10 / 22 )4536.7234042553261.744352995659473.4759242610291
Trimmed Mean ( 11 / 22 )4535.4888888888960.141840947444475.4132034776301
Trimmed Mean ( 12 / 22 )4533.1162790697758.823319831832177.0632513096733
Trimmed Mean ( 13 / 22 )4530.8536585365957.523362814446578.765451754825
Trimmed Mean ( 14 / 22 )4528.3076923076955.918066553966380.9811206175635
Trimmed Mean ( 15 / 22 )4527.5135135135154.640850606367982.8594991342589
Trimmed Mean ( 16 / 22 )4525.453.405004014432184.7373777703876
Trimmed Mean ( 17 / 22 )4523.0909090909152.735840474229885.7688218944986
Trimmed Mean ( 18 / 22 )4520.4516129032351.951649123848687.0126683009971
Trimmed Mean ( 19 / 22 )4517.7241379310350.853549424240388.8379314537595
Trimmed Mean ( 20 / 22 )4515.9629629629649.857988683457590.5765170679925
Trimmed Mean ( 21 / 22 )4514.3648.909436035731792.3003895751721
Trimmed Mean ( 22 / 22 )4513.565217391347.580546481789894.86156740799
Median4570
Midrange4886.5
Midmean - Weighted Average at Xnp4510.26470588235
Midmean - Weighted Average at X(n+1)p4525.4
Midmean - Empirical Distribution Function4525.4
Midmean - Empirical Distribution Function - Averaging4525.4
Midmean - Empirical Distribution Function - Interpolation4523.09090909091
Midmean - Closest Observation4510.26470588235
Midmean - True Basic - Statistics Graphics Toolkit4525.4
Midmean - MS Excel (old versions)4525.4
Number of observations67



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')