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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, 25 Nov 2011 05:45:35 -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/2011/Nov/25/t1322217954rozyav7nyd9kvub.htm/, Retrieved Fri, 02 Jun 2023 08:05:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147281, Retrieved Fri, 02 Jun 2023 08:05:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [Central Tendency] [2011-11-25 10:45:35] [f59ea4acf51788e47c4ec521df29536b] [Current]
- R       [Central Tendency] [] [2011-11-28 18:01:22] [74be16979710d4c4e7c6647856088456]
- R       [Central Tendency] [] [2011-11-28 18:02:19] [74be16979710d4c4e7c6647856088456]
- R       [Central Tendency] [] [2011-11-28 18:03:26] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
250.7826087
363.9254658
8.211180124
359.6283644
81.12836439
258.6283644
464.9616977
720.6283644
204.2950311
230.1283644
231.7950311
-210.7049689
155.6645963
185.8074534
-74.9068323
-28.48964803
62.01035197
22.51035197
-283.1563147
-126.489648
-535.8229814
7.010351967
-190.3229814
-276.8229814
-108.4534161
-341.310559
-126.0248447
-80.60766046
-223.1076605
-551.6076605
107.7256729
-418.6076605
-218.9409938
97.89233954
-516.4409938
-71.94099379
-416.5714286
-374.4285714
79.85714286
-92.72567288
116.7743271
-196.7256729
-288.3923395
-604.7256729
158.9409938
107.7743271
22.44099379
3.940993789
-321.689441
49.45341615
341.7391304
-210.8436853
14.6563147
189.1563147
79.48964803
-40.8436853
131.8229814
-342.3436853
218.3229814
81.82298137
2.192546584
-111.6645963
83.62111801
53.03830228
-51.46169772
278.0383023
-80.62836439
470.0383023
259.7049689
-100.4616977
234.2049689
473.7049689
438.0745342
228.2173913
-312.4968944




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147281&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147281&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147281&T=0

As an alternative you can also use a QR Code:  

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

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







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean-6.13332149512757e-1030.9275684550942-1.98312437786144e-11
Geometric MeanNaN
Harmonic Mean66.6668169780017
Quadratic Mean266.049003569447
Winsorized Mean ( 1 / 25 )-2.5840717752829.8700598694115-0.0865104317359011
Winsorized Mean ( 2 / 25 )-2.2609247752829.7457417568294-0.0760083508343142
Winsorized Mean ( 3 / 25 )-1.6887094552829.5169382507144-0.0572115387082579
Winsorized Mean ( 4 / 25 )2.0950862673866728.06775637553120.0746438810197567
Winsorized Mean ( 5 / 25 )-2.7124361659466727.0675521681831-0.10020988041671
Winsorized Mean ( 6 / 25 )0.31522429805333326.33156551780430.011971346627309
Winsorized Mean ( 7 / 25 )1.6401518273866725.46537752918060.0644071278938326
Winsorized Mean ( 8 / 25 )-5.0444030312824.2950870897116-0.207630580316635
Winsorized Mean ( 9 / 25 )-4.8898688792823.5199848406187-0.207902722404619
Winsorized Mean ( 10 / 25 )-3.8077432659466723.2767539805073-0.163585664441674
Winsorized Mean ( 11 / 25 )-1.4231193832822.4799258068735-0.0633062313241652
Winsorized Mean ( 12 / 25 )-3.2377777832821.9403398841707-0.14757190637762
Winsorized Mean ( 13 / 25 )-2.5577225632821.6908748344593-0.117916985036337
Winsorized Mean ( 14 / 25 )7.1580262207220.0052089078820.357808121558769
Winsorized Mean ( 15 / 25 )7.6091649407219.81850321617120.383942463147831
Winsorized Mean ( 16 / 25 )7.2257833087219.23746089136240.375610032401124
Winsorized Mean ( 17 / 25 )4.0775569580533318.76758937580050.217265887291367
Winsorized Mean ( 18 / 25 )3.7992960620533317.73307498403270.214249139840343
Winsorized Mean ( 19 / 25 )4.5729330460533417.36640016102640.26332072298529
Winsorized Mean ( 20 / 25 )14.430766059386713.88548478816861.03926987638794
Winsorized Mean ( 21 / 25 )13.643519683386713.73903315294010.993048021029557
Winsorized Mean ( 22 / 25 )10.862318843386712.20582903280710.889928804851412
Winsorized Mean ( 23 / 25 )7.2321601193866611.46460625986520.630824989141121
Winsorized Mean ( 24 / 25 )6.9095100073866610.74894476267260.6428082160568
Winsorized Mean ( 25 / 25 )9.4719668807210.4016026228550.910625720300801
Trimmed Mean ( 1 / 25 )-1.5877081033698629.0104197934135-0.0547288910217816
Trimmed Mean ( 2 / 25 )-0.5352112668450727.9945715374823-0.0191183946547804
Trimmed Mean ( 3 / 25 )0.40267650947826126.8673296853080.0149875895444294
Trimmed Mean ( 4 / 25 )1.1830444067761225.62627106229280.0461652966949563
Trimmed Mean ( 5 / 25 )0.91995540852307724.69452796632760.037253411354025
Trimmed Mean ( 6 / 25 )1.7848105453015923.89777480912120.0746852190029159
Trimmed Mean ( 7 / 25 )2.0859552680983623.14799600258850.0901138598721504
Trimmed Mean ( 8 / 25 )2.1669123093898322.4658994003630.0964533968025698
Trimmed Mean ( 9 / 25 )3.3529839114736821.91475242389850.153001222492351
Trimmed Mean ( 10 / 25 )4.6019010009818221.41087264554440.21493290241673
Trimmed Mean ( 11 / 25 )5.7919450010188720.83496113984310.277991639252104
Trimmed Mean ( 12 / 25 )6.7565258010588220.28962083292310.333004044614539
Trimmed Mean ( 13 / 25 )8.031309421510219.71192771429610.407433993159659
Trimmed Mean ( 14 / 25 )9.3311087649787219.0257842228910.490445421626928
Trimmed Mean ( 15 / 25 )9.5898090678666718.52952250925410.517542158092702
Trimmed Mean ( 16 / 25 )9.8201165245116317.91750686529530.548073825133137
Trimmed Mean ( 17 / 25 )10.116724742780517.2432975891210.586704758210705
Trimmed Mean ( 18 / 25 )10.799888519333316.45214945255730.656442402889465
Trimmed Mean ( 19 / 25 )11.588243525783815.65000180824920.740462759542656
Trimmed Mean ( 20 / 25 )12.379443955828614.64121211214810.845520429661499
Trimmed Mean ( 21 / 25 )12.146339171333314.24646932178680.85258592125406
Trimmed Mean ( 22 / 25 )11.973852937225813.70338885148990.873787722656936
Trimmed Mean ( 23 / 25 )12.104519170827613.36247643667170.905858972189333
Trimmed Mean ( 24 / 25 )12.692968331629613.04648475926910.972903319617317
Trimmed Mean ( 25 / 25 )13.4159006221612.75607356800741.0517265011553
Median14.6563147
Midrange57.95134575
Midmean - Weighted Average at Xnp6.10629835668421
Midmean - Weighted Average at X(n+1)p10.7998885193333
Midmean - Empirical Distribution Function10.7998885193333
Midmean - Empirical Distribution Function - Averaging10.7998885193333
Midmean - Empirical Distribution Function - Interpolation11.5882435257838
Midmean - Closest Observation6.10629835668421
Midmean - True Basic - Statistics Graphics Toolkit10.7998885193333
Midmean - MS Excel (old versions)10.7998885193333
Number of observations75

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & -6.13332149512757e-10 & 30.9275684550942 & -1.98312437786144e-11 \tabularnewline
Geometric Mean & NaN &  &  \tabularnewline
Harmonic Mean & 66.6668169780017 &  &  \tabularnewline
Quadratic Mean & 266.049003569447 &  &  \tabularnewline
Winsorized Mean ( 1 / 25 ) & -2.58407177528 & 29.8700598694115 & -0.0865104317359011 \tabularnewline
Winsorized Mean ( 2 / 25 ) & -2.26092477528 & 29.7457417568294 & -0.0760083508343142 \tabularnewline
Winsorized Mean ( 3 / 25 ) & -1.68870945528 & 29.5169382507144 & -0.0572115387082579 \tabularnewline
Winsorized Mean ( 4 / 25 ) & 2.09508626738667 & 28.0677563755312 & 0.0746438810197567 \tabularnewline
Winsorized Mean ( 5 / 25 ) & -2.71243616594667 & 27.0675521681831 & -0.10020988041671 \tabularnewline
Winsorized Mean ( 6 / 25 ) & 0.315224298053333 & 26.3315655178043 & 0.011971346627309 \tabularnewline
Winsorized Mean ( 7 / 25 ) & 1.64015182738667 & 25.4653775291806 & 0.0644071278938326 \tabularnewline
Winsorized Mean ( 8 / 25 ) & -5.04440303128 & 24.2950870897116 & -0.207630580316635 \tabularnewline
Winsorized Mean ( 9 / 25 ) & -4.88986887928 & 23.5199848406187 & -0.207902722404619 \tabularnewline
Winsorized Mean ( 10 / 25 ) & -3.80774326594667 & 23.2767539805073 & -0.163585664441674 \tabularnewline
Winsorized Mean ( 11 / 25 ) & -1.42311938328 & 22.4799258068735 & -0.0633062313241652 \tabularnewline
Winsorized Mean ( 12 / 25 ) & -3.23777778328 & 21.9403398841707 & -0.14757190637762 \tabularnewline
Winsorized Mean ( 13 / 25 ) & -2.55772256328 & 21.6908748344593 & -0.117916985036337 \tabularnewline
Winsorized Mean ( 14 / 25 ) & 7.15802622072 & 20.005208907882 & 0.357808121558769 \tabularnewline
Winsorized Mean ( 15 / 25 ) & 7.60916494072 & 19.8185032161712 & 0.383942463147831 \tabularnewline
Winsorized Mean ( 16 / 25 ) & 7.22578330872 & 19.2374608913624 & 0.375610032401124 \tabularnewline
Winsorized Mean ( 17 / 25 ) & 4.07755695805333 & 18.7675893758005 & 0.217265887291367 \tabularnewline
Winsorized Mean ( 18 / 25 ) & 3.79929606205333 & 17.7330749840327 & 0.214249139840343 \tabularnewline
Winsorized Mean ( 19 / 25 ) & 4.57293304605334 & 17.3664001610264 & 0.26332072298529 \tabularnewline
Winsorized Mean ( 20 / 25 ) & 14.4307660593867 & 13.8854847881686 & 1.03926987638794 \tabularnewline
Winsorized Mean ( 21 / 25 ) & 13.6435196833867 & 13.7390331529401 & 0.993048021029557 \tabularnewline
Winsorized Mean ( 22 / 25 ) & 10.8623188433867 & 12.2058290328071 & 0.889928804851412 \tabularnewline
Winsorized Mean ( 23 / 25 ) & 7.23216011938666 & 11.4646062598652 & 0.630824989141121 \tabularnewline
Winsorized Mean ( 24 / 25 ) & 6.90951000738666 & 10.7489447626726 & 0.6428082160568 \tabularnewline
Winsorized Mean ( 25 / 25 ) & 9.47196688072 & 10.401602622855 & 0.910625720300801 \tabularnewline
Trimmed Mean ( 1 / 25 ) & -1.58770810336986 & 29.0104197934135 & -0.0547288910217816 \tabularnewline
Trimmed Mean ( 2 / 25 ) & -0.53521126684507 & 27.9945715374823 & -0.0191183946547804 \tabularnewline
Trimmed Mean ( 3 / 25 ) & 0.402676509478261 & 26.867329685308 & 0.0149875895444294 \tabularnewline
Trimmed Mean ( 4 / 25 ) & 1.18304440677612 & 25.6262710622928 & 0.0461652966949563 \tabularnewline
Trimmed Mean ( 5 / 25 ) & 0.919955408523077 & 24.6945279663276 & 0.037253411354025 \tabularnewline
Trimmed Mean ( 6 / 25 ) & 1.78481054530159 & 23.8977748091212 & 0.0746852190029159 \tabularnewline
Trimmed Mean ( 7 / 25 ) & 2.08595526809836 & 23.1479960025885 & 0.0901138598721504 \tabularnewline
Trimmed Mean ( 8 / 25 ) & 2.16691230938983 & 22.465899400363 & 0.0964533968025698 \tabularnewline
Trimmed Mean ( 9 / 25 ) & 3.35298391147368 & 21.9147524238985 & 0.153001222492351 \tabularnewline
Trimmed Mean ( 10 / 25 ) & 4.60190100098182 & 21.4108726455444 & 0.21493290241673 \tabularnewline
Trimmed Mean ( 11 / 25 ) & 5.79194500101887 & 20.8349611398431 & 0.277991639252104 \tabularnewline
Trimmed Mean ( 12 / 25 ) & 6.75652580105882 & 20.2896208329231 & 0.333004044614539 \tabularnewline
Trimmed Mean ( 13 / 25 ) & 8.0313094215102 & 19.7119277142961 & 0.407433993159659 \tabularnewline
Trimmed Mean ( 14 / 25 ) & 9.33110876497872 & 19.025784222891 & 0.490445421626928 \tabularnewline
Trimmed Mean ( 15 / 25 ) & 9.58980906786667 & 18.5295225092541 & 0.517542158092702 \tabularnewline
Trimmed Mean ( 16 / 25 ) & 9.82011652451163 & 17.9175068652953 & 0.548073825133137 \tabularnewline
Trimmed Mean ( 17 / 25 ) & 10.1167247427805 & 17.243297589121 & 0.586704758210705 \tabularnewline
Trimmed Mean ( 18 / 25 ) & 10.7998885193333 & 16.4521494525573 & 0.656442402889465 \tabularnewline
Trimmed Mean ( 19 / 25 ) & 11.5882435257838 & 15.6500018082492 & 0.740462759542656 \tabularnewline
Trimmed Mean ( 20 / 25 ) & 12.3794439558286 & 14.6412121121481 & 0.845520429661499 \tabularnewline
Trimmed Mean ( 21 / 25 ) & 12.1463391713333 & 14.2464693217868 & 0.85258592125406 \tabularnewline
Trimmed Mean ( 22 / 25 ) & 11.9738529372258 & 13.7033888514899 & 0.873787722656936 \tabularnewline
Trimmed Mean ( 23 / 25 ) & 12.1045191708276 & 13.3624764366717 & 0.905858972189333 \tabularnewline
Trimmed Mean ( 24 / 25 ) & 12.6929683316296 & 13.0464847592691 & 0.972903319617317 \tabularnewline
Trimmed Mean ( 25 / 25 ) & 13.41590062216 & 12.7560735680074 & 1.0517265011553 \tabularnewline
Median & 14.6563147 &  &  \tabularnewline
Midrange & 57.95134575 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 6.10629835668421 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 10.7998885193333 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 10.7998885193333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 10.7998885193333 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 11.5882435257838 &  &  \tabularnewline
Midmean - Closest Observation & 6.10629835668421 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 10.7998885193333 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 10.7998885193333 &  &  \tabularnewline
Number of observations & 75 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147281&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]-6.13332149512757e-10[/C][C]30.9275684550942[/C][C]-1.98312437786144e-11[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]NaN[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]66.6668169780017[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]266.049003569447[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 25 )[/C][C]-2.58407177528[/C][C]29.8700598694115[/C][C]-0.0865104317359011[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 25 )[/C][C]-2.26092477528[/C][C]29.7457417568294[/C][C]-0.0760083508343142[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 25 )[/C][C]-1.68870945528[/C][C]29.5169382507144[/C][C]-0.0572115387082579[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 25 )[/C][C]2.09508626738667[/C][C]28.0677563755312[/C][C]0.0746438810197567[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 25 )[/C][C]-2.71243616594667[/C][C]27.0675521681831[/C][C]-0.10020988041671[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 25 )[/C][C]0.315224298053333[/C][C]26.3315655178043[/C][C]0.011971346627309[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 25 )[/C][C]1.64015182738667[/C][C]25.4653775291806[/C][C]0.0644071278938326[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 25 )[/C][C]-5.04440303128[/C][C]24.2950870897116[/C][C]-0.207630580316635[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 25 )[/C][C]-4.88986887928[/C][C]23.5199848406187[/C][C]-0.207902722404619[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 25 )[/C][C]-3.80774326594667[/C][C]23.2767539805073[/C][C]-0.163585664441674[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 25 )[/C][C]-1.42311938328[/C][C]22.4799258068735[/C][C]-0.0633062313241652[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 25 )[/C][C]-3.23777778328[/C][C]21.9403398841707[/C][C]-0.14757190637762[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 25 )[/C][C]-2.55772256328[/C][C]21.6908748344593[/C][C]-0.117916985036337[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 25 )[/C][C]7.15802622072[/C][C]20.005208907882[/C][C]0.357808121558769[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 25 )[/C][C]7.60916494072[/C][C]19.8185032161712[/C][C]0.383942463147831[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 25 )[/C][C]7.22578330872[/C][C]19.2374608913624[/C][C]0.375610032401124[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 25 )[/C][C]4.07755695805333[/C][C]18.7675893758005[/C][C]0.217265887291367[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 25 )[/C][C]3.79929606205333[/C][C]17.7330749840327[/C][C]0.214249139840343[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 25 )[/C][C]4.57293304605334[/C][C]17.3664001610264[/C][C]0.26332072298529[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 25 )[/C][C]14.4307660593867[/C][C]13.8854847881686[/C][C]1.03926987638794[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 25 )[/C][C]13.6435196833867[/C][C]13.7390331529401[/C][C]0.993048021029557[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 25 )[/C][C]10.8623188433867[/C][C]12.2058290328071[/C][C]0.889928804851412[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 25 )[/C][C]7.23216011938666[/C][C]11.4646062598652[/C][C]0.630824989141121[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 25 )[/C][C]6.90951000738666[/C][C]10.7489447626726[/C][C]0.6428082160568[/C][/ROW]
[ROW][C]Winsorized Mean ( 25 / 25 )[/C][C]9.47196688072[/C][C]10.401602622855[/C][C]0.910625720300801[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 25 )[/C][C]-1.58770810336986[/C][C]29.0104197934135[/C][C]-0.0547288910217816[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 25 )[/C][C]-0.53521126684507[/C][C]27.9945715374823[/C][C]-0.0191183946547804[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 25 )[/C][C]0.402676509478261[/C][C]26.867329685308[/C][C]0.0149875895444294[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 25 )[/C][C]1.18304440677612[/C][C]25.6262710622928[/C][C]0.0461652966949563[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 25 )[/C][C]0.919955408523077[/C][C]24.6945279663276[/C][C]0.037253411354025[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 25 )[/C][C]1.78481054530159[/C][C]23.8977748091212[/C][C]0.0746852190029159[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 25 )[/C][C]2.08595526809836[/C][C]23.1479960025885[/C][C]0.0901138598721504[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 25 )[/C][C]2.16691230938983[/C][C]22.465899400363[/C][C]0.0964533968025698[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 25 )[/C][C]3.35298391147368[/C][C]21.9147524238985[/C][C]0.153001222492351[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 25 )[/C][C]4.60190100098182[/C][C]21.4108726455444[/C][C]0.21493290241673[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 25 )[/C][C]5.79194500101887[/C][C]20.8349611398431[/C][C]0.277991639252104[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 25 )[/C][C]6.75652580105882[/C][C]20.2896208329231[/C][C]0.333004044614539[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 25 )[/C][C]8.0313094215102[/C][C]19.7119277142961[/C][C]0.407433993159659[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 25 )[/C][C]9.33110876497872[/C][C]19.025784222891[/C][C]0.490445421626928[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 25 )[/C][C]9.58980906786667[/C][C]18.5295225092541[/C][C]0.517542158092702[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 25 )[/C][C]9.82011652451163[/C][C]17.9175068652953[/C][C]0.548073825133137[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 25 )[/C][C]10.1167247427805[/C][C]17.243297589121[/C][C]0.586704758210705[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 25 )[/C][C]10.7998885193333[/C][C]16.4521494525573[/C][C]0.656442402889465[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 25 )[/C][C]11.5882435257838[/C][C]15.6500018082492[/C][C]0.740462759542656[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 25 )[/C][C]12.3794439558286[/C][C]14.6412121121481[/C][C]0.845520429661499[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 25 )[/C][C]12.1463391713333[/C][C]14.2464693217868[/C][C]0.85258592125406[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 25 )[/C][C]11.9738529372258[/C][C]13.7033888514899[/C][C]0.873787722656936[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 25 )[/C][C]12.1045191708276[/C][C]13.3624764366717[/C][C]0.905858972189333[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 25 )[/C][C]12.6929683316296[/C][C]13.0464847592691[/C][C]0.972903319617317[/C][/ROW]
[ROW][C]Trimmed Mean ( 25 / 25 )[/C][C]13.41590062216[/C][C]12.7560735680074[/C][C]1.0517265011553[/C][/ROW]
[ROW][C]Median[/C][C]14.6563147[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]57.95134575[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]6.10629835668421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]10.7998885193333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]10.7998885193333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]10.7998885193333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]11.5882435257838[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]6.10629835668421[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]10.7998885193333[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]10.7998885193333[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]75[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147281&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147281&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 Mean-6.13332149512757e-1030.9275684550942-1.98312437786144e-11
Geometric MeanNaN
Harmonic Mean66.6668169780017
Quadratic Mean266.049003569447
Winsorized Mean ( 1 / 25 )-2.5840717752829.8700598694115-0.0865104317359011
Winsorized Mean ( 2 / 25 )-2.2609247752829.7457417568294-0.0760083508343142
Winsorized Mean ( 3 / 25 )-1.6887094552829.5169382507144-0.0572115387082579
Winsorized Mean ( 4 / 25 )2.0950862673866728.06775637553120.0746438810197567
Winsorized Mean ( 5 / 25 )-2.7124361659466727.0675521681831-0.10020988041671
Winsorized Mean ( 6 / 25 )0.31522429805333326.33156551780430.011971346627309
Winsorized Mean ( 7 / 25 )1.6401518273866725.46537752918060.0644071278938326
Winsorized Mean ( 8 / 25 )-5.0444030312824.2950870897116-0.207630580316635
Winsorized Mean ( 9 / 25 )-4.8898688792823.5199848406187-0.207902722404619
Winsorized Mean ( 10 / 25 )-3.8077432659466723.2767539805073-0.163585664441674
Winsorized Mean ( 11 / 25 )-1.4231193832822.4799258068735-0.0633062313241652
Winsorized Mean ( 12 / 25 )-3.2377777832821.9403398841707-0.14757190637762
Winsorized Mean ( 13 / 25 )-2.5577225632821.6908748344593-0.117916985036337
Winsorized Mean ( 14 / 25 )7.1580262207220.0052089078820.357808121558769
Winsorized Mean ( 15 / 25 )7.6091649407219.81850321617120.383942463147831
Winsorized Mean ( 16 / 25 )7.2257833087219.23746089136240.375610032401124
Winsorized Mean ( 17 / 25 )4.0775569580533318.76758937580050.217265887291367
Winsorized Mean ( 18 / 25 )3.7992960620533317.73307498403270.214249139840343
Winsorized Mean ( 19 / 25 )4.5729330460533417.36640016102640.26332072298529
Winsorized Mean ( 20 / 25 )14.430766059386713.88548478816861.03926987638794
Winsorized Mean ( 21 / 25 )13.643519683386713.73903315294010.993048021029557
Winsorized Mean ( 22 / 25 )10.862318843386712.20582903280710.889928804851412
Winsorized Mean ( 23 / 25 )7.2321601193866611.46460625986520.630824989141121
Winsorized Mean ( 24 / 25 )6.9095100073866610.74894476267260.6428082160568
Winsorized Mean ( 25 / 25 )9.4719668807210.4016026228550.910625720300801
Trimmed Mean ( 1 / 25 )-1.5877081033698629.0104197934135-0.0547288910217816
Trimmed Mean ( 2 / 25 )-0.5352112668450727.9945715374823-0.0191183946547804
Trimmed Mean ( 3 / 25 )0.40267650947826126.8673296853080.0149875895444294
Trimmed Mean ( 4 / 25 )1.1830444067761225.62627106229280.0461652966949563
Trimmed Mean ( 5 / 25 )0.91995540852307724.69452796632760.037253411354025
Trimmed Mean ( 6 / 25 )1.7848105453015923.89777480912120.0746852190029159
Trimmed Mean ( 7 / 25 )2.0859552680983623.14799600258850.0901138598721504
Trimmed Mean ( 8 / 25 )2.1669123093898322.4658994003630.0964533968025698
Trimmed Mean ( 9 / 25 )3.3529839114736821.91475242389850.153001222492351
Trimmed Mean ( 10 / 25 )4.6019010009818221.41087264554440.21493290241673
Trimmed Mean ( 11 / 25 )5.7919450010188720.83496113984310.277991639252104
Trimmed Mean ( 12 / 25 )6.7565258010588220.28962083292310.333004044614539
Trimmed Mean ( 13 / 25 )8.031309421510219.71192771429610.407433993159659
Trimmed Mean ( 14 / 25 )9.3311087649787219.0257842228910.490445421626928
Trimmed Mean ( 15 / 25 )9.5898090678666718.52952250925410.517542158092702
Trimmed Mean ( 16 / 25 )9.8201165245116317.91750686529530.548073825133137
Trimmed Mean ( 17 / 25 )10.116724742780517.2432975891210.586704758210705
Trimmed Mean ( 18 / 25 )10.799888519333316.45214945255730.656442402889465
Trimmed Mean ( 19 / 25 )11.588243525783815.65000180824920.740462759542656
Trimmed Mean ( 20 / 25 )12.379443955828614.64121211214810.845520429661499
Trimmed Mean ( 21 / 25 )12.146339171333314.24646932178680.85258592125406
Trimmed Mean ( 22 / 25 )11.973852937225813.70338885148990.873787722656936
Trimmed Mean ( 23 / 25 )12.104519170827613.36247643667170.905858972189333
Trimmed Mean ( 24 / 25 )12.692968331629613.04648475926910.972903319617317
Trimmed Mean ( 25 / 25 )13.4159006221612.75607356800741.0517265011553
Median14.6563147
Midrange57.95134575
Midmean - Weighted Average at Xnp6.10629835668421
Midmean - Weighted Average at X(n+1)p10.7998885193333
Midmean - Empirical Distribution Function10.7998885193333
Midmean - Empirical Distribution Function - Averaging10.7998885193333
Midmean - Empirical Distribution Function - Interpolation11.5882435257838
Midmean - Closest Observation6.10629835668421
Midmean - True Basic - Statistics Graphics Toolkit10.7998885193333
Midmean - MS Excel (old versions)10.7998885193333
Number of observations75



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')