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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 18 Oct 2010 18:40:38 +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/Oct/18/t1287427301p7bcjaxdd5wbax5.htm/, Retrieved Sat, 04 May 2024 19:24:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=85224, Retrieved Sat, 04 May 2024 19:24:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP1W52
Estimated Impact105
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2010-10-18 18:40:38] [ca3ac3c31c98d146c448f7dbe5015da7] [Current]
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Dataseries X:
13,2
13,8
16,2
14,7
13,9
16,0
14,4
12,3
15,9
15,9
15,5
15,1
14,5
15,1
17,4
16,2
15,6
17,2
14,9
13,8
17,5
16,2
17,5
16,6
16,2
16,6
19,6
15,9
18,0
18,3
16,3
14,9
18,2
18,4
18,5
16,0
17,4
17,2
19,6
17,2
18,3
19,3
18,1
16,2
18,4
20,5
19,0
16,5
18,7
19,0
19,2
20,5
19,3
20,6
20,1
16,1
20,4
19,7
15,6
14,4
13,9
14,3
15,3
14,4
13,8
15,7
14,7
12,5
16,2
16,1
16
15,8
15,2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=85224&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=85224&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=85224&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'George Udny Yule' @ 72.249.76.132







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean16.59589041095890.24038146969920669.0398075680528
Geometric Mean16.4707613353066
Harmonic Mean16.3459959709283
Quadratic Mean16.7207647134555
Winsorized Mean ( 1 / 24 )16.59726027397260.23940226016427869.3279180513315
Winsorized Mean ( 2 / 24 )16.61643835616440.23518519613021170.6525692499993
Winsorized Mean ( 3 / 24 )16.63698630136990.22963894340395172.4484534493971
Winsorized Mean ( 4 / 24 )16.62054794520550.22600998503108373.538998477964
Winsorized Mean ( 5 / 24 )16.59315068493150.22039580390103075.2879609830626
Winsorized Mean ( 6 / 24 )16.59315068493150.21737090298367876.3356569677473
Winsorized Mean ( 7 / 24 )16.59315068493150.21737090298367876.3356569677473
Winsorized Mean ( 8 / 24 )16.60410958904110.20396972008843481.4047770514276
Winsorized Mean ( 9 / 24 )16.61643835616440.20206330761417582.2338234108898
Winsorized Mean ( 10 / 24 )16.60273972602740.19956166389584683.1960377655128
Winsorized Mean ( 11 / 24 )16.57260273972600.19422072634049885.3287033365933
Winsorized Mean ( 12 / 24 )16.58904109589040.19169953702492286.5366779353973
Winsorized Mean ( 13 / 24 )16.57123287671230.17726013282231393.4853912883132
Winsorized Mean ( 14 / 24 )16.53287671232880.17099465925908896.686509297805
Winsorized Mean ( 15 / 24 )16.55342465753420.161743287776397102.343812130359
Winsorized Mean ( 16 / 24 )16.55342465753420.161743287776397102.343812130359
Winsorized Mean ( 17 / 24 )16.57671232876710.151596282378038109.347749619806
Winsorized Mean ( 18 / 24 )16.57671232876710.151596282378038109.347749619806
Winsorized Mean ( 19 / 24 )16.57671232876710.144014529591390115.104443807163
Winsorized Mean ( 20 / 24 )16.57671232876710.136136634347112121.765257443496
Winsorized Mean ( 21 / 24 )16.60547945205480.124353585992358133.534383584847
Winsorized Mean ( 22 / 24 )16.48493150684930.0979172613967504168.355724738400
Winsorized Mean ( 23 / 24 )16.48493150684930.0979172613967504168.355724738400
Winsorized Mean ( 24 / 24 )16.48493150684930.0891288643650371184.956148878252
Trimmed Mean ( 1 / 24 )16.60.23274237707067271.3234959998686
Trimmed Mean ( 2 / 24 )16.60289855072460.22484219164665373.8424511393156
Trimmed Mean ( 3 / 24 )16.59552238805970.21814389953367576.0760324883523
Trimmed Mean ( 4 / 24 )16.580.21265492090383377.9666886123827
Trimmed Mean ( 5 / 24 )16.56825396825400.20738818351752979.8900578000074
Trimmed Mean ( 6 / 24 )16.56229508196720.20279689069767881.6693738498074
Trimmed Mean ( 7 / 24 )16.55593220338980.19803640377611683.6004486433043
Trimmed Mean ( 8 / 24 )16.54912280701750.19217334370024486.1156000534145
Trimmed Mean ( 9 / 24 )16.540.18825085348646987.8614874444057
Trimmed Mean ( 10 / 24 )16.52830188679250.18374386947092089.9529433791984
Trimmed Mean ( 11 / 24 )16.51764705882350.17863767431625792.4645213953076
Trimmed Mean ( 12 / 24 )16.51020408163270.17340735185257895.2105196535659
Trimmed Mean ( 13 / 24 )16.50.16725459054194798.652000800312
Trimmed Mean ( 14 / 24 )16.49111111111110.162674062866572101.375172049630
Trimmed Mean ( 15 / 24 )16.48604651162790.158116733422297104.265033528090
Trimmed Mean ( 16 / 24 )16.47804878048780.154150393586752106.895924149648
Trimmed Mean ( 17 / 24 )16.46923076923080.148730745412494110.731851195626
Trimmed Mean ( 18 / 24 )16.45675675675680.143818607627831114.427173424895
Trimmed Mean ( 19 / 24 )16.44285714285710.136909816007062120.099914107028
Trimmed Mean ( 20 / 24 )16.42727272727270.129339283041700127.009152524654
Trimmed Mean ( 21 / 24 )16.40967741935480.120870929001259135.761986401080
Trimmed Mean ( 22 / 24 )16.38620689655170.112157979048801146.099341620822
Trimmed Mean ( 23 / 24 )16.37407407407410.109074400572214150.118396142213
Trimmed Mean ( 24 / 24 )16.360.103923048454133157.424173399038
Median16.2
Midrange16.45
Midmean - Weighted Average at Xnp16.3702702702703
Midmean - Weighted Average at X(n+1)p16.4692307692308
Midmean - Empirical Distribution Function16.4692307692308
Midmean - Empirical Distribution Function - Averaging16.4692307692308
Midmean - Empirical Distribution Function - Interpolation16.4692307692308
Midmean - Closest Observation16.4692307692308
Midmean - True Basic - Statistics Graphics Toolkit16.4692307692308
Midmean - MS Excel (old versions)16.4692307692308
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 16.5958904109589 & 0.240381469699206 & 69.0398075680528 \tabularnewline
Geometric Mean & 16.4707613353066 &  &  \tabularnewline
Harmonic Mean & 16.3459959709283 &  &  \tabularnewline
Quadratic Mean & 16.7207647134555 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 16.5972602739726 & 0.239402260164278 & 69.3279180513315 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 16.6164383561644 & 0.235185196130211 & 70.6525692499993 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 16.6369863013699 & 0.229638943403951 & 72.4484534493971 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 16.6205479452055 & 0.226009985031083 & 73.538998477964 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 16.5931506849315 & 0.220395803901030 & 75.2879609830626 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 16.5931506849315 & 0.217370902983678 & 76.3356569677473 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 16.5931506849315 & 0.217370902983678 & 76.3356569677473 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 16.6041095890411 & 0.203969720088434 & 81.4047770514276 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 16.6164383561644 & 0.202063307614175 & 82.2338234108898 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 16.6027397260274 & 0.199561663895846 & 83.1960377655128 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 16.5726027397260 & 0.194220726340498 & 85.3287033365933 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 16.5890410958904 & 0.191699537024922 & 86.5366779353973 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 16.5712328767123 & 0.177260132822313 & 93.4853912883132 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 16.5328767123288 & 0.170994659259088 & 96.686509297805 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 16.5534246575342 & 0.161743287776397 & 102.343812130359 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 16.5534246575342 & 0.161743287776397 & 102.343812130359 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 16.5767123287671 & 0.151596282378038 & 109.347749619806 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 16.5767123287671 & 0.151596282378038 & 109.347749619806 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 16.5767123287671 & 0.144014529591390 & 115.104443807163 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 16.5767123287671 & 0.136136634347112 & 121.765257443496 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 16.6054794520548 & 0.124353585992358 & 133.534383584847 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 16.4849315068493 & 0.0979172613967504 & 168.355724738400 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 16.4849315068493 & 0.0979172613967504 & 168.355724738400 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 16.4849315068493 & 0.0891288643650371 & 184.956148878252 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 16.6 & 0.232742377070672 & 71.3234959998686 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 16.6028985507246 & 0.224842191646653 & 73.8424511393156 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 16.5955223880597 & 0.218143899533675 & 76.0760324883523 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 16.58 & 0.212654920903833 & 77.9666886123827 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 16.5682539682540 & 0.207388183517529 & 79.8900578000074 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 16.5622950819672 & 0.202796890697678 & 81.6693738498074 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 16.5559322033898 & 0.198036403776116 & 83.6004486433043 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 16.5491228070175 & 0.192173343700244 & 86.1156000534145 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 16.54 & 0.188250853486469 & 87.8614874444057 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 16.5283018867925 & 0.183743869470920 & 89.9529433791984 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 16.5176470588235 & 0.178637674316257 & 92.4645213953076 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 16.5102040816327 & 0.173407351852578 & 95.2105196535659 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 16.5 & 0.167254590541947 & 98.652000800312 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 16.4911111111111 & 0.162674062866572 & 101.375172049630 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 16.4860465116279 & 0.158116733422297 & 104.265033528090 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 16.4780487804878 & 0.154150393586752 & 106.895924149648 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 16.4692307692308 & 0.148730745412494 & 110.731851195626 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 16.4567567567568 & 0.143818607627831 & 114.427173424895 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 16.4428571428571 & 0.136909816007062 & 120.099914107028 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 16.4272727272727 & 0.129339283041700 & 127.009152524654 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 16.4096774193548 & 0.120870929001259 & 135.761986401080 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 16.3862068965517 & 0.112157979048801 & 146.099341620822 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 16.3740740740741 & 0.109074400572214 & 150.118396142213 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 16.36 & 0.103923048454133 & 157.424173399038 \tabularnewline
Median & 16.2 &  &  \tabularnewline
Midrange & 16.45 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 16.3702702702703 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 16.4692307692308 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 16.4692307692308 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 16.4692307692308 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 16.4692307692308 &  &  \tabularnewline
Midmean - Closest Observation & 16.4692307692308 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 16.4692307692308 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 16.4692307692308 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=85224&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]16.5958904109589[/C][C]0.240381469699206[/C][C]69.0398075680528[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]16.4707613353066[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]16.3459959709283[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]16.7207647134555[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]16.5972602739726[/C][C]0.239402260164278[/C][C]69.3279180513315[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]16.6164383561644[/C][C]0.235185196130211[/C][C]70.6525692499993[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]16.6369863013699[/C][C]0.229638943403951[/C][C]72.4484534493971[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]16.6205479452055[/C][C]0.226009985031083[/C][C]73.538998477964[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]16.5931506849315[/C][C]0.220395803901030[/C][C]75.2879609830626[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]16.5931506849315[/C][C]0.217370902983678[/C][C]76.3356569677473[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]16.5931506849315[/C][C]0.217370902983678[/C][C]76.3356569677473[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]16.6041095890411[/C][C]0.203969720088434[/C][C]81.4047770514276[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]16.6164383561644[/C][C]0.202063307614175[/C][C]82.2338234108898[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]16.6027397260274[/C][C]0.199561663895846[/C][C]83.1960377655128[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]16.5726027397260[/C][C]0.194220726340498[/C][C]85.3287033365933[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]16.5890410958904[/C][C]0.191699537024922[/C][C]86.5366779353973[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]16.5712328767123[/C][C]0.177260132822313[/C][C]93.4853912883132[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]16.5328767123288[/C][C]0.170994659259088[/C][C]96.686509297805[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]16.5534246575342[/C][C]0.161743287776397[/C][C]102.343812130359[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]16.5534246575342[/C][C]0.161743287776397[/C][C]102.343812130359[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]16.5767123287671[/C][C]0.151596282378038[/C][C]109.347749619806[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]16.5767123287671[/C][C]0.151596282378038[/C][C]109.347749619806[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]16.5767123287671[/C][C]0.144014529591390[/C][C]115.104443807163[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]16.5767123287671[/C][C]0.136136634347112[/C][C]121.765257443496[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]16.6054794520548[/C][C]0.124353585992358[/C][C]133.534383584847[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]16.4849315068493[/C][C]0.0979172613967504[/C][C]168.355724738400[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]16.4849315068493[/C][C]0.0979172613967504[/C][C]168.355724738400[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]16.4849315068493[/C][C]0.0891288643650371[/C][C]184.956148878252[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]16.6[/C][C]0.232742377070672[/C][C]71.3234959998686[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]16.6028985507246[/C][C]0.224842191646653[/C][C]73.8424511393156[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]16.5955223880597[/C][C]0.218143899533675[/C][C]76.0760324883523[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]16.58[/C][C]0.212654920903833[/C][C]77.9666886123827[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]16.5682539682540[/C][C]0.207388183517529[/C][C]79.8900578000074[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]16.5622950819672[/C][C]0.202796890697678[/C][C]81.6693738498074[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]16.5559322033898[/C][C]0.198036403776116[/C][C]83.6004486433043[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]16.5491228070175[/C][C]0.192173343700244[/C][C]86.1156000534145[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]16.54[/C][C]0.188250853486469[/C][C]87.8614874444057[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]16.5283018867925[/C][C]0.183743869470920[/C][C]89.9529433791984[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]16.5176470588235[/C][C]0.178637674316257[/C][C]92.4645213953076[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]16.5102040816327[/C][C]0.173407351852578[/C][C]95.2105196535659[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]16.5[/C][C]0.167254590541947[/C][C]98.652000800312[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]16.4911111111111[/C][C]0.162674062866572[/C][C]101.375172049630[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]16.4860465116279[/C][C]0.158116733422297[/C][C]104.265033528090[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]16.4780487804878[/C][C]0.154150393586752[/C][C]106.895924149648[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]16.4692307692308[/C][C]0.148730745412494[/C][C]110.731851195626[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]16.4567567567568[/C][C]0.143818607627831[/C][C]114.427173424895[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]16.4428571428571[/C][C]0.136909816007062[/C][C]120.099914107028[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]16.4272727272727[/C][C]0.129339283041700[/C][C]127.009152524654[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]16.4096774193548[/C][C]0.120870929001259[/C][C]135.761986401080[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]16.3862068965517[/C][C]0.112157979048801[/C][C]146.099341620822[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]16.3740740740741[/C][C]0.109074400572214[/C][C]150.118396142213[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]16.36[/C][C]0.103923048454133[/C][C]157.424173399038[/C][/ROW]
[ROW][C]Median[/C][C]16.2[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]16.45[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]16.3702702702703[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]16.4692307692308[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]16.4692307692308[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]16.4692307692308[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]16.4692307692308[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]16.4692307692308[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]16.4692307692308[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]16.4692307692308[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=85224&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=85224&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 Mean16.59589041095890.24038146969920669.0398075680528
Geometric Mean16.4707613353066
Harmonic Mean16.3459959709283
Quadratic Mean16.7207647134555
Winsorized Mean ( 1 / 24 )16.59726027397260.23940226016427869.3279180513315
Winsorized Mean ( 2 / 24 )16.61643835616440.23518519613021170.6525692499993
Winsorized Mean ( 3 / 24 )16.63698630136990.22963894340395172.4484534493971
Winsorized Mean ( 4 / 24 )16.62054794520550.22600998503108373.538998477964
Winsorized Mean ( 5 / 24 )16.59315068493150.22039580390103075.2879609830626
Winsorized Mean ( 6 / 24 )16.59315068493150.21737090298367876.3356569677473
Winsorized Mean ( 7 / 24 )16.59315068493150.21737090298367876.3356569677473
Winsorized Mean ( 8 / 24 )16.60410958904110.20396972008843481.4047770514276
Winsorized Mean ( 9 / 24 )16.61643835616440.20206330761417582.2338234108898
Winsorized Mean ( 10 / 24 )16.60273972602740.19956166389584683.1960377655128
Winsorized Mean ( 11 / 24 )16.57260273972600.19422072634049885.3287033365933
Winsorized Mean ( 12 / 24 )16.58904109589040.19169953702492286.5366779353973
Winsorized Mean ( 13 / 24 )16.57123287671230.17726013282231393.4853912883132
Winsorized Mean ( 14 / 24 )16.53287671232880.17099465925908896.686509297805
Winsorized Mean ( 15 / 24 )16.55342465753420.161743287776397102.343812130359
Winsorized Mean ( 16 / 24 )16.55342465753420.161743287776397102.343812130359
Winsorized Mean ( 17 / 24 )16.57671232876710.151596282378038109.347749619806
Winsorized Mean ( 18 / 24 )16.57671232876710.151596282378038109.347749619806
Winsorized Mean ( 19 / 24 )16.57671232876710.144014529591390115.104443807163
Winsorized Mean ( 20 / 24 )16.57671232876710.136136634347112121.765257443496
Winsorized Mean ( 21 / 24 )16.60547945205480.124353585992358133.534383584847
Winsorized Mean ( 22 / 24 )16.48493150684930.0979172613967504168.355724738400
Winsorized Mean ( 23 / 24 )16.48493150684930.0979172613967504168.355724738400
Winsorized Mean ( 24 / 24 )16.48493150684930.0891288643650371184.956148878252
Trimmed Mean ( 1 / 24 )16.60.23274237707067271.3234959998686
Trimmed Mean ( 2 / 24 )16.60289855072460.22484219164665373.8424511393156
Trimmed Mean ( 3 / 24 )16.59552238805970.21814389953367576.0760324883523
Trimmed Mean ( 4 / 24 )16.580.21265492090383377.9666886123827
Trimmed Mean ( 5 / 24 )16.56825396825400.20738818351752979.8900578000074
Trimmed Mean ( 6 / 24 )16.56229508196720.20279689069767881.6693738498074
Trimmed Mean ( 7 / 24 )16.55593220338980.19803640377611683.6004486433043
Trimmed Mean ( 8 / 24 )16.54912280701750.19217334370024486.1156000534145
Trimmed Mean ( 9 / 24 )16.540.18825085348646987.8614874444057
Trimmed Mean ( 10 / 24 )16.52830188679250.18374386947092089.9529433791984
Trimmed Mean ( 11 / 24 )16.51764705882350.17863767431625792.4645213953076
Trimmed Mean ( 12 / 24 )16.51020408163270.17340735185257895.2105196535659
Trimmed Mean ( 13 / 24 )16.50.16725459054194798.652000800312
Trimmed Mean ( 14 / 24 )16.49111111111110.162674062866572101.375172049630
Trimmed Mean ( 15 / 24 )16.48604651162790.158116733422297104.265033528090
Trimmed Mean ( 16 / 24 )16.47804878048780.154150393586752106.895924149648
Trimmed Mean ( 17 / 24 )16.46923076923080.148730745412494110.731851195626
Trimmed Mean ( 18 / 24 )16.45675675675680.143818607627831114.427173424895
Trimmed Mean ( 19 / 24 )16.44285714285710.136909816007062120.099914107028
Trimmed Mean ( 20 / 24 )16.42727272727270.129339283041700127.009152524654
Trimmed Mean ( 21 / 24 )16.40967741935480.120870929001259135.761986401080
Trimmed Mean ( 22 / 24 )16.38620689655170.112157979048801146.099341620822
Trimmed Mean ( 23 / 24 )16.37407407407410.109074400572214150.118396142213
Trimmed Mean ( 24 / 24 )16.360.103923048454133157.424173399038
Median16.2
Midrange16.45
Midmean - Weighted Average at Xnp16.3702702702703
Midmean - Weighted Average at X(n+1)p16.4692307692308
Midmean - Empirical Distribution Function16.4692307692308
Midmean - Empirical Distribution Function - Averaging16.4692307692308
Midmean - Empirical Distribution Function - Interpolation16.4692307692308
Midmean - Closest Observation16.4692307692308
Midmean - True Basic - Statistics Graphics Toolkit16.4692307692308
Midmean - MS Excel (old versions)16.4692307692308
Number of observations73



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')