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Author's title

Author*Unverified author*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationFri, 04 Mar 2016 14:28:08 +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/2016/Mar/04/t14571019409c6kixrdqw2cm4d.htm/, Retrieved Sat, 18 May 2024 16:45:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=293386, Retrieved Sat, 18 May 2024 16:45:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Central Tendency] [] [2016-03-04 14:28:08] [1b498ae19017f51f703ef2d779b672b0] [Current]
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Dataseries X:
8,9
9,2
12,8
11,1
11,2
13,1
12,6
10
12,3
12,5
11,4
11,5
10,4
11
15
12,7
11,6
13,9
12,6
11,2
15,8
15,3
14
14,6
11,5
12,8
16,2
12,8
13,5
12,5
13,2
12
14,2
17,5
13,8
13,9
11,3
12,1
16,2
11,6
12,5
15,6
12,3
12
12,1
13,9
12,3
10,5
14,2
13,2
13,7
14,2
15,3
16,3
15,1
13,4
14
15,5
12,5
12,9
12,9
13,4
15
14,4
14
15,2
15
12,4
18,7
20,6
17,3
11,4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293386&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293386&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293386&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'Herman Ole Andreas Wold' @ wold.wessa.net







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean13.35555555555560.24656393693249854.1667030536258
Geometric Mean13.1998588456001
Harmonic Mean13.0481212702141
Quadratic Mean13.5161837151698
Winsorized Mean ( 1 / 24 )13.33333333333330.23580183186812456.5446554324914
Winsorized Mean ( 2 / 24 )13.32222222222220.22088014139608460.3142597520014
Winsorized Mean ( 3 / 24 )13.33055555555560.2153230176100861.9095705768685
Winsorized Mean ( 4 / 24 )13.28055555555560.20111814675698566.0336014909817
Winsorized Mean ( 5 / 24 )13.30833333333330.19334335007238968.8326406279326
Winsorized Mean ( 6 / 24 )13.31666666666670.1919649648525269.3702972148973
Winsorized Mean ( 7 / 24 )13.28750.18249849936142172.8088178614848
Winsorized Mean ( 8 / 24 )13.26527777777780.1782935074899774.4013506971028
Winsorized Mean ( 9 / 24 )13.26527777777780.17399566174486676.2391294400718
Winsorized Mean ( 10 / 24 )13.25138888888890.16688944096876979.4022007142361
Winsorized Mean ( 11 / 24 )13.25138888888890.16688944096876979.4022007142361
Winsorized Mean ( 12 / 24 )13.25138888888890.16145602481227882.0742917726114
Winsorized Mean ( 13 / 24 )13.23333333333330.15842288053397683.5317050714483
Winsorized Mean ( 14 / 24 )13.23333333333330.15225226163741886.9171544055476
Winsorized Mean ( 15 / 24 )13.23333333333330.15225226163741886.9171544055476
Winsorized Mean ( 16 / 24 )13.32222222222220.13957265178416995.45009034308
Winsorized Mean ( 17 / 24 )13.22777777777780.12419100058089106.511564573168
Winsorized Mean ( 18 / 24 )13.20277777777780.113107553033805116.727640406399
Winsorized Mean ( 19 / 24 )13.150.105464914546559124.686015785797
Winsorized Mean ( 20 / 24 )13.20555555555560.0979422254903067134.830054038975
Winsorized Mean ( 21 / 24 )13.20555555555560.0979422254903067134.830054038975
Winsorized Mean ( 22 / 24 )13.14444444444440.0894446631477025146.956162412269
Winsorized Mean ( 23 / 24 )13.17638888888890.0852707428804007154.524147952714
Winsorized Mean ( 24 / 24 )13.20972222222220.0810764752833699162.929162572164
Trimmed Mean ( 1 / 24 )13.31571428571430.22213565059243259.9440668357443
Trimmed Mean ( 2 / 24 )13.29705882352940.20548846053012764.7095159953271
Trimmed Mean ( 3 / 24 )13.28333333333330.19542057130506967.9730554701779
Trimmed Mean ( 4 / 24 )13.2656250.18591551073790671.3529761306531
Trimmed Mean ( 5 / 24 )13.26129032258060.17997818245339173.6827661098028
Trimmed Mean ( 6 / 24 )13.250.17527218542327575.5967067335973
Trimmed Mean ( 7 / 24 )13.23620689655170.1698848098383377.9128334613782
Trimmed Mean ( 8 / 24 )13.22678571428570.16582127507957779.7653118270755
Trimmed Mean ( 9 / 24 )13.22037037037040.16182440876038281.6957742755985
Trimmed Mean ( 10 / 24 )13.21346153846150.1578281337565783.7205713833101
Trimmed Mean ( 11 / 24 )13.2080.15441370352638685.5364497992435
Trimmed Mean ( 12 / 24 )13.20208333333330.15001446689495688.0054011229316
Trimmed Mean ( 13 / 24 )13.1956521739130.14559411922545290.6331398830721
Trimmed Mean ( 14 / 24 )13.19090909090910.14055230011581393.8505387677044
Trimmed Mean ( 15 / 24 )13.18571428571430.13540370354412897.3807506041892
Trimmed Mean ( 16 / 24 )13.180.128512196368223102.558359225576
Trimmed Mean ( 17 / 24 )13.16315789473680.122353698314367107.582836285965
Trimmed Mean ( 18 / 24 )13.15555555555560.118284325495174111.219770671071
Trimmed Mean ( 19 / 24 )13.150.115489348692072113.863314227026
Trimmed Mean ( 20 / 24 )13.150.113414739896569115.946128448493
Trimmed Mean ( 21 / 24 )13.14333333333330.112104562575265117.24173424707
Trimmed Mean ( 22 / 24 )13.13571428571430.109739263580896119.699311414014
Trimmed Mean ( 23 / 24 )13.13461538461540.108548791963275121.001948958208
Trimmed Mean ( 24 / 24 )13.12916666666670.107420204065836122.222507216799
Median13
Midrange14.75
Midmean - Weighted Average at Xnp13.0947368421053
Midmean - Weighted Average at X(n+1)p13.1555555555556
Midmean - Empirical Distribution Function13.0947368421053
Midmean - Empirical Distribution Function - Averaging13.1555555555556
Midmean - Empirical Distribution Function - Interpolation13.1555555555556
Midmean - Closest Observation13.0947368421053
Midmean - True Basic - Statistics Graphics Toolkit13.1555555555556
Midmean - MS Excel (old versions)13.1333333333333
Number of observations72

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 13.3555555555556 & 0.246563936932498 & 54.1667030536258 \tabularnewline
Geometric Mean & 13.1998588456001 &  &  \tabularnewline
Harmonic Mean & 13.0481212702141 &  &  \tabularnewline
Quadratic Mean & 13.5161837151698 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 13.3333333333333 & 0.235801831868124 & 56.5446554324914 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 13.3222222222222 & 0.220880141396084 & 60.3142597520014 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 13.3305555555556 & 0.21532301761008 & 61.9095705768685 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 13.2805555555556 & 0.201118146756985 & 66.0336014909817 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 13.3083333333333 & 0.193343350072389 & 68.8326406279326 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 13.3166666666667 & 0.19196496485252 & 69.3702972148973 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 13.2875 & 0.182498499361421 & 72.8088178614848 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 13.2652777777778 & 0.17829350748997 & 74.4013506971028 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 13.2652777777778 & 0.173995661744866 & 76.2391294400718 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 13.2513888888889 & 0.166889440968769 & 79.4022007142361 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 13.2513888888889 & 0.166889440968769 & 79.4022007142361 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 13.2513888888889 & 0.161456024812278 & 82.0742917726114 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 13.2333333333333 & 0.158422880533976 & 83.5317050714483 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 13.2333333333333 & 0.152252261637418 & 86.9171544055476 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 13.2333333333333 & 0.152252261637418 & 86.9171544055476 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 13.3222222222222 & 0.139572651784169 & 95.45009034308 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 13.2277777777778 & 0.12419100058089 & 106.511564573168 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 13.2027777777778 & 0.113107553033805 & 116.727640406399 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 13.15 & 0.105464914546559 & 124.686015785797 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 13.2055555555556 & 0.0979422254903067 & 134.830054038975 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 13.2055555555556 & 0.0979422254903067 & 134.830054038975 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 13.1444444444444 & 0.0894446631477025 & 146.956162412269 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 13.1763888888889 & 0.0852707428804007 & 154.524147952714 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 13.2097222222222 & 0.0810764752833699 & 162.929162572164 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 13.3157142857143 & 0.222135650592432 & 59.9440668357443 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 13.2970588235294 & 0.205488460530127 & 64.7095159953271 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 13.2833333333333 & 0.195420571305069 & 67.9730554701779 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 13.265625 & 0.185915510737906 & 71.3529761306531 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 13.2612903225806 & 0.179978182453391 & 73.6827661098028 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 13.25 & 0.175272185423275 & 75.5967067335973 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 13.2362068965517 & 0.16988480983833 & 77.9128334613782 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 13.2267857142857 & 0.165821275079577 & 79.7653118270755 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 13.2203703703704 & 0.161824408760382 & 81.6957742755985 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 13.2134615384615 & 0.15782813375657 & 83.7205713833101 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 13.208 & 0.154413703526386 & 85.5364497992435 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 13.2020833333333 & 0.150014466894956 & 88.0054011229316 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 13.195652173913 & 0.145594119225452 & 90.6331398830721 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 13.1909090909091 & 0.140552300115813 & 93.8505387677044 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 13.1857142857143 & 0.135403703544128 & 97.3807506041892 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 13.18 & 0.128512196368223 & 102.558359225576 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 13.1631578947368 & 0.122353698314367 & 107.582836285965 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 13.1555555555556 & 0.118284325495174 & 111.219770671071 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 13.15 & 0.115489348692072 & 113.863314227026 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 13.15 & 0.113414739896569 & 115.946128448493 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 13.1433333333333 & 0.112104562575265 & 117.24173424707 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 13.1357142857143 & 0.109739263580896 & 119.699311414014 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 13.1346153846154 & 0.108548791963275 & 121.001948958208 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 13.1291666666667 & 0.107420204065836 & 122.222507216799 \tabularnewline
Median & 13 &  &  \tabularnewline
Midrange & 14.75 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 13.0947368421053 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 13.1555555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 13.0947368421053 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 13.1555555555556 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 13.1555555555556 &  &  \tabularnewline
Midmean - Closest Observation & 13.0947368421053 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 13.1555555555556 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 13.1333333333333 &  &  \tabularnewline
Number of observations & 72 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=293386&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]13.3555555555556[/C][C]0.246563936932498[/C][C]54.1667030536258[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]13.1998588456001[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]13.0481212702141[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]13.5161837151698[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]13.3333333333333[/C][C]0.235801831868124[/C][C]56.5446554324914[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]13.3222222222222[/C][C]0.220880141396084[/C][C]60.3142597520014[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]13.3305555555556[/C][C]0.21532301761008[/C][C]61.9095705768685[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]13.2805555555556[/C][C]0.201118146756985[/C][C]66.0336014909817[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]13.3083333333333[/C][C]0.193343350072389[/C][C]68.8326406279326[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]13.3166666666667[/C][C]0.19196496485252[/C][C]69.3702972148973[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]13.2875[/C][C]0.182498499361421[/C][C]72.8088178614848[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]13.2652777777778[/C][C]0.17829350748997[/C][C]74.4013506971028[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]13.2652777777778[/C][C]0.173995661744866[/C][C]76.2391294400718[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]13.2513888888889[/C][C]0.166889440968769[/C][C]79.4022007142361[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]13.2513888888889[/C][C]0.166889440968769[/C][C]79.4022007142361[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]13.2513888888889[/C][C]0.161456024812278[/C][C]82.0742917726114[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]13.2333333333333[/C][C]0.158422880533976[/C][C]83.5317050714483[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]13.2333333333333[/C][C]0.152252261637418[/C][C]86.9171544055476[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]13.2333333333333[/C][C]0.152252261637418[/C][C]86.9171544055476[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]13.3222222222222[/C][C]0.139572651784169[/C][C]95.45009034308[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]13.2277777777778[/C][C]0.12419100058089[/C][C]106.511564573168[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]13.2027777777778[/C][C]0.113107553033805[/C][C]116.727640406399[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]13.15[/C][C]0.105464914546559[/C][C]124.686015785797[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]13.2055555555556[/C][C]0.0979422254903067[/C][C]134.830054038975[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]13.2055555555556[/C][C]0.0979422254903067[/C][C]134.830054038975[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]13.1444444444444[/C][C]0.0894446631477025[/C][C]146.956162412269[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]13.1763888888889[/C][C]0.0852707428804007[/C][C]154.524147952714[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]13.2097222222222[/C][C]0.0810764752833699[/C][C]162.929162572164[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]13.3157142857143[/C][C]0.222135650592432[/C][C]59.9440668357443[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]13.2970588235294[/C][C]0.205488460530127[/C][C]64.7095159953271[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]13.2833333333333[/C][C]0.195420571305069[/C][C]67.9730554701779[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]13.265625[/C][C]0.185915510737906[/C][C]71.3529761306531[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]13.2612903225806[/C][C]0.179978182453391[/C][C]73.6827661098028[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]13.25[/C][C]0.175272185423275[/C][C]75.5967067335973[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]13.2362068965517[/C][C]0.16988480983833[/C][C]77.9128334613782[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]13.2267857142857[/C][C]0.165821275079577[/C][C]79.7653118270755[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]13.2203703703704[/C][C]0.161824408760382[/C][C]81.6957742755985[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]13.2134615384615[/C][C]0.15782813375657[/C][C]83.7205713833101[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]13.208[/C][C]0.154413703526386[/C][C]85.5364497992435[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]13.2020833333333[/C][C]0.150014466894956[/C][C]88.0054011229316[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]13.195652173913[/C][C]0.145594119225452[/C][C]90.6331398830721[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]13.1909090909091[/C][C]0.140552300115813[/C][C]93.8505387677044[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]13.1857142857143[/C][C]0.135403703544128[/C][C]97.3807506041892[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]13.18[/C][C]0.128512196368223[/C][C]102.558359225576[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]13.1631578947368[/C][C]0.122353698314367[/C][C]107.582836285965[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]13.1555555555556[/C][C]0.118284325495174[/C][C]111.219770671071[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]13.15[/C][C]0.115489348692072[/C][C]113.863314227026[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]13.15[/C][C]0.113414739896569[/C][C]115.946128448493[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]13.1433333333333[/C][C]0.112104562575265[/C][C]117.24173424707[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]13.1357142857143[/C][C]0.109739263580896[/C][C]119.699311414014[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]13.1346153846154[/C][C]0.108548791963275[/C][C]121.001948958208[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]13.1291666666667[/C][C]0.107420204065836[/C][C]122.222507216799[/C][/ROW]
[ROW][C]Median[/C][C]13[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]14.75[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]13.0947368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]13.1555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]13.0947368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]13.1555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]13.1555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]13.0947368421053[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]13.1555555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]13.1333333333333[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]72[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=293386&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=293386&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 Mean13.35555555555560.24656393693249854.1667030536258
Geometric Mean13.1998588456001
Harmonic Mean13.0481212702141
Quadratic Mean13.5161837151698
Winsorized Mean ( 1 / 24 )13.33333333333330.23580183186812456.5446554324914
Winsorized Mean ( 2 / 24 )13.32222222222220.22088014139608460.3142597520014
Winsorized Mean ( 3 / 24 )13.33055555555560.2153230176100861.9095705768685
Winsorized Mean ( 4 / 24 )13.28055555555560.20111814675698566.0336014909817
Winsorized Mean ( 5 / 24 )13.30833333333330.19334335007238968.8326406279326
Winsorized Mean ( 6 / 24 )13.31666666666670.1919649648525269.3702972148973
Winsorized Mean ( 7 / 24 )13.28750.18249849936142172.8088178614848
Winsorized Mean ( 8 / 24 )13.26527777777780.1782935074899774.4013506971028
Winsorized Mean ( 9 / 24 )13.26527777777780.17399566174486676.2391294400718
Winsorized Mean ( 10 / 24 )13.25138888888890.16688944096876979.4022007142361
Winsorized Mean ( 11 / 24 )13.25138888888890.16688944096876979.4022007142361
Winsorized Mean ( 12 / 24 )13.25138888888890.16145602481227882.0742917726114
Winsorized Mean ( 13 / 24 )13.23333333333330.15842288053397683.5317050714483
Winsorized Mean ( 14 / 24 )13.23333333333330.15225226163741886.9171544055476
Winsorized Mean ( 15 / 24 )13.23333333333330.15225226163741886.9171544055476
Winsorized Mean ( 16 / 24 )13.32222222222220.13957265178416995.45009034308
Winsorized Mean ( 17 / 24 )13.22777777777780.12419100058089106.511564573168
Winsorized Mean ( 18 / 24 )13.20277777777780.113107553033805116.727640406399
Winsorized Mean ( 19 / 24 )13.150.105464914546559124.686015785797
Winsorized Mean ( 20 / 24 )13.20555555555560.0979422254903067134.830054038975
Winsorized Mean ( 21 / 24 )13.20555555555560.0979422254903067134.830054038975
Winsorized Mean ( 22 / 24 )13.14444444444440.0894446631477025146.956162412269
Winsorized Mean ( 23 / 24 )13.17638888888890.0852707428804007154.524147952714
Winsorized Mean ( 24 / 24 )13.20972222222220.0810764752833699162.929162572164
Trimmed Mean ( 1 / 24 )13.31571428571430.22213565059243259.9440668357443
Trimmed Mean ( 2 / 24 )13.29705882352940.20548846053012764.7095159953271
Trimmed Mean ( 3 / 24 )13.28333333333330.19542057130506967.9730554701779
Trimmed Mean ( 4 / 24 )13.2656250.18591551073790671.3529761306531
Trimmed Mean ( 5 / 24 )13.26129032258060.17997818245339173.6827661098028
Trimmed Mean ( 6 / 24 )13.250.17527218542327575.5967067335973
Trimmed Mean ( 7 / 24 )13.23620689655170.1698848098383377.9128334613782
Trimmed Mean ( 8 / 24 )13.22678571428570.16582127507957779.7653118270755
Trimmed Mean ( 9 / 24 )13.22037037037040.16182440876038281.6957742755985
Trimmed Mean ( 10 / 24 )13.21346153846150.1578281337565783.7205713833101
Trimmed Mean ( 11 / 24 )13.2080.15441370352638685.5364497992435
Trimmed Mean ( 12 / 24 )13.20208333333330.15001446689495688.0054011229316
Trimmed Mean ( 13 / 24 )13.1956521739130.14559411922545290.6331398830721
Trimmed Mean ( 14 / 24 )13.19090909090910.14055230011581393.8505387677044
Trimmed Mean ( 15 / 24 )13.18571428571430.13540370354412897.3807506041892
Trimmed Mean ( 16 / 24 )13.180.128512196368223102.558359225576
Trimmed Mean ( 17 / 24 )13.16315789473680.122353698314367107.582836285965
Trimmed Mean ( 18 / 24 )13.15555555555560.118284325495174111.219770671071
Trimmed Mean ( 19 / 24 )13.150.115489348692072113.863314227026
Trimmed Mean ( 20 / 24 )13.150.113414739896569115.946128448493
Trimmed Mean ( 21 / 24 )13.14333333333330.112104562575265117.24173424707
Trimmed Mean ( 22 / 24 )13.13571428571430.109739263580896119.699311414014
Trimmed Mean ( 23 / 24 )13.13461538461540.108548791963275121.001948958208
Trimmed Mean ( 24 / 24 )13.12916666666670.107420204065836122.222507216799
Median13
Midrange14.75
Midmean - Weighted Average at Xnp13.0947368421053
Midmean - Weighted Average at X(n+1)p13.1555555555556
Midmean - Empirical Distribution Function13.0947368421053
Midmean - Empirical Distribution Function - Averaging13.1555555555556
Midmean - Empirical Distribution Function - Interpolation13.1555555555556
Midmean - Closest Observation13.0947368421053
Midmean - True Basic - Statistics Graphics Toolkit13.1555555555556
Midmean - MS Excel (old versions)13.1333333333333
Number of observations72



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')